[tex]\displaystyle \text{To solve this problem, let's assume the distance of the run is denoted by 'x' miles, and the distance of the bicycle race is denoted by '48 - x' miles.}[/tex]
[tex]\displaystyle \text{We can use the formula: time} = \text{distance/velocity to find the time taken for each segment of the race.}[/tex]
[tex]\displaystyle \text{For the run:}[/tex]
[tex]\displaystyle \text{Time taken} = \text{Distance/Velocity}[/tex]
[tex]\displaystyle t_1 = \frac{x}{5}[/tex]
[tex]\displaystyle \text{For the bicycle race:}[/tex]
[tex]\displaystyle \text{Time taken} = \text{Distance/Velocity}[/tex]
[tex]\displaystyle t_2 = \frac{48 - x}{23}[/tex]
[tex]\displaystyle \text{Given that the total time for the race is 6 hours, we can write the equation:}[/tex]
[tex]\displaystyle t_1 + t_2 = 6[/tex]
[tex]\displaystyle \text{Substituting the expressions for } t_1 \text{ and } t_2, \text{ we get:}[/tex]
[tex]\displaystyle \frac{x}{5} + \frac{48 - x}{23} = 6[/tex]
[tex]\displaystyle \text{To solve this equation, we can simplify it by multiplying through by the common denominator, which is 115:}[/tex]
[tex]\displaystyle 23x + 5(48 - x) = 6 \times 115[/tex]
[tex]\displaystyle \text{Simplifying further:}[/tex]
[tex]\displaystyle 23x + 240 - 5x = 690[/tex]
[tex]\displaystyle 18x = 450[/tex]
[tex]\displaystyle x = \frac{450}{18}[/tex]
[tex]\displaystyle x = 25[/tex]
[tex]\displaystyle \text{Therefore, the distance of the run is 25 miles, and the distance of the bicycle race is } 48 - 25 = 23 \text{ miles.}[/tex]
100 POINTS Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry for the function below.
The x-intercepts, y-intercept, vertex, and axis of symmetry for the given function g(x) = x² + 4x + 3 have been plotted on the graph below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function g(x) = x² + 4x + 3 is positive 1, we can logically deduce that the parabola would open upward and the x-intercept (roots) is given by the ordered pair (-3, 0) and (-1, 0).
In conclusion, the vertex is given by the ordered pair (-2, -1) and the minimum value is -1.
Read more on quadratic functions here: brainly.com/question/29499209
#SPJ1
Answer:
x-intercepts = (-3, 0) and (-1, 0)
y-intercept = (0, 3)
Vertex = (-2, -1)
Axis of symmetry: x = -2
Step-by-step explanation:
Given quadratic function:
[tex]g(x) = x^2 + 4x + 3[/tex]
[tex]\hrulefill[/tex]
x-interceptsTo find the x-intercepts of the given function g(x), set g(x) equal to zero and solve for x.
Set g(x) = 0:
[tex]x^2 + 4x + 3 = 0[/tex]
Factor the quadratic equation:
[tex]x^2+x+3x+3=0[/tex]
[tex]x(x+1)+3(x+1)=0[/tex]
[tex](x + 3)(x + 1) = 0[/tex]
Set each factor equal to zero and solve for x:
[tex]x + 3 = 0 \implies x = -3[/tex]
[tex]x + 1 = 0 \implies x = -1[/tex]
Therefore, the x-intercepts are at (-3, 0) and (-1, 0).
[tex]\hrulefill[/tex]
y-interceptTo find the y-intercept of g(x), substitute x = 0 and solve for y.
[tex]\begin{aligned}x=0 \implies y&= (0)^2 + 4(0) + 3\\y& = 0 + 0 + 3 \\y&= 3\end{aligned}[/tex]
Therefore, the y-intercept is at (0, 3).
[tex]\hrulefill[/tex]
VertexThe x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a.
For the function g(x), a = 1, and b = 4.
