The critical numbers of the function are; θ = π/6, 5π/6
How to find the critical value of a trigonometric function?
We are given the trigonometric function as;
f(θ) = 6secθ + 3tanθ ; 0 < θ < 2π
The critical points of a function are defined as those points of the domain where the function is not differentiable or those points for which the derivative is equal to zero.
Let us find the first derivative;
f'(θ) = 6(-sin θ/cos² θ) + 3(1/cos² θ)
f'(θ) = (3 - 6sin θ)/cos² θ
At f'(θ) = 0, we have;
3 - 6sin θ = 0
θ = sin⁻¹(3/6)
Since sin is positive, then;
θ = π/6, 5π/6
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If we used the formula f(x)= 10x to get the values for f(x) in the range from x =1 to x(limits are inclusive) We would end up with which lists?
The range for the given function, with x=1 is 10.
The given function is f(x)=10x.
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Here, put x=1 in the function y=10x, we get
y=10(1)
y=10
So, the range for the given x=1 is y=10.
Therefore, the range for the given function, with x=1 is 10.
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Find how long it takes $2500 to double if it is invested at 6% interest compounded semiannually. Use the formula A=P(1+r/n) to solve the compound interest problem.
It will take approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
In 11.71 years the amount will double to the principal amount
What is Compound interest:The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal amount and Compounded interest. This is the major distinction between compound and simple interest is this.
The formula used for
Amount, A = P(1+r/n)^ntwhere P = Principal amount
r = Rate of interest in decimal
n = Number of compounds per year
t = Time period
Here from the given data,
Principal amount, p = $ 2500
Rate of interest, r = 6% = 6/100 = 0.06
Number of compounds, n = 2 [ ∵ 12/6 = 2 ]
Here we need to find the time period
Let's assume that after 'n' years the amount will be doubled i.e $ 5000
From the given problem,
Amount, A = 2500(1+0.06/2)²ⁿ
= 2500(1+0.06/2)²ⁿ
= 2500(1 + 0.03)²ⁿ
= 2500 (1.03)²ⁿ
As we assumed after 'n' years the amount is $ 5000
=> 2500 (1.03)²ⁿ = 5000
=> (1.03)²ⁿ = 2
Apply to log on both sides
=> log (1.3)²ⁿ = log 2
=> 2t log (1.3) = log 2
=> 2t = log 2/ log(1.03)
=> 2t = 0.301029996/(0.0128372247)
[ use calculator for log (1.03) and log 2]
=> 2t = 23.4497722
=> t = 11.7248861
=> t = 11.71 ≅ 11 years
Therefore,
In 11.71 years the amount will double to the principal amount
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The graph shows the coordinates of triangle ABC. What are the coordinates of B' after a
reflection over the y-axis.
Answer:
(-4,5)
Step-by-step explanation:
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Moussa sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
81 visitors purchased no costume.
6 visitors purchased exactly one costume.
3 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase more than one costume as a decimal to the nearest hundredth.
The required probability for purchasing more than one costume is 0.03.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The given problem can be solved as follows,
The number of visitors purchasing no costume, exactly one and more than one costumes are given as 81, 6 and 3 respectively.
Then, the total number is 81 + 6 + 3 = 90
Now, the probability of purchasing more than one costume is given as,
P(More than one costume) = 3/90
= 1/30
= 0.03
Hence, probability that the next person will purchase more than one costume is 0.03.
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Find the missing length indicated.
The missing length in the given figure is 14.
What is meant by ratio?A ratio in mathematics depicts the product of two numbers. For instance, the proportion of oranges to lemons in a serving of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8. (or 3:4). (or 4:7).
Any number of numbers, including counts of people or things, weights, lengths, and times, among other values, can be a component of a ratio. In settings, both numbers are often restricted to positive values.
A ratio's two constituent numbers can be specified as "a" and "b," or they can both be omitted.
From the given figure,
AC/BC=EC/DC
28+x/18=x/6
28+x=3x
2x=28
x=14
Therefore, the missing length in the given figure is 14.
