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3 years ago

Instructions: Find the value of the trigonometric ratio. Make sure to

Mathematics

1 answer:

defon3 years ago

5 0

Answer:

4/3

Step-by-step explanation:

Tan Z

= 32/24

= 4/3

Answered by GAUTHMATH

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3 years ago

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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

The right triangle ABC shown below is inscribed inside a parabola. Point B is also the maximum point of the parabola (vertex) an

kherson [118]

H = -b / 2a = 2 : x coordinate of the vertex of the parabola k = -(2)2 + 4(2) + C = 4 + C : y coordinate of vertex x = (2 + √(4 + C)) , x = (2 - √(4 + C)) : the two x intercepts of the parabola. length of BA = k = 4 + C length of AC = 2 + √(4 + C) - 2 = √(4 + C) area = (1/2)BA * AC = (1/2) (4 + C) * √(4 + C) (1/2) (4 + C) * √(4 + C) = 32 : area is equal to 32 C = 12 : solve above for C.

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4 years ago