Therefore, the x-coordinate of the vertex is:
[tex]\textsf{$x$-coordinate of vertex} = \dfrac{-b}{2a} = \dfrac{-4}{2(1)} = -2[/tex]
To find the y-coordinate of the vertex, substitute x = -2 into function g(x):
[tex]\begin{aligned}x=-2 \implies y &= (-2)^2 + 4(-2) + 3\\y& = 4-8 + 3 \\y&= -1\end{aligned}[/tex]
Therefore, the vertex is at (-2, -1).
[tex]\hrulefill[/tex]
Axis of symmetryThe axis of symmetry of a vertical parabola is the x-coordinate of its vertex.
As the x-coordinate of the vertex is -2, the axis of symmetry is x = -2.
[tex]\hrulefill[/tex]
SummaryThe x-intercepts are at (-3, 0) and (-1, 0).The y-intercept is at (0, 3).The vertex is at (-2, -1).The axis of symmetry is x = -2.Which shows 2 products that both result in negative values
These are two instances where the product of two numbers yields a negative result.
To demonstrate two products that both result in negative values, we can choose two numbers with opposite signs and multiply them together. Here are two examples:
Example 1:
Let's consider the numbers -3 and 4. When we multiply these numbers, we get:
(-3) * (4) = -12
The product -12 is a negative value.
Example 2:
Let's consider the numbers 5 and -2. When we multiply these numbers, we get:
(5) * (-2) = -10
Once again, the product -10 is a negative value.
In both examples, we have chosen two numbers with opposite signs, and the multiplication of these numbers results in a negative value. Therefore, these are two instances where the product of two numbers yields a negative result.
for such more question on numbers yields
https://brainly.com/question/20884766
#SPJ8
For g(x,y) = [tex]sin^{-1}[/tex](x² + y² — 3),
the domain of the function is the area between two circles.
The larger circle has a radius of
The smaller circle has a radius of
We conclude that there is no valid domain for the given function g(x, y) = sin^-1(x² + y² - 3). Thus, the concept of circles with radii does not apply in this case.
To determine the domain of the function g(x, y) = sin^-1(x² + y² - 3), we need to examine the range of the arcsine function. The arcsine function, [tex]sin^{(-1)[/tex](z), is defined for values of z between -1 and 1, inclusive. Therefore, for the given function, we have:
-1 ≤ x² + y² - 3 ≤ 1
Rearranging the inequality, we get:
-4 ≤ x² + y² ≤ -2
Now, let's analyze the inequalities separately:
x² + y² ≤ -2:
This inequality is not possible since the sum of squares of two non-negative numbers (x² and y²) cannot be negative. Therefore, there are no points that satisfy this inequality.
x² + y² ≤ -4:
Similarly, this inequality is also not possible since the sum of squares of two non-negative numbers cannot be less than or equal to -4. Therefore, there are no points that satisfy this inequality either.
Based on the analysis, we conclude that there is no valid domain for the given function g(x, y) = sin^-1(x² + y² - 3). Thus, the concept of circles with radii does not apply in this case.
It's important to note that the arcsine function has a restricted range of -π/2 to π/2, and for a valid domain, the input of the arcsine function must be within the range of -1 to 1. In this particular case, the given expression x² + y² - 3 exceeds the range of the arcsine function, resulting in no valid domain.
For more such questions on domain visit:
https://brainly.com/question/30096754
#SPJ8
NO LINKS!! URGENT HELP PLEASE!!
Answer:
a. 5π cm
b. 144π in²
c. 6 ft
Step-by-step explanation:
a.
The circumference of a circle is given by:
Circumference pf circle= πd
where d is the diameter.
In this case, d = 5 cm,
Therefore, Circumference of circle = π*5=5π cm
b.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, the diameter is d = 24 in,
so, the radius is r = d/2 = 24/2=12in
Therefore, Area of circle=π*12²=144π in²
c.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, Area is 36π ft²
Now substituting value
36π=πr²
dividing both side by π, we get
36=r²
[tex]r=\sqrt{36}=6[/tex]
r=6 ft.
