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3 years ago

Find the missing side Lengths.

Mathematics

1 answer:

Ludmilka [50]3 years ago

4 0

Answer:

5.23606798

Step-by-step explanation:

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If 2% of a number equals 8, find 10% of that number.

torisob [31]

Answer:

Step-by-step explanation:

2% of 400 is 8

400 x 0.02 = 8

10% of 400 is 40

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2 years ago

Javier used the expression below to represent his score in a game of mini-golf

Paul [167]

Sorry but u should write ur expression so i can solve it....

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3 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

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

5 0

3 years ago

How do you solve the problem 6-3x=-2x

jolli1 [7]

6-3x=2x

In order to solve these, you first want to get all the variables on one side. So, you add 3x to both sides.

6=x

The answer is x=6

Hope this helps!

3 0

3 years ago

Read 2 more answers

The floor area of a square room is 225 sq. ft. What is the measure of each side of the room in feet?

I am Lyosha [343]

Answer:

56.25 feet

Step-by-step explanation:

225 divided by 4 is 65.25

8 0

3 years ago

Find the missing side Lengths.​

Find the missing side Lengths.