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3 years ago

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which equation represents this sentence? one-half the sum of a number and four is three less than the quotient of five and the n

umber. 1/2n 4=5/n−3 1/2(n 4)=3−5/n 1/2(n 4)=5/n−3 1/2n 4=3−5/n

1 answer:

MariettaO [177]3 years ago

6 0

Let the number be n,
1/2 (n + 4) = 5/n - 3

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It has to be true because

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3 years ago

The scale in the drawing is 2 cm : 5 m. Select from the drop down the correct numbers into the boxes to give the length, width,

Gelneren [198K]

The length, width, and area will be 25m, 15m, and 375m².

<h3>How to calculate the area?</h3>

From the information given, the scale in the drawing is 2cm : 5m and the length and width are given as 10cm and 6cm respectively.

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2 years ago

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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
<span>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

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(c)

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

A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time

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

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

HELP! You might have to zoom in

xeze [42]

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3 years ago