Use the limit definition of the derivative to find the instantaneous rate of change of
SOLUTION:
Step 1:
In this question, we are given the following:
Use the limit definition of the derivative to find the instantaneous rate of change of
Step 2:
The details of the solution are as follows:
An alternative way to find the use the limit definition of the derivative to find the instantaneous rate of change of:
[tex]f(x)\text{ =}\sqrt[]{4x+8\text{ }}\text{ at x = 4}[/tex]Let us take the derivative of the function and we have that:
[tex]\begin{gathered} f(x)\text{ = }\sqrt[]{4x+8}=(4x+8)^{\frac{1}{2}} \\ \end{gathered}[/tex][tex]\begin{gathered} f^I(x)\text{ = }\frac{1}{2}(4x+8)^{-\frac{1}{2}}(4) \\ f^I(x)=2(4x+8)^{-\frac{1}{2}},\text{ when x = 4, we have that:} \\ f^I(4)=2(4(4)+8)^{-\frac{1}{2}} \end{gathered}[/tex][tex]\begin{gathered} f^I(4)=2(16+8)^{-\frac{1}{2}} \\ f^I(4)\text{ = 2 x }\frac{1}{\sqrt[]{24}} \end{gathered}[/tex][tex]f^I(4)\text{ =}\frac{2}{\sqrt[]{24}}[/tex][tex]f^I(4)=\frac{2}{\sqrt[]{24}}=\frac{2}{\sqrt[]{4}X\sqrt[]{6}}=\frac{2}{2X\sqrt[]{6}}=\frac{1}{\sqrt[]{6}}[/tex][tex]f^I(4)\text{ =}\frac{1}{\sqrt[]{6}}[/tex]
Explain how you can use addition of groups to show that 4 x ( -3) = 12
The technique of repeated addition involves combining equal groups.
4 x ( -3) = 12.
Repeated addition is the combining of equal groupings. It offers a basis for comprehending multiplication. For instance, 3 x 5 can be expressed as 5 + 5 + 5 to represent 3 groups of 5 counters.
We have been given that
4 x ( -3) = 12
By using repeated addition for multiplication
Add 4 three times or add 3 for times ..
In question negative 3 is given so we add negative 4 , three times
(-4) + (-4) + (-4)
-12.
Or
Add negative 3 , four times
(-3) + (-3 )+ (-3) + (-3)
-12.
Hence, we solved given multiplication by the using repeated addition method.
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Al got an estimate for repairs on his bike. Theparts will cost $17.50, and the parts and labortogether will not be more than $40. Whatinequality shows the possible labor costs, L?
Let's list down the pieces of information given the scenario:
Cost of bike parts = $17.50
Bike parts and labor together = not more than $40/ lesser than or equal to $40.
Let's now generate the equation based on the given information,
Let,
L = Labor cost
[tex]\text{ Cost of parts+Labor Cost }\leq\text{ \$40 ;since the total must not be more than \$40}[/tex][tex]\text{ \$17.50 + L }\leq\text{ \$40 ; inequality showing the possible total cost}[/tex]Let's now generate the inequality showing the possible labor cost, L
[tex]\text{ \$17.50 + L }\leq\text{ \$40 }\rightarrow\text{ L }\leq\text{ \$40 - \$17.50}[/tex][tex]\text{ L }\leq\text{ \$22.50}[/tex]Therefore, the cost of labor must not be more than $22.50.
