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Yuki888 [10]
2 years ago
5

What is the length of AB??

Mathematics
1 answer:
trapecia [35]2 years ago
7 0

Answer:

i  took my ruler and i would say that AB is about an inch long

Step-by-step explanation:

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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)
5 0
3 years ago
What is the product in simplest form x^2+9x+18/x+2 times x^2-3x-10/x^2+2x-24
german
\dfrac{x^2+9x+18}{x+2}\cdot\dfrac{x^2-3x-10}{x^2+2x-24}=\dfrac{x^2+6x+3x+18}{x+2}\cdot\dfrac{x^2-5x+2x-10}{x^2+6x-4x-24}\\\\=\dfrac{x(x+6)+3(x+6)}{x+2}\cdot\dfrac{x(x-5)+2(x-5)}{x(x+6)-4(x+6)}

=\dfrac{(x+6)(x+3)}{x+2}\cdot\dfrac{(x-5)(x+2)}{(x+6)(x-4)}=\dfrac{(x+3)(x-5)}{x-4}\\\\=\dfrac{x^2-5x+3x-15}{x-4}=\dfrac{x^2-2x-15}{x-4}
5 0
3 years ago
Read 2 more answers
Jake is arranging a poetry reading. There will be 6 poets. The reading should run 90 minutes. Each poet will read for the same l
valentinak56 [21]

Answer:

Each poet reads for exactly 15 minutes.

Step-by-step explanation:

If it should run for 90 minutes, and there is 6 poets, therefore I'm pretty sure you divide 90 by 6, which is 15.

5 0
3 years ago
Read 2 more answers
What is the value of |-29|?
ki77a [65]
<span><span>Number                       27283031
</span><span>Absolute Value            272830<span>31</span></span></span>
4 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=56x%5E%7B2%7D%20%5Csqrt%7Bx%7D%2077" id="TexFormula1" title="56x^{2} \sqrt{x} 77" alt="56x^{2}
ELEN [110]

Answer:

4312  { x }^{ \frac{5}{2} }

Step-by-step explanation:

56*77=4312

x ^{2}  \times   \sqrt{x}  = x ^{2}  \times   {x}^{ \frac{1}{2} }  =  {x}^{ \frac{5}{2} }

3 0
3 years ago
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