Determine the number of solutions to each system of equations

Mathematics

2 answers:

kow [346]3 years ago

4 0

Just switch the gray ones

alekssr [168]3 years ago

3 0

Just switch the grey ones

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Sin(x2 y2 da r , where r is the region in the first quadrant between the circles with center the origin and radii 1 and 5

Rudik [331]

I assume there's a plus sign missing above...

Convert to polar coordinates, using

$\begin{cases}x(r,\theta)=r\cos\theta\\y(r,\theta)=r\sin\theta\end{cases}$

Then the Jacobian is

$\dfrac{\partial(x,y)}{\partial(r,\theta)}=\begin{vmatrix}x_r&y_r\\x_\theta&y_\theta\end{vmatrix}=\begin{vmatrix}\cos\theta&\sin\theta\\r\sin\theta&-r\cos\theta\end{vmatrix}=-r$

Then

$\mathrm dA=\mathrm dx\,\mathrm dy=|-r|\,\mathrm dr\,\mathrm d\theta=r\,\mathrm dr\,\mathrm d\theta$

so the integral can be written as

$\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^5r\sin(r^2)\,\mathrm dr\,\mathrm d\theta$

Let $s=r^2$ , so that $\dfrac{\mathrm ds}2=r\,\mathrm dr$ .

$\displaystyle\frac12\int_0^{\pi/2}\int_1^{25}\sin s\,\mathrm ds\,\mathrm d\theta=-\frac12(\cos25-\cos1)\int_0^{\pi/2}\mathrm d\theta=\frac\pi4(\cos1-\cos25)$

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3 years ago

Simplify the following surds 45 <------ the 45 is a surd

Anika [276]

I think the answer is 3 route 5
First find a perfect square that goes into 45 in this case 9
Then as it's 9x5 simplify the nine to 3
Hope this helps

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3 years ago

What method can be used to prove the triangles are congruent ?

RUDIKE [14]

C is the answer to the problem

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3 years ago

Washington Corporation issued 4,000 shares of its $20 par value common stock for $23 per share. The entry to record the issuance

charle [14.2K]

Ok so you sold 4,000 stock at $3 above par value
Cash=92,000 (4,000x23)
commonstock issuance=80000 (4,000x20)
Additional paid in capital-common stock (or commonstock-apic)=12,000 (3x4000 or 92,000-80,000)
Debit Cash 92,000
Credit Commonstock Issuance 80,000
Credit Apic-Commonstock 12,000

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3 years ago

Help me please i need to do 3 months of hw in 2 hours help me please

Scrat [10]

3 months of homework, w t h have u been doinggg

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3 years ago

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