2. Refer to the figure shown.a. What is JK?b. What is KM?
Point J is located at 5
Point K is located at 12
Point M is located at 27
a. The length of the segment JK is: 12 - 5 = 7
b. The length of the segment KM is: 27 - 12 = 15
1messageJosh wants to estimate the mean age in a population of trees. He'll sample n trees and build a 95% confidence interval for the mean age. He doesn't want the margin of error to exceed 3 years. Preliminary data suggests that the standard deviation for the ages of trees in this population is 16 years.Which of these is the smallest approximate sample size required to obtain the desired margin of error?11 trees110 trees144 trees43 trees87 trees
The formula for the margin of error is
[tex]\begin{gathered} \text{MOE}=SE\times critical\text{ value} \\ SE\Rightarrow\text{standard error} \end{gathered}[/tex]The critical value for 95% confidence interval is 1.96
The standard error is
[tex]\begin{gathered} SE=\frac{\sigma}{\sqrt[]{n}} \\ \sigma\Rightarrow standard\text{ deviation} \\ n\Rightarrow\text{sample size} \end{gathered}[/tex]To know which of the list of options will yield approximately the desired margin of error, we will have to calculate the margin of error with the following values
For 110 trees, n= 110, standard dev. =16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{110}}=1.53 \\ \text{MOE}=1.53\times1.96=2.9988 \end{gathered}[/tex]For 144 trees, n=144, standard dev=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{144}}=\frac{16}{12}=1.33 \\ \text{MOE}=1.33\times1.96=2.61 \end{gathered}[/tex]For 43 trees, n=43 , standard dev.=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{43}}=2.44 \\ \text{MOE}=2.44\times1.96=4.782 \end{gathered}[/tex]For 87 trees, n= 87, standard dev=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{87}}=1.72 \\ \text{MOE}=1.72\times1.96=3.3712 \end{gathered}[/tex]Hence, from the above calculations, the most prefered is the sample size of 110 trees (because the margin of error of 2.9988 is approximately 3 )
Answer is 110 trees
A stand at the farmers market sells different types of apples, as shown in the table.
Cost ($)
Weight
Apple A Apple B Apple C
4.90
4 lb
1.00
10 oz
0.45
lb
Which type of apple costs the least per pound? Apple A
The cost of Apple A: $1.225
What is Weight?
The weight of an object is the force exerted on it by gravity. Some standard textbooks define weight as a vector quantity, the force of gravity acting on an object. Some define weight as a scalar quantity that is the magnitude of gravity.
Cost of the different types of the apple have been given as,
Apple A = costing $4.90 for 4 lb
Apple B = costing $1.00 for 10 oz
Apple C = costing $0.45 for 1/2 lb
For Apple A,
Since, cost of 4 lb = $4.90
Therefore, cost of 1 lb = 4.90/4
= $1.225
For Apple B,
Since, 1 oz = 0.0625 lb
Therefore, 10 oz = 0.0625 × 10
= 0.625 lb
Since, cost of 10 oz = $1.00
Therefore, cost of 0.625 lb = $1.00
And cost of 1 lb = 1/0.625
= $1.6
For Apple C,
Since, cost of 1/2 lb = $0.45
Therefore, cost of 1 lb = 0.45 × 2
= $0.90
Hence, Cost of Apple A will be the least with $1.225 per pound.
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10. A recipe calls for 5 cups of flour. If you only have a ½ cup to measure, how many ½ cups will you need for
the recipe?
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
The given statement is false: vertical angle do not depend on the line being parallel. A pair of vertical angles are always congruent.
Vertical angle:
Vertical angle means that the angles opposite each other when two lines cross.
Given,
Here we have the diagram and we also know that angle 7 is congruent to angle 5.
Now we need to find the given statement is true or not.
Through the given diagram, we have identified that, the eight angles will together form four pairs of corresponding angles.
Angles 1 and 5 constitutes one of the pairs.
We know that all the corresponding angles are congruent.
All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.
Through that we know that basically, the vertical angles are always congruent, which means that they are equal. So, it is not necessary for them to be parallel.
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Write 92.5% in a fraction or mixed number in simplest form
what value of x is the answer to the equation x - 2 = 16
The value of x is the answer to the equation x - 2 = 16 which is 18.
What is the solution for an equation?An equation is an expression that shows the relationship between two or more numbers and variables. The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.
We have been given a linear equation as; x - 2 = 16
We need to find the value of x as the answer to the equation x - 2 = 16.
Therefore, we will eliminate the 2.
x - 2 = 16
Add 2 on both sides of the equation;
x - 2 + 2= 16+ 2
Then ;
x = 18
Hence, the value of x is the answer to the equation x - 2 = 16 which is 18.
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A 250 N force acts on a 20 kg object. What would be the acceleration of the object?
Answer:
a = 12.5 m/s2
Step-by-step explanation:
anwser 12.5
3/9 - 6/9 = ?