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Solve using the Square Root Property.
y^2 = 1/16
Answer:
1/4
Step-by-step explanation:
The square root of 16 is 4, so its the same with fractions.
QR is a midsegment of triangle WUV. What is the length of segment QR?
The length of segment QR is 8 units.
What is the mid-point segment of the triangle?
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
We have,
In ΔWUV
UV = 16 units
A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
Mid-point segment of the triangle:
QR = 1/2(UV) .............(1)
QR = 1/2(16)
QR = 8
Hence, the length of segment QR is 8 units.
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5. Which value is closest to (7.5 x 10³)+(5.2 x 105) ?
A.
B.
C.
D.
11.7 x 105
11.7 x 104
5.275 x 105
5.275 x 104
Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x-coordinate of point D.
The coordinate of point D and point E will be (x, y) and (-x, y), respectively.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in the m:n ratio, finding the mid-point of the line, etc.
Let the coordinate of the point D be (x, y).
Point E has a similar y-coordinate as point D. Then the ordinate of the points will be the same.
And the x-direction of point E is something contrary to the x-direction of point D. Then the coordinate of point E will be (-x, y).
The coordinate of point D and point E will be (x, y) and (-x, y), respectively.
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Find the nth term of this quadratic sequence
The nth term of the quadratic sequence is aₙ = n² + 2n
What is a quadratic sequence?
Finding the nth term rule of a quadratic sequence: The nth term rule of a quadratic sequence can always be written in the form an² + bn + c.
To find this rule, we need to find a, b and c
Given data ,
Let the expression be represented as = A
Now , the value of A is
A = 3 , 8 , 15 , 24 , 35 ..
Now , taking the difference of the second term and first term , we get
d₁ = 8 - 3 = 5
d₂ = 15 - 8 = 7
d₃ = 24 - 15 = 9
So , the difference of the numbers in the sequence is odd multiples
Therefore , the sequence goes in the multiples of ( n + 2 )
Now , when n = 1
a₁ = 3
when n = 2
a₂ = 8
So , a₂ = n ( n + 2 )
substituting the value for n = 2 , we get
a₂ = 2 ( 2 + 2 )
a₂ = 2 x 4
a₂ = 8
when n = 3
a₃ = 15
So , a₃ = n ( n + 2 )
substituting the value for n = 3 , we get
a₃ = 3 ( 3 + 2 )
a₃ = 3 x 5
a₃ = 15
Therefore , the nth term of the quadratic sequence will be
aₙ = n ( n + 2 )
aₙ = n² + 2n
Therefore , the sequence is aₙ = n² + 2n
Hence , The nth term of the quadratic sequence is aₙ = n² + 2n
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True or False :for a fixed value of the standard deviation and a fixed sample size, a confidence interval on the population mean will become wider as the level of confidence increases; for example, from 96% to 99%.
When the level of confidence interval increases from 96% to 99% then the population mean will also become wider for a given fixed value of standard deviation and its fixed sample size, so the given statement is true.
As given in the question,
Let us consider 'σ' be the fixed standard deviation
And 'n' be the fixed sample size
Population mean = [tex]\bar{x}[/tex] ± z ( σ /√n )
Range of confidence interval increases from 96% to 99%
For a fixed standard deviation and sample size range of population mean become wider .
For fixed [tex]\bar{x}[/tex] , standard deviation 'σ' , and sample size 'n' the value of population mean get varied as per the change in confidence interval z-score.
Therefore, the given statement when level of confidence interval increases from 96% to 99% then population mean will get wider is a true statement.
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Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm
Answer:
12
Step-by-step explanation:
Pythag
Write the form of the partial fraction decomposition of the function (as in Example 4). Do not determine the numerical values of the coefficients.
The partial fraction decomposition of the function is given as follows:
A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².
