Ap calculus help please

Mathematics

1 answer:

vaieri [72.5K]3 years ago

6 0

9514 1404 393

Answer:

4 in

Step-by-step explanation:

The distance in inches can be found by integrating the velocity in inches per second.

$\displaystyle\int_0^1{(4t^3+3t^2+2t+1)\,dt}=\left.t^4+t^3+t^2+t\right|_0^1=4-0=\boxed{4}$

This integral is designed to be easy enough to do <em>without a calculator</em>. A calculator can do integrals like this pretty easily.

You might be interested in

What is the equation of a line passing through the points (-3,<br> -2) and (2, 0)?

Lostsunrise [7]

Answer:

$y=0.400x+-0.800$

Step-by-step explanation:

Given the following question:

point A = (-3, -2)
point B = (2, 0)

To write the equation of the line that passes through two points we have to write the points in slope intercept form.

Formula for slope intercept:

$y=mx+b$

M is equal to the slope of the two points, so first we need to fine the slope of the two points.

$(-3,-2)=(x1,y1)$
$(2,0)=(x2,y2)$

$m=\frac{y2-y1}{x2-x1}$
$m=\frac{0--2}{2--3} =\frac{2}{5}$
$m=\frac{2}{5} =0.400$

$y=mx+b$
$y=-2$
$m=0.400$
$x=-3$
$-2=0.400(-3)+b$
$0.400\times-3=-1.20$
$-2+1.2=-0.800$
$b=-0.800$

$y=0.400x+-0.800$

Hope this helps.