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2 years ago

Write the prime factorization of 90. Use exponents where possible.

Mathematics

1 answer:

Gala2k [10]2 years ago

6 0

Answer: 3^2×5×2

Step-by-step explanation:

90=30×3

=10×3×3

=5×2×3×3

=5×2×3^2

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Evaluate the given integral by changing to polar coordinates. sin(x2 + y2) dA R , where R is the region in the first quadrant be

koban [17]

Set

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta$

The region $R$ is given in polar coordinates by the set

$R=\left\{(r,\theta)\mid2\le r\le3,0\le\theta\le\dfrac\pi2\right\}$

So we have

$\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_2^3r\sin(r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac\pi4(\cos4-\cos9)}$

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3 years ago

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Reika [66]

9514 1404 393

Answer:

f^-1(x) = (x +4)/3

Step-by-step explanation:

The inverse function is found by swapping x and y, then solving for y.

y = 3x -4 . . . . . function y = f(x)

x = 3y -4 . . . . . inverse relation

x +4 = 3y . . . . add 4

(x +4)/3 = y . . . divide by 3. This is the inverse function

f^-1(x) = (x +4)/3

6 0

3 years ago

PLEASE HELP DUE IN AN HOUR NO LINKS PLEASE.

Korolek [52]

Answer:

y = 3/2 when x = 15

Step-by-step explanation:

y = k / √1+x

2 = k / √1+8 = k/3

k = 6

y' = 6 / √1+15 = 6/4 = 3/2

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2 years ago

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Oliga [24]

Answer: X=1

Step-by-step explanation:

Please see picture for steps

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2 years ago

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vampirchik [111]

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2 years ago