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2 years ago

what is the function rule for the transformed with vertical stretch by a factor of 2 and translated down 6

1 answer:

5 0

Answer: Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 6, and the equation of a function stretched horizontally by a factor of 2 and then shifted 6 units left is y = f ( (x - 6)) = f ( x - ). Example: f (x) = 2x2.

Step-by-step explanation:

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Integrate the following w.r.t x 1) 2x^2/3. <br>2) (5-x)^23<br>

Kryger [21]

Answer:

A) $\int\frac{2x^2}{3}dx=\frac{2x^3}{9}+C$

B) $\int(5-x)^{23}dx=-\frac{(5-x)^{24}}{24}+C$

Step-by-step explanation:

So we have the integral:

$\int\frac{2x^2}{3}dx$

First, remove the constant multiple:

$=\frac{2}{3}\int x^2\dx$

Use the power rule, where:

$\int x^ndx=\frac{x^{n+1}}{x+1}$

Therefore:

$\frac{2}{3}\int x^2\dx\\=\frac{2}{3}(\frac{x^{2+1}}{2+1})$

Simplify:

$=\frac{2}{3}(\frac{x^{3}}{3})$

And multiply:

$=\frac{2x^3}{9}$

And, finally, plus C:

$=\frac{2x^3}{9}+C$

We have the integral:

$\int(5-x)^{23}dx$

To solve, we can use u-substitute.

Let u equal 5-x. Then:

$u=5-x\\du=-1dx$

So:

$\int(5-x)^{23}dx\\=\int-u^{23}du$

Move the negative outside:

$=-\int u^{23}du$

Power rule:

$=-(\frac{u^{23+1}}{23+1})$

Add:

$=-(\frac{u^{24}}{24})$

Substitute back 5-x:

$=-(\frac{(5-x)^{24}}{24})$

Constant of integration:

$=-\frac{(5-x)^{24}}{24}+C$

And we're done!

8 0

3 years ago

Jamal walked 34 mile yesterday morning and 18 mile yesterday afternoon. What was the total distance walked by Jamal?

grin007 [14]

The answer is 52 miles

8 0

2 years ago

Read 2 more answers

The men's world record for swimming 1500.0 m in a long course pool (as of 2007) is 14 min 34.56s. At this rate, how many seconds

Tcecarenko [31]

We must first find the rate taken to cover 1500.0 m within 14 min and 34.56 sec. We can first convert the time into seconds and hence, we have time = 14(60) + 34.56 = 874.56 seconds. Recall that rate = distance/ time. And using the given for the men's world record, we have rate = 1500.0 m / 874.56s = 1.715 m/s Now, to find the time taken to cover 0.350 miles, we can first convert the distance to meters then use the equation given below. time = distance/rate where distance is equal to 0.350(1609) = 563.15 m. Hence, we have time = 563.15 / 1.715 = 328.37 s From this, we can see that it will takes 328.37 seconds to cover 0.350 miles. <span>Answer: 328.37 seconds</span>

5 0

2 years ago

8 yards converted into feet?

Ksivusya [100]

Answer:

24 feet

Step-by-step explanation:

a yard is 3 feet

8 yards is

8 × 3

24 feet

5 0

2 years ago

What is the volume of this solid?

Alex787 [66]

Answer:

A- 276

Step-by-step explanation:

Rectangular prism= a b c

=6x6x6

=216

Pyramid= 1/3 bh

=1/3 36x5

=60

add them

7 0

3 years ago