A function is given. Determine the average rate of change of the function between the given values of the variable: f(x)= 4x^2; x=3, x=3+h

Answers

Answer 1

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------[/tex]

[tex]\bf f(x)= 4x^2 \qquad \begin{cases} x_1=3\\ x_2=3+h \end{cases}\implies \cfrac{f(3+h)-f(3)}{(3+h)~-~(3)} \\\\\\ \cfrac{[4(3+h)^2]~~-~~[4(3)^2]}{\underline{3}+h-\underline{3}}\implies \cfrac{4(3^2+6h+h^2)~~-~~4(9)}{h} \\\\\\ \cfrac{4(9+6h+h^2)~~-~~36}{h}\implies \cfrac{\underline{36}+24h+4h^2~~\underline{-~~36}}{h} \\\\\\ \cfrac{24h+4h^2}{h}\implies \cfrac{\underline{h}(24+4h)}{\underline{h}}\implies 24+4h[/tex]

Related Questions

An investment grows by 20% over a 20 year period. What is its effective annual percent growth rate?

Answers

Final answer:

The effective annual percent growth rate is 3.97%.

Explanation:

The effective annual percent growth rate can be calculated using the formula:

Effective Annual Growth Rate = (1 + Growth Rate)^(1/n) - 1

Given that the investment grows by 20% over a 20-year period, the growth rate would be 0.20.

Substituting the values into the formula:

Effective Annual Growth Rate = (1 + 0.20)^(1/20) - 1

Simplifying further:

Effective Annual Growth Rate = (1.20)^(0.05) - 1

Effective Annual Growth Rate = 0.0397 or 3.97%

Final answer:

The effective annual percent growth rate for an investment that grows by 20% over a 20-year period is approximately 0.949%.

Explanation:

To calculate the effective annual percent growth rate, we need to use the formula for compound interest:

A = P(1 + r)^n

where:

A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of years the money is invested for.

We can rearrange this formula to solve for r:

r = (A/P)^(1/n) - 1

Given that the investment grows by 20% over 20 years, this means A = 1.20P, as it has increased by 20%. With P as the original amount and n as 20 years, the calculation is:

r = (1.20)^(1/20) - 1

Now we compute the value:

r = (1.20)^(0.05) - 1

r ≈ 0.00949

Converting this into a percentage:

r ≈ 0.949%

Therefore, the effective annual percent growth rate is approximately 0.949%.

The sum of the squares of two consecutive odd integers is 1570. find the integers

Answers

Let's look at a few examples of two consecutive odd integers.
1, 3
11, 13
55, 57
Notice that the larger integer is always 2 more than the smaller one.

If you let the smaller one be x, then the larger one is x + 2.

Now we square the two numbers.
The square of x is x^2.
The square of x + 2 is (x + 2)^2.

Now we add those two squares and set equal to 1570.

x^2 + (x + 2)^2 = 1570

x^2 + x^2 + 4x + 4 = 1570

2x^2 + 4x + 4 = 1570

2x^2 + 4x - 1566 = 0

x^2 + 2x - 783 = 0

783 is 290 * 27

(x - 27)(x + 29) = 0

x - 27 = 0 or x + 29 = 0

x = 27 or x = -29

Remember that x is the smaller of the two integers.

If x = 27, then x + 2 is 29.
If x = -29, then x + 2 is -27.

The answer is:
There are two pairs of integers
One pair is 27 and 29.
The other pair is -29 and -27.

Final answer:

Two consecutive odd integers whose squares sum to 1570 are found by setting up a quadratic equation. Solving this equation gives us 27 and 29 as the required integers.

Explanation:

The question requires us to find two consecutive odd integers whose squares add up to 1570. Let's consider the smaller integer to be n, which means the next consecutive odd integer would be n + 2 (since there is always a difference of 2 between consecutive odd numbers). Our equation based on the given information will be:

[tex]n^2 + (n + 2)^2[/tex] = 1570

To solve for n, we will expand the equation and simplify:

[tex]n^2 + n^2 + 4n + 4[/tex] = 1570[tex]2n^2 + 4n + 4[/tex] = 1570[tex]2n^2 + 4n - 1566[/tex] = 0Divide the entire equation by 2: n2 + 2n - 783 = 0

Solving the quadratic equation, we find that n = 27 and n = -29.

As we are looking for positive integers, we take n = 27. Therefore, the two consecutive odd integers are 27 and 29.