How to obtain the partial fraction decomposition of the function?The function in this problem is defined as follows:
(x^4 + x² + 1)/(x²(5x² + 9)²)
Then the partial fraction decomposition is built considering the terms of denominator, as follows:
x².(5x² + 9)².When a term is elevated to a power, the terms with the lower powers also have to be considered. For example, for the denominator x², x is also considered, hence the denominators are given as follows:
x.x².5x² + 9.(5x² + 9)².Then, considering the coefficients A, B, C and D, the partial fraction decomposition of the function is given as follows:
A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².
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help wanted proportinal relationship
Answer:
guy or girl
Step-by-step explanation:
Solve the system. Nearest tenth accepted.
y=2
y=3/5x+4
The value of x for which the equation satisfies is -10/3 .
What is an equation?
In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =
Main Body:
According to the question:
y = 2
and ,
y = 3/5 x+4
to solve the equation , we need to substitute the value of y in other equation.
2 = 3/5 x +4
now take like terms to one side for solving,
2 - 4 = 3/5 x
-2 = 3/5 x
multiplying by 5 on both sides,
-2 *5 = (3/5)*5x
-10 = 3 x
x = -10/3
Hence the value of x is -10/3.
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Question 9 of 25 Choose the equation that represents this situation. Use p to represent the price of a phone and to represent the total cost. An online business adds a $6 shipping fee to the price of each phone it sells. O A. t = 6p OB. t=p+6 O C. p=t+ 6 O D. t + p = 6
Choose the equation that represents this situation.
Use p to represent the price of a phone and t to represent the total cost. An online business adds a $6 shipping fee to the price of each phone it sells.
A. t = 6p
B. t = p + 6
C. p = t + 6
D. t + p = 6
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The circle's radius is the same as the radius of the circle whose equation is x2 + y2 = 9.
What is the equation of circle?A circle's standard equation is written as:
x² + y² + 2gx + 2fy + C = 0
The radius of the center is (-g, -f) and radius = √g² + √f² - C
Given a circle with the equation,
x² + y² - 2x - 8 = 0
Find the circle's center.
2gx = -2x
2g = -2
g = -1
Likewise, 2fy = 0.
f = 0
(-(-1), 0) = Centre (1, 0)
This demonstrates that the circle's center is on the x-axis.
r = radius
= √g² + √f² - C
By substituting,
radius = √1² + 0² - (-8)
=√9
= 3 units radius
The circle's radius is three units.
The radius of the circle x² + y² = 9 is written as:
r² = 9
radius = 3 units
As a result, the radius of this circle equals the radius of the circle whose equation is x² + y² = 9.
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4x -8y = 20
3x + 4y = 5
How can you eliminate the y-terms in this system?
4x-8y=20
3x + 4y = 5
Multiply by ?
2
3
4
5
on both sides.
Solve for y: . The solution is blank. The solution is 2(3y-4)=3(y-2/3)
Answer: y=2
Step-by-step explanation:
6y-8=3y-2
3y=6
y=2
HELP THANK YOU SO MUCH!!
Find the length of the diagonals. Find WY.
W: (-4,5)
Y: (3,-6)
See image Below:
Length of diagonal WY is 13.03 units
What is Distance Formula?
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).
This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
According to the given question:
WXYZ is a rectangle and diagonals of a rectangle are equal in length
Coordinates of W = (-4,5) and Y = (3,-6)
To find the length of diagonal WY, we need to find distance between points W and Y.
Using distance formula to find WY
= √((3 – (-4))² + (-6 – 5)²)
= √170
= 13.03 units
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Write the equation of the line that passes through the points (8, 5) and (-8, 1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
(y - 5) = 1/4 (x - 8)
Step-by-step explanation:
Point-slope form is written in the form:
(y - y) = m (x - x)
Where the two y's and two x's are from the points, and m is the slope. To write the equation, you'd plug your points into the equation and solve for m, the slope.
(1 - 5) = m (-8 - 8)
-4 = m (-16)
m = 4/16 = 1/4
Plug m into the point-slope form equation as well as one of your points, and you have an equation.