Therefore, Radius is 6 ft.
PLS HELP ACTUAL ANSWERS
A random survey was conducted to gather information about age and employment status. The table shows the data collected.
0-17 years old 18+ years old Total
607
Has a Job
Does Not Have a Job
Total
A
B
C
240
679
What is the probability that a randomly selected student does NOT have a job, given that they are 18+ years old?
97
337
97
679
240
240
265
97
679
337
P
look at photo for reference
Answer: 337
Step-by-step explanation: it is 337 because if you subtract it all you get that
3. Pi is defined as the ratio of the circumference of a circle to the diameter of that circle. Which of the following correctly explains why the formula for the circumference of a circle is 2 mr 7 (1 point)
Two times equals the distance from one side of the circle to the other. When you multiply that by r, you get the distance around the circle, or the circumference.
Pi times requals the diameter of the circle. The diameter is half the circle, so when you multiply it by 2, you get the distance around the entire circle, or the circumference.
Two times requals the diameter of the circle. Pi is needed for all circle formulas, so you multiply by since you are finding the circumference.
Two times requals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.
Answer:
The correct answer is "Two times r equals the diameter of the circle. When you multiply that by pi, you get the distance around the circle, or the circumference." This is because the circumference of a circle is equal to the distance around it, which is the same as the length of its perimeter. The diameter of a circle is the straight line that passes through the center of the circle and touches both sides. Therefore, if you multiply the diameter by pi, which is the ratio of the circumference to the diameter of a circle, you get the circumference. Alternatively, you can also use the formula C = 2πr, where C is the circumference and r is the radius of the circle. Since the radius is half the diameter, the formula can also be stated as C = πd, where d is the diameter of the circle.
Step-by-step explanation:
NO LINKS!! URGENT HELP PLEASE!!
33. Use the diagram to name the following.
Answer:
[tex]\textsf{a)} \quad \textsf{Radius = $\overline{HG}$}[/tex]
[tex]\textsf{b)} \quad \textsf{Chord = $\overline{GF}$}[/tex]
[tex]\textsf{c)} \quad \textsf{Diameter = $\overline{JF}$}[/tex]
[tex]\textsf{d)} \quad \textsf{Secant = $\overleftrightarrow{GF}$}[/tex]
[tex]\textsf{e)} \quad \textsf{Tangent = $\overleftrightarrow{GK}$}[/tex]
[tex]\textsf{f)} \quad \textsf{Point of tangency = $\overset{\bullet}{G}$}[/tex]
[tex]\textsf{g)} \quad \textsf{Circle $H$}[/tex]
Step-by-step explanation:
a) RadiusThe radius is the distance from the center of a circle to any point on its circumference. The center of the circle is point H. Therefore, the radius of the given circle is line segment HG.
b) ChordA chord is a straight line joining two points on the circumference of the circle. There are two chords in the given circle: line segments GF and JF. Therefore, a chord of the given circle is line segment GF.
c) DiameterThe diameter of a circle is a straight line segment passing through the center of a circle, connecting two points on its circumference.
Therefore, the diameter of the given circle is line segment JF.
e) SecantA secant is a straight line that intersects a circle at two points.
Therefore, the secant of the given circle is line GF.
f) TangentA tangent is a straight line that touches a circle at only one point.
Therefore, the tangent line of the given circle is line GK.
g) Point of tangencyThe point of tangency is the point where the line touches the circle.
Therefore, the point of tangency of the given circle is point G.
h) CircleA circle is named by its center point. Therefore, as the center point of the circle is point H, the name of the circle is "Circle H".
A grocery store owner polled ten customers to determine how many times they went to the grocery store in April. The results of his poll are shown below.
12,9,4,8,25,6,8,5,18,13
Determine the appropriate shape of the distribution.
A. The data does not show a latter
B. Left skewed
C. Symmetrical
D. Right skewed
Answer:
D. Right skewed
Step-by-step explanation:
To determine the shape of the distribution, we can examine the given data:
12, 9, 4, 8, 25, 6, 8, 5, 18, 13
One way to determine the shape of the distribution is by visualizing it using a histogram or a box plot. However, without the exact frequency of each value, we cannot create an accurate visual representation.