,,,,,,,,,,,,,,,,,,,,,,,
Answer:
-3/9 or -1/3
Step-by-step explanation:
:]
Answer: -1/3
Step-by-step explanation- To subtract fractions, you first make the the denominators the same. The denominator is the bottom number. To make the denominator the same, you look for the lowest common denominator. Making the answer -1/3
The safe load, L. of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d. and inversely as the length. I. A wooden beam 8 in. wide. 6 in. deep, and 10 ft long holds up 1966 lb. What load would a beam 3 in. wide 9 in. deep and 11 ft long of the same material support? (Round off your answer to the nearest pound.)
The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17
Analyzing the given conditions in the question, we get
The safe load, L is directly proportional to width (w) and square of depth (d²)
also,
L is inversely as length (l) i.e L = k/l
combining the above conditions, we get an equation as:
L = k(wd²/l)
now, for the first case we have been given
w = 8 in
d = 6 in
l = 10 ft
L = 1966 lbs
thus,
1966 lb = k ((8 × 6²)/10)
or
k = 68.26 lbs/(ft.in³)
Now,
Using the calculated value of k to calculate the value of L in the second case
in the second case, we have
w = 3 in
d =9 in
l = 11 ft
Final Safe load L' = 68.26 × (6 × 3²/12)
or
L' =307.17 lb
Therefore, The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17
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You want to have $15,000 in 11 years. You will invest how much into an account that has an annual rate of 4.4% compounded daily? Round your answer to two decimal places and assume 365 days per year.
Given:
Future Value = $15,000
time (t) = 11 years
rate (r) = 4.4% or 0.044
number of conversions per year (m) = 365
Find: Initial amount or the Principal
Solution:
Formula for Compound Interest is:
[tex]F=P(1+\frac{r}{m})^{mt}[/tex]From that, we can derive the formula for the Principal or the initial amount.
[tex]P=\frac{F}{(1+\frac{r}{m})^{mt}}[/tex]Let's plug in the given data above to the formula of the principal value.
[tex]P=\frac{15,000}{(1+\frac{0.044}{365})^{365\times11}}[/tex]Then, solve for P.
[tex]P=\frac{15,000}{(1.000120548)^{4015}}=\frac{15,000}{1.622504316}\approx9,244.97[/tex]Answer: You must invest $9, 244.97 to the account in order to get $15,000 after 11 years.
Write an equation describing the relationship of the given variables
how far apart is -1 1/3 and 4 2/5 on a number line
In gym class, a student can do 40 sit-ups in 60 seconds and 100 sit-ups in 150 seconds.
Graph the proportional relationship.
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 30
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
Answer:
(a) graph with line through (90, 60)
Step-by-step explanation:
You want a graph of the proportional relationship between sit-ups and seconds if a student can do 40 sit-ups in 60 seconds.
GraphSeconds are plotted on the x-axis, and sit-ups are plotted on the y-axis The graph will match that shown in the attachment.
<95141404393>
Complete both transformations below.
Then enter the final coordinates of the figure.
A(-1,3)
B(2,1)
C(1-1)
1) <2,3>
2) Dilate K = 2
A" ([?], [])
B" ([][])
C" ([],[])
Enter
Answer:
A" (2, 12)
B" (8,8)
C" (6, 4)
Step-by-step explanation:
For each point P(x, y) of the image, the translations are as follows:
Translate P(x, y) by <2, 3> [tex]\longrightarrow[/tex] P'(x + 2, y + 3) [tex]\longrightarrow[/tex] P'(x', y')
Dilate P'(x', y') by 2 [tex]\longrightarrow[/tex] P'' (x'', y'') [tex]\longrightarrow[/tex] P(2x', 2y')
Point [tex]\longrightarrow[/tex] Translate <2, 3> [tex]\longrightarrow[/tex] Dilate by 2
A(-1, 3) [tex]\longrightarrow[/tex] A'(-1 +2, 3 + 3) => A'(1, 6) [tex]\longrightarrow[/tex] A''(2, 12)
B(2, 1) [tex]\longrightarrow[/tex] B'(2 + 2, 1 + 3) => B'(4, 4) [tex]\longrightarrow[/tex] B"(8, 8)
C(1, -1) [tex]\longrightarrow[/tex] C'(1 + 2, -1 + 3) => C'(3, 2) [tex]\longrightarrow[/tex] C"(6, 4)
calcula la suma de los quince primeros multiplos de 9
Answer:
Step-by-step explanation:
9*(15/2)[2+14] = 9*15*16 = 2160.
