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FromTheMoon [43]

3 years ago

12

Me.Pete is building a rectangular fence around his house.The fence will be 32 feet long and 29 feet wide.What will be the perime

ter of the fence?

1 answer:

Bad White [126]3 years ago

3 0

Answer:

122

Step-by-step explanation:

32+32+29+29=122

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Find three consecutive integers whose sum is 51.

Julli [10]

Answer:

16,17,18

your welcome

7 0

3 years ago

You can spend at most $60 on beads. A bag containing red beads costs $2 per bag. A bag containing blue beads costs $3 per bag. Y

nexus9112 [7]

For this case, the first thing we must do is define variables.
We have then:
x: number of blue beads
y: number of red beads
We now write the inequations system:
$3x + 2y \leq 60

x\ \textgreater \ y$
Answer:
a system of linear inequations that represents the situation is:
$3x + 2y \leq 60 x\ \textgreater \ y$

8 0

3 years ago

Read 2 more answers

Evaluate g(-4) when g(b)<br> =<br> - 4(12.5b - 2)<br><br> Can someone help please?

Stolb23 [73]

The answer to your problem is 50b+8

3 0

3 years ago

Can you guys help with me

Anika [276]

Answer:

x=8

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

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
<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

____________

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

5 0

3 years ago