Alternatively, we can examine the skewness of the distribution. Skewness is a measure of the asymmetry of a distribution. If the data is skewed to the left, it is left-skewed or negatively skewed. If it is skewed to the right, it is right-skewed or positively skewed. If the data is symmetric and evenly distributed, it is considered a symmetrical distribution.
Let's calculate the skewness of the given data to determine the shape:
Skewness = (3 * (mean - median)) / standard deviation
First, let's calculate the mean, median, and standard deviation of the data:
Mean = (12 + 9 + 4 + 8 + 25 + 6 + 8 + 5 + 18 + 13) / 10 = 10.8
Median = the middle value when the data is arranged in ascending order:
4, 5, 6, 8, 8, 9, 12, 13, 18, 25
Median = (8 + 9) / 2 = 8.5
Next, let's calculate the standard deviation:
Step 1: Calculate the squared differences from the mean for each value:
(12 - 10.8)^2, (9 - 10.8)^2, (4 - 10.8)^2, (8 - 10.8)^2, (25 - 10.8)^2, (6 - 10.8)^2, (8 - 10.8)^2, (5 - 10.8)^2, (18 - 10.8)^2, (13 - 10.8)^2
Step 2: Calculate the sum of squared differences:
(1.44 + 2.88 + 45.76 + 8.64 + 228.01 + 22.09 + 8.64 + 32.49 + 47.04 + 4.84) = 411.73
Step 3: Calculate the variance:
Variance = sum of squared differences / (n - 1) = 411.73 / (10 - 1) = 45.75
Step 4: Calculate the standard deviation:
Standard deviation = square root of variance = √45.75 = 6.76 (approximately)
Now we can calculate the skewness:
Skewness = (3 * (mean - median)) / standard deviation
Skewness = (3 * (10.8 - 8.5)) / 6.76
Skewness = 6.4 / 6.76
Skewness ≈ 0.95
Since the skewness is positive (0.95), the data is right-skewed or positively skewed. Therefore, the appropriate shape of the distribution is:
D. Right skewed
The following pie chart shows the number of rabbits, sheep, cattle, pigs on a farm rabbits 900 sheep 700 cattle 300 Pig 500 a. How many animals are on the farm? b.What represents the number of sheep on the farm c. what percentage of the total number of animals are rabbits d. Calculate the angle that represents number of pigs
a) There are 2400 animals on the farm.
b) The number of sheep on the farm is 700.
c) The percentage of rabbits in relation to the total number of animals is 37.5%.
d) The angle that represents the number of pigs is 75 degrees.
a) To determine the total number of animals on the farm, we add up the number of rabbits, sheep, cattle, and pigs:
Total number of animals = 900 (rabbits) + 700 (sheep) + 300 (cattle) + 500 (pigs) = 2400 animals.
b) The number of sheep on the farm is given as 700.
c) To calculate the percentage of rabbits in relation to the total number of animals, we divide the number of rabbits by the total number of animals and multiply by 100:
Percentage of rabbits = (900 / 2400) * 100 = 37.5%.
d) To calculate the angle that represents the number of pigs, we need to find the proportion of the total number of animals that pigs make up, and then convert it to an angle on the pie chart.
Proportion of pigs = 500 / 2400 = 0.2083.
To find the angle in degrees, we multiply the proportion by 360 degrees:
Angle representing pigs = 0.2083 * 360 = 75 degrees.
for such more question on percentage
https://brainly.com/question/24877689
#SPJ8
Combine like terms I need help pls!!!!
Answer:
21 - 12p
Step-by-step explanation:
I hope this helps and I'm super sorry if I'm wrong!
A box contains 240 lumps of sugar. Five lumps are fitted across the box and there were three layers. How many lumps are fitted along the box?