Suppose that a certain basketball athlete earned $17,250,000 to play 80 games, each lasting 48 minutes. (Assume no overtime games.)
The amount paid for each is;
1) Amount earned per game = $215625 per game
2) Amount earned per minute played = $4492.1875
3) Amount earned each minute for 2/3 games = $6738.28
4) Amount earned per hour = 4492.1875 * 60 = $269531.25
How to find the rate per game?We are given;
Amount earned by athlete = $17,250,000
Number of games played = 80 Games
Number of minutes per game = 48 minutes
1) Amount earned per game = Amount earned by athlete/Number of games played = 17250000/80 = $215625 per game
2) If he played entire games for the entire minutes;
Amount earned per minute played = 17250000/(80 * 48)
Amount earned per minute played = $4492.1875
3) He played 2/3 of every game. Thus;
Amount earned each minute for 2/3 games = 17250000/((2/3) * 80 * 48)
Amount earned each minute for 2/3 games = $6738.28
4) Since amount earned for every minute is $4492.1875, then we say that;
Amount earned per hour = 4492.1875 * 60 = $269531.25
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Lottery numbers in a particular state consist of 5 digits. Each lottery cube that is drawn/rolled has six sides, numbered 1-6. How many different lottery numbers are possible? O 720 lottery number O 7776 lottery numbers
As per the concept of probability, there are 7776 different lottery numbers are possible.
Probability:
Probability means the concept that is based on the possible chances of something to happen.
Given,
Lottery numbers in a particular state consist of 5 digits. Each lottery cube that is drawn/rolled has six sides, numbered 1-6.
Here we need to find how many different lottery numbers are possible.
Through the given question we know that,
The number of digits in a lottery ticket = 5
Side in cube = 6
So, in each time they will roll the dice 5 times to get one number.
So, the possible options of that event are,
For the first time we have 6 options
Second time we got 6 options
Third time also we got six option
Fourth time = 6 options
Fifth time = 6 options.
Therefore, it can be written as,
=> 6 x 6 x 6 x 6 x 6
=> 6⁵
=> 7776.
Therefore, there are 7776 different lottery numbers are possible.
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question 1.P(A)=0.25 P(B)=0.65 P(A or B)=?a.0.45b.0.2c.0.65d.0.9question 2P(A)=0.45 P(B)=0.35 P(A or B)=?a.0.75b.0.85c.0.8d.0.35
Given,
1)P(A) = 0.25
P(B) = 0.65
The value of P( A or B) is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)_{} \\ P(A\cup B)=0.25+0.65 \\ P(A\cup B)=0.90 \end{gathered}[/tex]Hence, option d is correct.
2)P(A) = 0.45
P(B) = 0.35
The value of P( A or B) is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)_{} \\ P(A\cup B)=0.45+0.35 \\ P(A\cup B)=0.80 \end{gathered}[/tex]Hence, option c is correct.
In isosceles triangle ABC,AB=BC. AB and Bc are called_____a.bases b.verticesc.hypotenused. legs
In an isosceles triangle, there are
2 legs (equal sides)
1 base
The 2 legs are the equal sides
The base is the third side
In the isosceles triangle ABC:
Since AB = BC, then
AB and BC are the legs of the triangle, then
AB and BC are called legs
The answer is d
The cranes shown in the figure are lifting an object that weighs 20,290 pounds. Find the tension in the cable of each crane. (Round your answers to the nearest whole number.)TL= lbsTR= lbs
we have that
TLy+TRy=20,290 ------> equation A
and
sin(24.3)=TLy/TL
TLy=TLsin(24.3) ------> equation B
sin(44.5)=TRy/TR
TRy=TRsin(44.5) ------> equation C
and
TLx=TRx
TLcos(24.3)=TRcos(44.5)
TL=TRcos(44.5)/cos(24.3) --------> equation D
substitute equation B and equation C in equation A
TLsin(24.3)+TRsin(44.5)=20,290 -------> equation E
substitute equation D in equation E
(TRcos(44.5)/cos(24.3))sin(24.3)+TRsin(44.5)=20,290
solve for TR
factor TR
TR[cos(44.5)/cos(24.3))sin(24.3)+sin(44.5)]=20,290
TR=19,835 pounds
Find TL
TL=(19,835)cos(44.5)/cos(24.3)
TL=
express the form in lowest terms 1/3x^3
The expression in the lowest term will be 3^-1x³.