An employee works at a spin casting machine in a cast iron pipe manufacturing company located
in Charlotte, NC. She has various noise exposures throughout her 8-hour shift. The employee is
currently wearing MSA ear muffs with an NRR of 18 dB.
You have been asked to evaluate her noise exposure and determine if the current hearing protection
provided adequately protects her. You have a type II sound level meter to take noise measurements.
You have set he meter on A scale - slow response. Because the spin casting operation produces wind currents you also are using a wind screen.
After interviewing the employee and taking noise measurements with the sound level meter over the shift you have determined the following about her noise exposures:
95 dBA – for 6 hours while the spin casting machine is spinning
94 dBA – for 1.5 hours while the machine is set up between spins
82 dBA – for 30 minutes while in the lunchroom during breaks
a) What is her TWA noise exposure in dBA over the 8-hour shift?
b) Is the hearing protection adequate?
Answer:
ijsjsjdjdjjejjeks she e nsjksid the Earth travels in around the sun 6.2 Seasonal changes 6.3 Plants and animals are
Step-by-step explanation:
www2 and I 3333333 uth the sun is a bit better now and the Sun 6.2 is better off the moon
Using the Weshcler IQ test, adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. b) Find the score of an individual who is at the 85th percentile.
The 85th percentile of a normal distribution is the score that is greater than or equal to 85% of the scores in the distribution. This means that the score at the 85th percentile is the same as the score that would be earned by the top 15% of individuals in the distribution.
To find the score at the 85th percentile, we can use the standard normal distribution table or use a calculator to find the z-score corresponding to the 85th percentile. The z-score is the number of standard deviations that a score is above or below the mean of the distribution.
Using a calculator or table, we find that the z-score corresponding to the 85th percentile is 1.04. Since the mean of the distribution is 100 and the standard deviation is 15, this means that the score at the 85th percentile is 100 + (1.04 * 15) = 120.4.
Therefore, the score of an individual who is at the 85th percentile on the Weshcler IQ test is 120.4.
9. If x+2-6x=-13 , what is the value of 2x+3?
The value of the expression 2x+3 when x = 3 is 9.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given linear equation is
x + 2 - 6x = -13
Combine like terms:
(x - 6x) + 2 = -13
-5x + 2 = -13
The additive inverse of 2 is -2.
Add -2 on both sides:
-5x + 2 -2 = -13 -2
-5x = -15
Divide both sides by -5:
-5x/-5 = -15/-5
x = 3
Putting x = 3 in the expression 2x + 3
2x + 3 = (2×3) + 3
2x + 3 =6 + 3
2x + 3 = 9
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In constructing a confidence interval for the mean, when the population standard deviation is unknown, then we use
a. normal distribution
b. binomial distribution
c. t-distribution
d. Poisson distribution
While constructing a confidence interval for the mean, when the population standard deviation is unknown, then we use normal distribution .
The error bound EBM and confidence interval are calculated using a standard normal distribution when the population standard deviation is unknown. We must determine the value of z that places an area in the centre of the standard normal distribution Z N that is equal to the confidence level (in decimal form) (0, 1).
We rarely know the population standard deviation in practise. When the sample size was huge is the , statisticians were not hindered by this. As an estimate for, they used the sample standard deviations, and they then carried out the same steps as before to compute a confidence range that produced near enough findings.
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Given: AD ≅ BC and AD ║ BC.
Prove: ΔABC ≅ ΔCDA.
From the 2 column proof below, we have been able to prove the congruent triangles that ΔABC ≅ ΔCDA.
How to prove congruent triangles?We will use a two column proof to prove that ΔABC ≅ ΔCDA.
Statement 1; AD ≅ BC
Reason 1; Given
Statement 2; AD ║ BC
Reason 2; Given
Statement 3; AC ≅ AC
Reason 3; Reflexive Property of congruence
Statement 4; ∠DAC ≅ ∠ACB
Reason 4; If 2 parallel lines are cut by a transversal, the alternate interior angles are congruent.