(03.01 MC)
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
three to the fourth power all over nine equals three squared
By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors
The correct answer is By finding the quotient of the bases to be one third and canceling common factors. Option D.
The Quotient of Powers Property states that when dividing two powers with the same base, you can subtract the exponents. In the given expression, we have three to the fourth power divided by nine.
To simplify this expression using the Quotient of Powers Property, we first need to recognize that nine can be written as three squared, since 3 multiplied by itself gives 9.
So, we have (3^4) / (3^2). According to the Quotient of Powers Property, we subtract the exponents: 4 - 2.
This gives us 3^(4-2), which simplifies to 3^2. Therefore, the expression three to the fourth power all over nine equals three squared.
It states that we find the quotient of the bases to be one third and cancel common factors. In this case, the bases are 3 and 3, and their quotient is indeed one third. Additionally, there are no common factors that can be canceled, as the expression does not contain any variables or additional terms.
Therefore, By finding the quotient of the bases to be one third and canceling common factors. accurately describes the steps involved in simplifying the expression using the Quotient of Powers Property.
We find the quotient of the bases (one third) and cancel common factors (which is not applicable in this case). Option D is correct.
For more question on factors visit:
https://brainly.com/question/28998304
#SPJ8
Note the complete question is
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
Three to the fourth power all over nine equals three squared
A.) By simplifying 9 to 32 to make both powers base three and adding the exponents
B.) By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C.) By finding the quotient of the bases to be one third and simplifying the expression
D.) By finding the quotient of the bases to be one third and cancelling common factors
There are 40 black marbles, 20 blue marbles, and 4 red marbles in a jar.
а. What is the probability of selecting one red marble?
b. What is the probability of selecting one black marble?
c. What is the probability of selecting one blue marble?
d. Which has the highest probability of being selected?
e. Which has the lowest probability of being selected?
Step-by-step explanation:
a. 4/64= 1/16 for red marble
b. 40/64= 5/8 black marbles
c. 20/64= 5/16 blue marble
d. highest: black marble
e. lowest: red marble
The graph of line I is shown below. Which of the following represents the slope of a line parallel to line P
Answer:
C) -1/3
Step-by-step explanation:
Slope=rise/run
Slope=-1/3
what does a fraction that is horizontally compressed versus vertically compressed look like?
Answer:
Fractions are like pancakes: you can flatten them horizontally or vertically. Horizontal flattening means you shrink the x-value by multiplying it by a huge number before doing anything else. Vertical flattening means you squish the y-value by multiplying the whole function by a tiny number. For example, if f (x) = x^2, then f (2x) is horizontally flattened by 2 and f (0.5x^2) is vertically flattened by 0.5. Don't worry, it's not rocket science, it's just math.
Yesterday, Janie walked 3
5
mile to a friend’s house, 1
4
mile to the store, and 3
8
mile to another friend’s house. Which is the best estimate of the distance Janie walked?
Answer:
be more clear of what u mean edit the question so we can tell what u mean and answer correctly
Step-by-step explanation:
no explanation
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with x-axis labeled study time in hours and y-axis labeled grade percent. Points are plotted at 1 comma 50, 2 comma 50, 2 comma 60, 2 comma 70, 3 comma 70, 3 comma 80, 4 comma 85, and 4 comma 90, and a line of fit drawn passing through the points 0 comma 30 and 2 comma 60
Determine the equation of the line of fit.
y = 15x + 60
y = 15x + 30
y = 30x + 60
y = 30x + 30
The equation of the line of fit is y = 15x + 30.
To determine the equation of the line of fit, we can use the given data points (0,30) and (2,60). We can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Using the two data points, we can calculate the slope (m) as the change in y divided by the change in x:
m = (60 - 30) / (2 - 0) = 30 / 2 = 15
Now that we have the slope, we can substitute one of the data points into the equation to solve for the y-intercept (b). Let's use the point (0,30):
30 = 15(0) + b
30 = 0 + b
b = 30
Therefore, the equation of the line of fit is y = 15x + 30. This means that for every additional hour of study time (x), the grade percent (y) increases by 15, and the line intersects the y-axis at 30.