What is a expression?It should be noted that an expression simply has to do with the relationship that can be illustrated having a mathematical operator.
It should be noted that based on the information given, this will be illustrated as:
= 1/3(x³)
This can be illustrated as:
1/3 = 3^-1 multiplied by x³.
= 3^-1x³
This shows the concept of exponents.
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damion started solving this equation in an even different way what did he do first
With the help of Linear equation we can say that Damion added 12 on both sides.
What is linear equations?Equations with variables whose maximum power is 1 are said to be linear equations. A linear equation has a straight line as its graph.The given equation was,
12x + 4 = 20x-12If we will add 12 on both sides ,
12x + 16= 20xHence we can say that Damion added 12 to both sides.
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How much interest is earned in an investment if $720 is deposited monthly at 7.8% compounded monthly if the term of the investment is 6 years?$__________Round to the nearest cent
Given:
The initial investment is, P = $720.
The rate of interest is, r = 7.8% = 0.078.
The number of years of investment is, t = 6 years.
Explanation:
The general formula to find the compound interest is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n represents the number of times compounded in a year. It is given that the amount is compounded monthly, so the value of n = 12.
To find total amount after 6 years:
Now, substitute the given values in the general equation.
[tex]\begin{gathered} A=720(1+\frac{0.078}{12})^{12(6)} \\ =720(1+0.0065)^{72} \\ =1147.95 \end{gathered}[/tex]Thus, the total amount earned is $1147.95.
To fnd interest amount:
Now, the amount of interest can be calculated as,
[tex]\begin{gathered} I=A-P \\ =1147.95-720 \\ =427.95 \end{gathered}[/tex]Hence, the interest amount earned is $427.95 and the total amount earned is $1147.95.
solve the following compound inequality.-6x+7<55 AND 5x-4≤16OA. x<-8 AND x < 4OB. -9< x≤4OC. -8 < x≤4OD. x≤4
The given compound inequality is:
[tex]-6x+7\lt55\text{ and }5x-4\leq16[/tex]Solve the first inequality:
[tex]\begin{gathered} -6x+7<55 \\ -6x<55-7 \\ -6x<48 \\ \text{ Divide both sides by }-6\text{ and reverse the inequality sign:} \\ -\frac{6x}{-6}\gt\frac{48}{-6} \\ x\gt-8 \end{gathered}[/tex]Solve the second inequality:
[tex]\begin{gathered} 5x-4\leq16 \\ \text{ Add }4\text{ to both sides of the inequality:} \\ 5x-4+4\leq16+4 \\ 5x\leq20 \\ \frac{5x}{5}\leq\frac{20}{5} \\ x\leq4 \end{gathered}[/tex]Therefore, the correct answer is choice C:
-8 < x ≤ 4
Consideremos la recta y=6x-4.
¿Cuál es la pendiente de una recta paralela a esta recta?
¿Cuál es la pendiente de una recta perpendicular a esta recta?
Pendiente de una recta paralela:
Pendiente de una recta perpendicular:
Slope of a parallel line: 6
Slope of a perpendicular line: -1/6
What is Slope ?
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
Given equation,
y=6x-4
The equation of a line with slope m is given as:
y=mx+c
Rearranging the given equation:
y=(6)x+(-4)
By equating the equations we get,
m= 6
Which is slope of a parallel line
Now any parallel line would have the same slope.
And slope of a perpendicular line would be −1/m.
i.e. m(perpendicular)= -1/6
Hence, Slope of a parallel line is 6 and Slope of a perpendicular line is -1/6
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
C(x) = 75x + 1908
Step-by-step explanation:
C(x) is the cost function.
The cost of making x bicycles is the sum of the fixed costs and the cost per bicycle.
The fixed cost is $1908.
The cost per bicycle is $75, so the per bicycle cost for x bicycles is 75x.
Add the two costs, and you get:
C(x) = 75x + 1908