For the function f(t)=pe rt , if p=9 and r=0.09 then what is the value of f(9) to the nearest tenth

Answers

Answer: f(9) = 20.2 .
_______________________________
Explanation:
_______________________________
f(9) = pe^(r*t) = 9* e^(0.09 * 9) ;
_______________________________
Note: 0.09 *9 = 0.81 .
______________________________
→ f(9) = pe^(r*t) = 9* e^0.81 ) ;
_______________________________
Note: e^(0.81) = 2.24790798668.

f(9) = 9 * 2.24790798668 ;

= 20.2311718801 ;

→ Round to the nearest tenth:

f(9) = 20.2 .
_________________________________

A rectangle's length is 5 units more than the width. the perimeter is 9 times the width. what are the length and the width of the rectangle described?

Answers

L=5+w
2(l+w)=9w
2l+2w=9w
2l=7w
2(5+w)=7w
10+2w=7w
10=5w
W=2, l=5+w=5+2=7

Find the value of x and the value of y.

Answers

ans is
x= 7 and y= 4√2

What is the slope of the line whose equation is 12=4x−6y ? Enter your answer in the box.

Answers

12=4x-6y
2-(4/6)x=y

Slope is -4/6 or -2/3

Answer:

Slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .

Step-by-step explanation:

The slope line form is denoted by

y = mx + c

Where m is the slope and c is the y- intercept .

As given

The equation of the line is given by .

12=4x−6y

It is also written as

6y = 4x - 12

[tex]y = \frac{4x}{6} -\frac{12}{6}[/tex]

Simplify the above

[tex]y = \frac{2x}{3} -2[/tex]

(Compare with y = mx + c )

Thus

[tex]m = \frac{2}{3}[/tex]

Therefore the slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .

Imagine a 10 kg block moving with a velocity of 20 m/s to the left. Calculate the kinetic energy of this block

Answers

k.e = ½mv²
= ½×10×20×20
= 5×20×20
= 2000j or 2Kj

Which answer is the solution set to the given inequality |x+7| < 17

Answers

X Can't get greater than 10 but it can be -10 so x has to be lesser then 10.

x must be lesser than 10 or else this wont make sense(please leave me a thank you)

During the first quarter of the year, 351,875 people downloaded an app for their smartphones. During the second quarter of the year, 101,949 fewer people downloaded the app than during the first quarter. How many downloads occurred during the two quarters of the year?
a. Round each number to the nearest hundred thousand to estimate how many downloads occurred during the first two quarters ofthe year.

Answers

The number of people who downloaded the app in the first quarter is 351,875 people.
Those who downloaded in the second quarter are 101,949 fewer people than those in first quarter.
This means that:
number of people who downloaded in 2nd quarter = number of people who downloaded in 1st quarter - 101,949
number of people in 2nd quarter = 351,875 - 101,949 = 249,926 people

Therefore, the total number of people who downloaded the app can be calculated as follows:
Total number = 351,875 + 249,926 = 601,801 people

Rounding this number to the nearest hundred thousands, we can get the estimated number of people who downloaded the app as 600,000 people

What is the value of f(−1) when f(x)=2x+2 ?

Enter your answer in the box.
f(−1)=

Answers

f(-1)=2(-1)+2
f(-1)=-2+2
f(-1)=0

When u.s. students took the timss, 53 percent of them: a. overestimated their math skills. b. were realistic about their math skills?

Answers

The answer is B. were realistic with their math skills because Trends in International Mathematics and Science Study (TIMSS) provides genuine and updated statistics on mathematics and science performance of U.S. students and also they assess advance mathematics and physics performance of last year of secondary schools over the countries.

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.

Which equations can be used to solve for y, the length of the room? Check all that apply.

y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0

Answers

The first one is right because if y=25 then25(25+5)=750

the correct answer is

B)y2 – 5y = 750

C)750 – y(y – 5) = 0

E)(y + 25)(y – 30) = 0

I JUST took the test

Greg made $306 for 17 hours of work. at the same rate, how much would he make for 12 hours of work?

Answers

Divide pay by the hours work to get the rate per hour.

$306/17hrs = $18 per hour rate.

So, if he work 12hrs at $18 per hour his pay will be 12*18 = $216

The answer is $216

When it is 10:00 am solar time at location x, at which location is 11:00 am solar time being observed?

Answers

There are a total of 360 degrees and a total of 24 hours, therefore there are 15 degrees per hour.

Location x is located at 45 degrees, so therefore the location after 1 hour must be at 60 degrees.