For more such questions fit,click on
https://brainly.com/question/1441182
#SPJ8
The equation 4x – 4 – 5x = 7 – x + 5 has what type of solution set? Question 3 options: A) No solutions B) Two solutions C) One solution D) Infinitely many solutions
Answer:
A) No solutions
Step-by-step explanation:
First of all, we know that option B will always be incorrect. You cannot have two solutions. To illustrate this, try drawing two lines. You will find that they will either intersect once (one solution), or they will not intersect, (no solutions, parallel lines), or they are the same line and thus they will always intersect (infinitely many solutions).
With that in mind, let's solve the equation.
4x-4-5x=7-x+5
First, combine all like terms.
-x-4=12-x
Now add 4 to both sides to leave x by itself.
-x=16-x
This statement cannot be true. Therefore, this equation has no solutions (parallel lines. One line starts from 0, or the origin. That line is -x. The other line starts from 16. That line is -x+16.)
Hope this helps!
please help will give brainliest...........
A
no, because they are both right triangles and
the one on the left is 88° at the right anglr
Solve the quadratic by taking square roots.
32=25x^2-4
Hello!
[tex]32 = 25x^2 - 4\\\\32 + 4 = 25x^2\\\\36 = 25x^2\\\\25x^2 - 36 = 0\\\\x = \dfrac{-b \±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-0 \±\sqrt{0^2 - 4 \times 25 \times (-36) } }{2 \times 25} \\\\\\x = \dfrac{\±60}{50} \\\\\boxed{x = \±\frac{6}{5} }[/tex]
Find the sum of the measures of the angles of a five sided polygon
Answer:540 degrees
The sum of the measures of the angles of a five-sided polygon (pentagon) is 540 degrees123. This can be calculated using the angle sum formula, S = (n − 2) × 180°, where n is the number of sides in the polygon12. Since a pentagon has five sides, the sum of the interior angles is (5 − 2) × 180° = 540°123.
Step-by-step explanation:
Answer:
540°
Step-by-step explanation:
Since a pentagon has n=5 sides, then we have:
[tex]180(n-2)=180(5-2)=180(3)=540^\circ[/tex]
1.Lim as x approaches 0 (sin3x)/(2x-Sinx)
2. Lim as x approaches infinity x^-1 lnx
3. Lim x approaches infinity x/ e^x
Using L’Hospals rule for all
1. The limit of (sin3x)/(2x - sinx) as x approaches 0 is -27.
2. The limit of x^(-1)lnx as x approaches infinity is -1.
3. The limit of x/e^x as x approaches infinity is 0.
1. To find the limit of (sin3x)/(2x - sinx) as x approaches 0 using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (sin3x) = 3cos3x
Denominator: d/dx (2x - sinx) = 2 - cosx
Now, we can find the limit of the differentiated function as x approaches 0:
lim x->0 (3cos3x)/(2 - cosx)
Again, differentiating the numerator and denominator:
Numerator: d/dx (3cos3x) = -9sin3x
Denominator: d/dx (2 - cosx) = sinx
Taking the limit as x approaches 0:
lim x->0 (-9sin3x)/(sinx)
Now, substituting x = 0 into the function gives:
(-9sin0)/(sin0) = 0/0
Since we obtained an indeterminate form of 0/0, we can apply L'Hôpital's rule again.
Differentiating the numerator and denominator:
Numerator: d/dx (-9sin3x) = -27cos3x
Denominator: d/dx (sinx) = cosx
Taking the limit as x approaches 0:
lim x->0 (-27cos3x)/(cosx)
Now, substituting x = 0 into the function gives:
(-27cos0)/(cos0) = -27/1 = -27
Therefore, the limit of (sin3x)/(2x - sinx) as x approaches 0 is -27.
