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3 years ago

11

Consider the function f ( x ) = 5 x 3 − 3 x on the interval [ − 2 , 2 ] . Find the average or mean slope of the function on this

interval.

1 answer:

Slav-nsk [51]3 years ago

7 0

Answer:

V

Step-by-step explanation:

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Alenkinab [10]

Answer:

Total change in Sales of Bushels =116

Step-by-step explanation:

Total Bushels of Wheat= 220

Average Sale= per day

Average Sale per week =

Total change in Sales of Bushels = Total Bushels of Wheat - Average Sales per week

Total change in Sales of Bushels=

Step-by-step explanation:

3 0

3 years ago

Solution for dy/dx+xsin 2 y=x^3 cos^2y

vichka [17]

Rearrange the ODE as

$\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y$
$\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3$

Take $u=\tan y$ , so that $\dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}$ .

Supposing that $|y|$ , we have $\tan^{-1}u=y$ , from which it follows that

$\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}$
$\sec^2y=1+\tan^2y=1+u^2$

So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

which is linear in $u$ . Multiplying both sides by $e^{x^2}$ , we have

$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
$\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
$e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx$

Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

$\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt$

Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
$\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)$

You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$

5 0

3 years ago

In a school with 615 students, 18 classes are formed. If the classes are equal in size, and far as possible, how many classes ar

german

The answer is c or 2!

6 0

3 years ago

Read 2 more answers

Given the two points (-1,-4) and (2,5): a. Find the slope between these two points

Dvinal [7]

Easy, using $\frac{y1-y2}{x1-x2}$ to find the intercept:

$\frac{-4-5}{-1-2}$ =

$\frac{-9}{-3}$ =3

This is your slope. m=3

To find y=mx+b form

-4=3(-1)+b

-4=-3+b

-1=b

y=3x-1 in y=mx+b form

4 0

3 years ago

I’ll give brainliest!!!

Maslowich

14a. =

15b. 2/3 is less than 0.667

16c. 3 7/8 is greater than 3.375

17d. 3/8 is less than 1/2

6 0

2 years ago