Answer:

Answer:

it is letter D

Step-by-step explanation:

its letter D when I was doing it, in go formative

Justin is constructing a line through point Q that is perpendicular to line n. He has already constructed the arcs shown. A line n and an arc with center Q is drawn. Center Q lies above the line n. The arc cuts the line on two points A and B. A is left of B. Another arc is made with a center at A. The arc cut the line segment A B near point B. The arc is symmetric to line A B. He places his compass on point B to construct an arc. What must be true about the width of the compass opening when Justin draws the arc?

Answers

I believe that this problem has the following choices:

It must be equal to BQ .
It must be wider than when he constructed the arc centered at point A.
It must be equal to AB .
It must be the same as when he constructed the arc centered at point A.

The correct answer is the last one:

It must be the same as when he constructed the arc centered at point A.

Answer:

The compass must be the same width as it was when he constructed the arc from point A.

Step-by-step explanation:

In order to construct a perpendicular line to a given line, we need to construct a point above and a point below the line such that the segment through them meets the line at a right angle.

When he constructed the arc from point A, it gave him one piece to creating these points. An arc from point B, intersecting the arc from point A at two points, will give him the two points he needs.

In order for the arc from point B to intersect the arc from point A, however, the width of the compass must be the same as it was when he constructed the arc from point A.

How many times can 5/8 go into 12?

Answers

Okay. All you have to do is 12/ 5/8 Or the Keep, Change, Flip rule. 12/1 * 8/5 = 96/5 or 19 1/5 when simplified. If you’re looking for the answer rounded to the whole number, the answer of 19. Or, if you’re looking for the answer just plain, the answer is 19 1/5.

What is the relationship between the “solution” to a quadratic equation and the graph of a quadratic equation? How many possible real solutions might there be when you solve a quadratic equation and how do these possible solutions affect the position the parabola on a coordinate plane?

Answers

The solutions of a quadratic equations are the x value of the x-intercepts of the graph.

If there are 0 real solutions, the parabola will not touch the x-axis.

If there is 1 real solution, the parabola's vertex will be on the x-axis.

If there are 2 real solutions, the parabola will intersect the x-axis in two distinct positions.

Hope this helps!

Final answer:

Solutions of a quadratic equation represent points where the graph of the equation (a parabola) intersects the x-axis, and there could be zero, one, or two real solutions.

Explanation:

The relationship between the 'solution' of a quadratic equation and the graph of a quadratic equation is that the solutions of a quadratic equation correspond to the points where the graph of this equation, also known as a parabola, intersects with the x-axis on a two-dimensional (x-y) graph. A quadratic equation can have zero, one, or two real solutions. These solutions are represented graphically by where the curve of the parabola intersects the x-axis.

When the parabola intersects the x-axis twice, there are two distinct real solutions. If the parabola is tangent to the x-axis, then there is exactly one real solution, also known as a repeated root, whereas if the parabola does not intersect or touch x-axis at all, then there are no real solutions, indicating that the roots are complex or imaginary.

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Find two positive numbers whose product is 36 and whose sum is a minimum.

Answers

Final answer:

To find two positive numbers whose product is 36 and whose sum is a minimum, set up an equation using the arithmetic mean and geometric mean inequality. Solve for the two numbers.

Explanation:

To find two positive numbers whose product is 36 and whose sum is a minimum, we can use the concept of the arithmetic mean and geometric mean inequality. Let the two numbers be x and y. Since the product of the numbers is 36, we have xy = 36. Using the arithmetic mean and geometric mean inequality, we know that the minimum value of the sum of two positive numbers is attained when the two numbers are equal. Therefore, x = y. Substituting this into the equation xy = 36, we have x^2 = 36. Taking the square root of both sides, we get x = √36 = 6. So, the two positive numbers are x = 6 and y = 6.

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Final answer:

The two positive numbers whose product is 36 and whose sum is a minimum are 6 and 6.

Explanation:

To find two positive numbers whose product is 36 and whose sum is a minimum, we can use the concept of the Arithmetic Mean-Geometric Mean Inequality.

Let x and y be the two numbers.

According to the inequality, the minimum sum occurs when the numbers are equal.

So, we have x = y = √36 = 6.

Therefore, the two positive numbers whose product is 36 and whose sum is a minimum are 6 and 6.

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A proof uses logical reasoning that starts with accepted ideas and proceeds through logic to reach a conclusion.

Which type of reasoning does a mathematical proof use?

deductive or inductive

Answers

Inductive reasoning looks at given information, and makes generalizations about them, Deductive reasoning comes to conclusions based on previously known facts. The answer should be Deductive Reasoning.

Choose all the numbers that are perfect squares.