2. To find the limit of x^(-1)lnx as x approaches infinity using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (lnx) = 1/x
Denominator: d/dx (x^(-1)) = -x^(-2) = -1/x^2
Now, we can find the limit of the differentiated function as x approaches infinity:
lim x->∞ (1/x)/(-1/x^2)
Simplifying the expression:
lim x->∞ -x/x = -1
Therefore, the limit of x^(-1)lnx as x approaches infinity is -1.
3. To find the limit of x/e^x as x approaches infinity using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (x) = 1
Denominator: d/dx (e^x) = e^x
Now, we can find the limit of the differentiated function as x approaches infinity:
lim x->∞ (1)/(e^x)
Since the exponential function e^x grows much faster than any polynomial function, the denominator goes to infinity much faster than the numerator. Therefore, the limit of (1)/(e^x) as x approaches infinity is 0.
Thus, the limit of x/e^x as x approaches infinity is 0.
for such more question on limit
https://brainly.com/question/12017456
#SPJ8
Tamika practiced oboe for 1/4 hour in the morning and 5/6 hour in the afternoon how long did she practice in all write your answer as a mixed number
Please awnser asap i
Will brainlist
The row operation on the matrix [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
How to perform the row operation on the matrixFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
The row operation is given as
1/2R₁
This means that we divide the entries on the first row by 2
Using the above as a guide, we have the following:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
Hence, the row operation on the matrix is [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
Read more about matrix at
https://brainly.com/question/11989522
#SPJ1
8. Given AABC~AEDC
What is the value of x?
C. 30
D. 20
A. 15
B. 12
E
60
X
C
D
10
40
B
The calculated value of x in the triangle is 15
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The triangles ABC and EDC
Since the triangles are similar, then we have
(3x - 5)/(5x - 5) = 32/56
This gives
32(5x - 5) = 56(3x - 5)
When solved for x, we have
x = 15
Hence, the value of x is 15
Read more about triangles at
https://brainly.com/question/32215211
#SPJ1
La semana pasada, una tienda de velas recibió $355,60 por vender 20 velas. Las velas pequeñas se vendieron a $10,98 y las velas grandes a $27,98. ¿Cuántas velas grandes vendió la tienda?
Answer:
Para resolver este problema, podemos plantear un sistema de ecuaciones. Si definimos "p" como el número de velas pequeñas y "g" como el número de velas grandes, podemos expresar la información del problema de la siguiente manera:
p + g = 20 (la tienda vendió un total de 20 velas) 10.98p + 27.98g = 355.60 (el ingreso total por la venta de velas fue de $355.60)
Podemos resolver este sistema de ecuaciones utilizando el método de sustitución. Despejando "p" de la primera ecuación, obtenemos:
p = 20 - g
Luego, sustituimos esta expresión de "p" en la segunda ecuación:
10.98(20 - g) + 27.98g = 355.60
220.20 - 10.98g + 27.98g = 355.60
17.00g = 135.40
g = 8
Por lo tanto, la tienda vendió 8 velas grandes.
Step-by-step explanation:
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
The dependent variable is t.
When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155."
The dependent variable is f(t).
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t.
The independent variable
The correct statements are
The dependent variable is t.
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t. Option A,D,E,F.
Let's analyze each statement to understand why it is true:
A) The dependent variable is t: In the given function, f(t), the value of f depends on the value of t. Therefore, t is the independent variable, and f is the dependent variable.
D) When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced": Here, the value of t is 2, representing the year 2002, and the value of f(t) is 1,323, representing the amount of garbage produced in tons.
E) When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced": Similar to statement D, the value of t is 4, representing the year 2004, and the value of f(t) is 1,458.6, representing the amount of garbage produced in tons.
F) The independent variable is t: As mentioned in statement A, t is the independent variable in the given function. It is the variable that we can change or manipulate, and the value of f depends on the value of t.
Statements B, C, and G are incorrect:
B) When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155": This statement is incorrect because in the given function, t represents the time in years after 2000, not the amount of garbage produced.
C) The dependent variable is f(t): This statement is incorrect because, as mentioned earlier, t is the independent variable, and f is the dependent variable.