Statement 5; ΔABC ≅ ΔCDA
Reason 5; Side Angle Side(SAS) Congruence Postulate
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17. Geometry The figure shown is a rectangle. The green shape in the figure is a square. The blue anc white shapes are rectangles, and the area of the blue rectangle is 24 square inches.
a. Write an expression for the area of the entire figure that includes an exponent. Then find the area.
b. Find the dimensions of the entire figure.
The expression for the area that includes an exponent is 6² + (6 × 2) + 24
Area of the entire figure is 72 square inches
The dimension of the entire figure is 9 inches by 8 inches
Calculating the area of a figureFrom the question, we are to write an expression for the area of the entire figure
Area of the entire figure = Area of green shape + Area of white shape + Area of blue shape
Area of the entire figure = 6² + (6 × 2) + 24 square inches
The expression is 6² + (6 × 2) + 24
Thus,
Evaluating
Area of the entire figure = 6² + (6 × 2) + 24
Area of the entire figure = 36 + 12 + 24
Area of the entire figure = 72 square inches
b. The dimension of the entire figure
Width of the entire figure = Length of the green square + Width of the white rectangle
Width of the entire figure = 6 inches + 2 inches
Width of the entire figure = 8 inches
Then,
Length of the entire figure = Length of the white rectangle + Width of the blue rectangle
First, we will determine the width of the blue rectangle
Using the formula,
Area = l × w
Where l is the length
and w is the width
24 = (2 + 6) × w
24 = 8 × w
w = 24/8
w = 3 inches
Therefore,
Length of the entire figure = 6 inches + 3 inches
Length of the entire figure = 9 inches
Hence, the dimension is 9 inches by 8 inches
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Jenny and Julie each drank a cup of hot chocolate after playing in the snow. Jenny put 6 more marshmallows in her cup than Julie. Together Jenny and Julie had a total of 6 marshmallows. How many marshmallows did Jenny (x) and Julie (y) each have in their hot chocolate?
Jenny has 6 marshmallows in her hot chocolate and Julie has 0 marshmallows in her hot chocolate
System of equations: Determining the number of marshmallows in hot chocolateFrom the question, we are to determine the number of marshmallows Jenny and Julie each have in their hot chocolate
From the given information,
"Jenny put 6 more marshmallows in her cup than Julie"
Then, we can write that
x - y = 6 ---------- (1)
Also,
"Together Jenny and Julie had a total of 6 marshmallows"
That is,
x + y = 6 ---------- (2)
Add equations (1) and (2) together
x - y = 6
+ [x + y = 6
--------------------
2x = 12
x = 12/2
x = 6
Substitute the value of x into equation (2)
x + y = 6
6 + y = 6
y = 6 - 6
y = 0
Hence, Jenny has 6 and Julie has 0
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If BC = 16.7 ft, what is AY?
Please helpppp
Answer:
16.7
Step-by-step explanation:
YX is similar to AX
XZ is similar to XB
so the triangle AXB is similar to YXZ thus AB is YC
The same goes for the rest of the triangles (YAC and CBZ)
See image attached.
Sabina used long division to divide 3x³ + x + 2 by a x+ 2. Her work is shown. which error or error did sabrina make?
I'm not sure if those are the real answers
The correct option for the errors made by Sabina are-
Sabina did not use a coefficient placeholder for any missing terms.Sabina did not find the correct term of the quotient.Explain the long division method?You can divide huge numbers into numerous smaller groups or portions with the long division tool. The quantity of groups that may be formed when a dividend is divided by a divisor is given by the quotient, and the number of elements or integers that will remain ungrouped is given by the remainder.For the stated expression-
3x³ + x + 2 by when divided by (x + 2) by the long division method, the following is the quotient.
_____________
x + 2 ) 3x³ + x + 2 ( 3x² - 6x + 7
- 3x³ - 6x²
__________
- 6x² + x + 2
+ 6x² + 6x
____________
7x + 2
-7x - 16
__________
- 14
___________
Thus, the correct quotient for the polynomial is 3x² - 6x + 7.
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