64
24
12
49
144
84
4

Answers

The answer is 64 which goes into evenly 8 times 8, 49 7 times 7, 4, 2 times 2, 144 12 times 12

4, 49, 64, and 144 are all perfect squares. Because if you think back to it 2^2 is 4, 3^2 is 9, 4^2 is 16, 5^2 is 25. 6^2 is 36, 7^2 is 49, 8^2 is 64, 9^2 is 81, 10^2 is 100. 11^2 is 121. 12^2 is 144 and so on. 12, 24, and 84 do not show up in those numbers, so they are not perfect squares.

This circle is centered at the point (4,5) and the length of its radius is 3. What is the equation of the circle

Answers

[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &4&5&3 \end{array} \\\\\\ (x-4)^2+(y-5)^2=3^2\implies (x-4)^2+(y-5)^2=9[/tex]

A segment has endpoints with coordinates - 3 and 4. What is the length of the segment?

Answers

Answer: 7 units

Step-by-step explanation: In this problem, the given numbers -3 and 4 represent the coordinates of the endpoints of a segment and we are asked to find the length of the segment.

To find the length of a segment, we take the greater endpoint coordinate minus the lesser endpoint coordinate.

In this case, the greater endpoint coordinate is 4 and the lesser endpoint coordinate is -3.

So, we have 4 - (-3) which can also be thought of as 4 + 3 which equals 7.

Therefore, the length of this segment is 7 units.

What is the answer of 6=1-2n+5

Answers

6 = 1 - 2n +5
5 = -2n +5
0 = -2n

n=0

IF you are solving for N, then I think this is the way to do it.

6=1-2n+5

combine light terms:
6=(1+5)-2n
6=-2n+6
now try to get N by itself so you subtract 6 on both side:

6=-2n+6
-6 -6
now you have 0=-2n or -2n=0
now divide both sides by -2
-2n/-2 = 0/-2

so it's a no solution. but if it doesn't give you that option, then n=0

The table below shows the average yearly balance in a savings account where interest is compounded annually. no money is deposited or withdrawn after the initial amount is deposited. which type of function best models the given data?
a. linear function with a negative rate of change
b. linear function with a positive rate of change
c. exponential decay function
d. exponential growth function

Answers

Final answer:

The given data represents the average yearly balance in a savings account where interest is compounded annually. The function that best models the data is an exponential growth function.

Explanation:

The given data represents the average yearly balance in a savings account where interest is compounded annually. Since the balance is increasing over time, the function that best models the data is an exponential growth function. Option d, exponential growth function, is the correct answer.

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How many solutions does the equation have?

2x + 3 = 4x + 2

A. no solutions

B. 1 solution

C. many solutions

Answers

2x + 3 = 4x + 2
3 - 2 = 4x - 2x
1 = 2x
x = 1/2

Its B 1 solution

the answer is B. 1 solution

Solution for 5y-4=9y+8 equation

Answers

5y-4=9y+8

5y=9y+8-4

5y-9y=8-4

-4y=4

y = -1

A rectangular box has a length of 7 ft a width of 3 ft and a height of 2ft what is the volume

Answers

42 because 7x3x2=42 i know im right im a

the answer is 42 beacuse all you do to solve these problems is 7x3x2 so WxFxH

Landscapers plan to spread a layer of stone on a path. The number ss of bags of stone needed varies directly with the depth dd (in inches) of the layer. They need 20 bags to spread a layer of stone that is 2 inches deep. How deep will the layer of stone be when they use 15 bags of stone?

Answers

2/20 = x/15

cross multiply

20x/30

x = 30/20 = 1.5

it will be 1.5 inches deep

2/20 = x/15

cross multiply

20x/30

x = 30/20 = 1.5

it will be 1.5 inches deep

PLEASE HELP ASAP!!!
Draw a Venn diagram to illustrate this conditional:
Cars are motor vehicles.

Answers

The answer is A because cars are motor vehicles

Answer:

The Venn diagram that illustrates the given conditional statement is:

Option: a

Step-by-step explanation:

Cars are motor vehicles.

This means that all the cars are motor vehicles but converse need not be true.

i.e. all the motor vehicles cant be cars.

i.e. Cars are contained in Motor Vehicles.

Hence, the correct Venn diagram is: Option: a

( Option: b represent the statement

Some cars are Motor vehicles and some motor vehicles are cars.

Option: c represent the statement

Motor vehicles are Cars.

Option: d represent the statement:

Some motor vehicles are cars and some cars are motor vehicles.)

2x+4=3y can someone solve it?

Answers

2x+4=3y

No specific directions were given here. I'll assume that you want to solve y.

Simply divide both sides by 3.

This will isolate y, which is what you want.

(2x + 4)/3 = y

Done!

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