Can you guys hurry pls I only have 20 more minutes

<img src="https://tex.z-dn.net/?f=If%20w%3D2x%2C%20then%20%5Cint%5Climits%5E2_0%20%7Bf%282x%29%7D%20%5C%2C%20dx%20%3D" id="TexFo

elena-14-01-66 [18.8K]

First, you should solve for $f(2x)$ , which equals $2*(2x)=4x$ . Now, solve the integral of $f(2x)$ = $2*(2x)=4x$ , to get that $\int\ {(f(2x)=4x)} \, dx= 2x^2$ . You can check this by taking the integral of what you got. Now by the Fundamental Theorem $\int\limits^2_0 {4x} \, dx=[2x^2] ^{2}_{0}=2(2)^{2}-2(0)^2=8$ .

This should be the answer to your question, if I understood what you were asking correctly.

8 0

3 years ago

Towns X, Y, and Z are on the same straight road. Town Y is between Town X and Town Z. Town X is 57 miles from Town Z, and Town Y

Ber [7]

29 miles
because town y is between town x and town z so you can take the distance between town x and town z and subtract the distance from town y to town z

3 0

4 years ago

Ellen makes and sells bookmarks. She graphs the number of bookmarks sold compared to the total money earned. What is the rate of

VashaNatasha [74]

IfIf she graphs the number of bookmarks sold compared to the total money earned. The rate of change for the function graphed to the left is: 5/2.

<h3>Rate of change</h3>

Based on the graph the coordinate are:

(4,0), (8,10), (12,20)

Using slope formula to find the rate of change Slope=y2-y1/x2-x1

Hence,

(x1-y1)=(4,0) & (x2 -y2)= (8,10)

Let plug in the formula

Slope=10-0/8-4

Slope=10/4

Slope=5/2

Therefore If she graphs the number of bookmarks sold compared to the total money earned. The rate of change for the function graphed to the left is: 5/2.

Learn more about rate of change here:brainly.com/question/9869638

#SPJ1

4 0

1 year ago

Approximate area under the curve f(x) =-x^2+2x+4 from x=0 to x=3 by using summation notation with six rectangles and use the the

bekas [8.4K]

Answer:

Summation notation:

$\frac{1}{2}\sum_{k=1}^6f((.5k))$

or after using your function part:

$\frac{1}{2}\sum_{k=1}^6(-(.5k)^2+2(.5k)+4)$

After evaluating you get 11.125 square units.

Step-by-step explanation:

The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.

The distance between x=0 and x=3 is (3-0)=3.

We want to divide that length of 3 units by 6 which gives a length of a half per each base length.

We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).

The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).

The next will be at x=2.5-.5=2, and the third rectangle will have a height of f(2).

The fourth rectangle will have a height of f(2-.5)=f(1.5).

The fifth one will have a height of f(1.5-.5)=f(1).

The last one because it is the sixth one will have a height of f(1-.5)=f(.5).

So to find the area of a rectangle you do base*time.

So we just need to evaluate:

$\frac{1}{2}f(3)+\frac{1}{2}f(2.5)+\frac{1}{2}f(2)+\frac{1}{2}f(1.5)+\frac{1}{2}f(1)+\frac{1}{2}f(.5)$

or by factoring out the 1/2 part:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

To find f(3) replace x in -x^2+2x+4 with 3:

-3^2+2(3)+4

-9+6+4

1

To find f(2.5) replace x in -x^2+2x+4 with 2.5:

-2.5^2+2(2.5)+4

-6.25+5+4

2.75

To find f(2) replace x in -x^2+2x+4 with 2:

-2^2+2(2)+4

-4+4+4

4

To find (1.5) replace x in -x^2+2x+4 with 1.5:

-1.5^2+2(1.5)+4

-2.25+3+4

4.75

To find f(1) replace x in -x^2+2x+4 with 1:

-1^2+2(1)+4

-1+2+4

5

To find f(.5) replace x in -x^2+2x+4 with .5:

-.5^2+2(.5)+4

-.25+1+4

4.75

Now let's add those heights. After we obtain this sum we multiply by 1/2 and we have our approximate area:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

$\frac{1}{2}(1+2.75+4+4.75+5+4.75)$

$\frac{1}{2}(22.25)$

$11.125$

Okay now if you wanted the summation notation for:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

is it

$\frac{1}{2}\sum_{k=1}^{6}(f(.5+.5(k-1)))$

or after simplifying a bit:

$\frac{1}{2}\sum_{k=1}^6 f((.5+.5k-.5))$

$\frac{1}{2}\sum_{k=1}^6f((.5k))$

If you are wondering how I obtain the .5+.5(k-1):

I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)

6 0

3 years ago

Alberta Doan worked 6 hours at time-and-a-half pay and 3 ¼ hours at double-time pay. Her regular pay rate was $9.72 an hour. Wha

natka813 [3]

Answer:

Alberta's total overtime pay of the week was $ 145.80.

Step-by-step explanation:

Given that Alberta worked 6 hours at time-and-a-half pay, and 3 hours at double-time pay, and that the value of her regular work hour is $ 9.72, to determine the value of the pay of his overtime, the following equation must be performed:

6x1.5x9.72 + 3x2x9.72 = X

9x9.72 + 6x9.72 = X

87.48 + 58.32 = X

145.8 = X

Therefore, Alberta's total overtime pay of the week was $ 145.80.

3 0

3 years ago