G) The independent variable f(t): This statement is incorrect because f(t) represents the amount of garbage produced, which is the dependent variable in the given function.
So Option A,D.E.F. Are correct.
For more question on variable visit:
https://brainly.com/question/28248724
#SPJ8
Note the complete question is
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
A.) The dependent variable is t.
B.) When f(12) = 2,155, 12 represents "12 tons of garbage produced," and 2,155 represents "the year 2155."
C.) The dependent variable is f(t).
D.) When f(2) = 1,323, 2 represents "the year 2002," and 1,323 represents "1,323 tons of garbage produced."
E.) When f(4) = 1,458.6, 4 represents "the year 2004," and 1,458.6 represents "1,458.6 tons of garbage produced."
F.) The independent variable is t.
G.) The independent variable f(t)
Given cos=
a.
b.
sin 8
4
and csc <0, find sine and tan
9
-4
9
A
B
tan =
csc0= 4√√9, tane=
9
4
65
9
C.
d.
sin = 4, tan 9 =
sin =
Please select the best answer from the choices provided
65
19
-4√65
9
tan 9 =
The best answer that matches the calculated values is C. sin θ = -1/3, tan θ = -3/(2√2)
Let's break down the given values and find the values of sine and tangent.
We are given:
cos θ = √(8/9)
csc θ < 0
Using the Pythagorean identity, sin^2θ + cos^2θ = 1, we can find the value of sin θ.
sin^2θ + (√(8/9))^2 = 1
sin^2θ + 8/9 = 1
sin^2θ = 1 - 8/9
sin^2θ = 1/9
Taking the square root of both sides, we get:
sin θ = ±1/3
Since csc θ is negative (csc θ < 0), we can conclude that sin θ is negative. Therefore, sin θ = -1/3.
Next, let's find the value of tan θ.
tan θ = sin θ / cos θ
tan θ = (-1/3) / (√(8/9))
tan θ = -√9/√8
tan θ = -√9/√(4*2)
tan θ = -√9/(2√2)
tan θ = -3/(2√2)
So, the values are:
sin θ = -1/3
tan θ = -3/(2√2)
The best selection from the available options that matches the calculated values is:
C. sin θ = -1/3, tan θ = -3/(2√2)
for such more question on tangent
https://brainly.com/question/19132778
#SPJ8
Pls help I’m stuck Tysm I can’t thank any more
Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B
How much shorter is the perimeter of C than the total perimeter of A and B?To solve this problem, we have to know the perimeter of the polygon C.
The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The perimeter of the figures are;
Using the concept of perimeter of a rectangle;
a. figure A = 2(4 + 11) = 30cm
b. figure B = 2(8 + 4) = 24cm
c figure C = 11 + 4 + 8 + 4 = 27cm
Now, we can add A and B and then subtract c from it.
30 + 24 - 27 = 27cm
Learn more perimeter of polygon here;
https://brainly.com/question/27083382
#SPJ1
A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation?
T1, –9(x, y)
T–1, –9(x, y)
T–9, 1(x, y)
T–9, –1(x, y)
The function rule that describes the given translation is T-9, 1(x, y).
The first value in the function rule represents the horizontal translation, while the second value represents the vertical translation. In this case, the square is translated 1 unit to the right, indicating a positive horizontal translation.
Additionally, the square is translated 9 units down, indicating a negative vertical translation. Therefore, the correct function rule is T-9, 1(x, y).
In the coordinate plane, the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position. When we apply the function rule T-9, 1 to the coordinates of the square, we subtract 9 from the y-coordinate and add 1 to the x-coordinate.
This results in the square being moved 9 units down and 1 unit to the right from its original position.
The negative sign in front of the 9 indicates a downward movement, and the positive sign in front of the 1 indicates a rightward movement. Hence, the translation is accurately described by the function rule T-9, 1(x, y).
for such more questions on function
https://brainly.com/question/11624077
#SPJ8
Answer:
C
Step-by-step explanation: