All categories

2 years ago

Chloe kicks a soccer ball across a field. The height of the ball above the ground is given by the equation

Mathematics

1 answer:

Reika [66]2 years ago

4 0

Answer:

It takes 3.5 seconds for the ball to hit the ground

Step-by-step explanation:

By finding the x intercepts you can determine when the ball hits the ground.

the second x intercept is (3.5,0), which means the ball hits the ground at 3.5 seconds

You might be interested in

Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

2 years ago

How can you express 5 1/3 + (-7 2/3) as the sum of its integer and fractional parts

Yuliya22 [10]

Answer:

-7/3

Step-by-step explanation:

-7 2/3=-23/3

5 1/3=16/3

-----------------

16/3+(-23/3)

16/3-23/3

-7/3

6 0

2 years ago

Help plz I WILL GIVE BRAINLIEST JUST PLZ HELP

-Dominant- [34]

Answer:

3x-4=107* why vertical angles

Step-by-step explanation:

3x-4=107

add 4 on both sides

3x=111*

x=37

6 0

2 years ago

Read 2 more answers

What is 0.326 in expanded form

12345 [234]

0.300 + .020 + 0.006 would be 0.326 in expanded form.

3 0

3 years ago

There are 57 students in the orchestra and twice that number in the band. There are 18 boys and 28 girls in the choir. If each s

Klio2033 [76]

There are 217 students total

7 0

3 years ago

Read 2 more answers