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2 years ago

Armando found the volume of the figure below by using the steps shown.

Mathematics

2 answers:

Alexus [3.1K]2 years ago

7 0

Armando use the wrong demensions for the triangular prism?Answer:

Step-by-step explanation:

Gnesinka [82]2 years ago

5 0

Answer:

Armando use the wrong demensions for the triangular prism?

Step-by-step explanation:

The height is actually 8 inches.

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B is 50 and A is all of them?

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3 years ago

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Your answer is, Negative Correlation

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2 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

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3 years ago

Use the Pythagorean Theorem to find the value of x

sammy [17]

Answer:

Yes

Step-by-step explanation:

It is A

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2 years ago

If you can solve 20 multiplication facts in one minute how long will it take to solve 50 facts

mezya [45]

Answer:

150s or 2 min and 30 s

Step-by-step explanation:

20 facts = 1 min

10 facts = 30s

50 facts = ? min

50 / 10 = 5

30 * 5 = 150s

150s = 2 min and 30 s

5 0

3 years ago

Read 2 more answers