Which of the expressions are equivalent to the one below? Check all that

Mathematics

1 answer:

lutik1710 [3]2 years ago

6 0

Answer:

Only B,

Step-by-step explanation:

Because it is all addition it does not mater what order they are in,..

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A sequence is defined recursively using the formula f(n + 1) = –0.5 f(n) . If the first term of the sequence is 120, what is f(5

Svetllana [295]

7.5
f(1) = 120
f(2) = -60
f(3) = 30
f(4) = -15
f(5) = 7.5

6 0

3 years ago

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Solve for 'm': m - 7 = -13 + m

lesya [120]

Answer:

m - 7 = -13 + m

Step-by-step explanation:

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3 years ago

Choose the best coordinate system to find the volume of the portion of the solid sphere rho <_4 that lies between the cones φ

MrRissso [65]

Answer:

So, the volume is:

$\boxed{V=\frac{128\sqrt{2}\pi}{3}}$

Step-by-step explanation:

We get the limits of integration:

$R=\left\lbrace(\rho, \varphi, \theta):\, 0\leq \rho \leq 4,\, \frac{\pi}{4}\leq \varphi\leq \frac{3\pi}{4},\, 0\leq \theta \leq 2\pi\right\rbrace$

We use the spherical coordinates and we calculate a triple integral:

$V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}\int_0^4 \rho^2 \sin \varphi \, d\rho\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \left[\frac{\rho^3}{3}\right]_0^4\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \cdot \frac{64}{3} \, d\varphi\, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} [-\cos \varphi]_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} \sqrt{2} \, d\theta\\\\$