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Mathematics

1 answer:

Roman55 [17]3 years ago

7 0

Answer:

Step-by-step explanation:

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Step-by-step explanation:

Just plug each number in calculator and do multiply buy 3 and divide by 4 then add them together

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3 years ago

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2 years ago

6. Jason's class projects are graded on a scale of 250 points.

Nady [450]

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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

His composite shape is a rectangle with a semicircle attached on one end. The diameter of the semicircle is 6 feet.

Vera_Pavlovna [14]

We can solve by figuring the area of the rectangle then add it to the area of the semicircle.

Area of the rectangle: length · width = 6 · 10 = 60 ft²

Area of the semicircle: (πd²)/8 = (3.14 · 6²)/8 = (3.14 · 36)/8 = 14.13 ft²

Total area of the figure: 60 + 14.13 = 74.13 ft² ≈ 74 ft²

4 0

3 years ago

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Help!! I'll give brainlist...​

Help!! I'll give brainlist...