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3 years ago

What’s the correct answer for this question?

Mathematics

1 answer:

Maksim231197 [3]3 years ago

8 0

Answer

C. 14

Explanation

The area of triangle = 1/2(base)(height)

The height:

the height is the distance from point (2,-3) perpendicular to the base intersecting it at point (2,1)

the height is then the distance between the 2 points = 4

The base:

the base is the distance between points (7,1)and (0,1) = 7

The area:

the area = 1/2 x 4 x 7 = 28/2 = 14 units²

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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

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

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4 years ago

Solve The Following ( Solving equations)

kondaur [170]

1. 15/2 | 2. 1 … if you need examples just reply here

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2 years ago

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I dont know how to do graphing pls help

yarga [219]

Answer:

Solution: (-1, -1)

Step-by-step explanation:

y=4x+2

y=-4/3x-2

Solve by graphing.

First, you need to plot the y-intercept.

y=4x+2

2 will be your y-intercept.

Next, you plot your slope.

y=4x+2

From your y-intercept, you will go up 4 and right one space, if you run out of space go down 4 and left 1.

Now repeat the same steps for the next one.

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Plot your y-intercept.

y=-4/3x-2

because your slope is negative you will go down 4 and right 3, if you run out of room go up 4 and left 3.

Then draw connecting lines and wherever the lines intersect, that's going to be your solution. In this case, the solution is (-1, -1).

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3 years ago

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Consider the equation 30÷x=6.

8090 [49]

Part A : 30 - x - x - x - x - x - x = 0

^ since 30 divided by 5 is 6, that answer is the same as doing 5 + 5 + 5 + 5 + 5 + 5

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3 years ago

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The Burger Palace serves 17,822 items in 7 days. 12,460 of those items are burgers and the rest are hot dogs. If they sell the s

Brums [2.3K]

answer:

a. 16.

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picking out the common factors:

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3 years ago