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3 years ago

15

Which image shows the triangle's incenter? Appreciate the help!

1 answer:

Bogdan [553]3 years ago

5 0

It's the last image. The one with D

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2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One

Stells [14]

$y'=(t+y)^2-1$

Substitute $u=t+y$ , so that $u'=y'$ , and

$u'=u^2-1$

which is separable as

$\dfrac{u'}{u^2-1}=1$

Integrate both sides with respect to $t$ . For the integral on the left, first split into partial fractions:

$\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1$

$\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt$

$\dfrac12(\ln|u-1|-\ln|u+1|)=t+C$

Solve for $u$ :

$\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C$

$\ln\left|1-\dfrac2{u+1}\right|=2t+C$

$1-\dfrac2{u+1}=e^{2t+C}=Ce^{2t}$

$\dfrac2{u+1}=1-Ce^{2t}$

$\dfrac{u+1}2=\dfrac1{1-Ce^{2t}}$

$u=\dfrac2{1-Ce^{2t}}-1$

Replace $u$ and solve for $y$ :

$t+y=\dfrac2{1-Ce^{2t}}-1$

$y=\dfrac2{1-Ce^{2t}}-1-t$

Now use the given initial condition to solve for $C$ :

$y(3)=4\implies4=\dfrac2{1-Ce^6}-1-3\implies C=\dfrac3{4e^6}$

so that the particular solution is

$y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}$

3 0

3 years ago

What is the volume of a right trianular prism with the dimesions of 15 11 17

Harlamova29_29 [7]

Answer:

1402.5 Cubic Units

Step-by-step explanation:

Volume of a Triangular Prism: V = $\frac{1}{2}bhl$

b - base

h - height

l - length

15 is the height, 17 is the length, and 11 is the width (assuming which is the base).

$V=0.5 * (11 * 15 * 17) \\V=0.5*2085\\V=1402.5$

The volume of the prism should be 1402.5 cubic units.

3 0

3 years ago

Convert the following equation into standard form<br><img src="https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B4x%7D%7B5%7D%20%20

musickatia [10]

(y=4x/5-9/5) 5
5y=4x-9
(-4x+5y=-9) -1
4x+5y=9

Hope this helped you!! :)

6 0

3 years ago

Suppose the letter H is drawn on a coordinate axis and is rotated about a fixed point. Which statement is NOT true regarding the

stiks02 [169]

The answer for the first question: C The rotated image may be larger than the original image.

7 0

4 years ago

Kerry read 2/3 of her chemistry book containing 420 pages. David read 3/4 of the same. Who read more pages and by how many pages

Alika [10]

Answer:

Kerry = 2/3 * 420 = 280

David = 3/4 * 420 = 315

David read more pages compared to Kerry.

3 0

3 years ago