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3 years ago

Find the value of x

Mathematics

1 answer:

marishachu [46]3 years ago

5 0

Answer:

x = 5

Step-by-step explanation:

6 - 8x = 6x - 8x - 24

(add the x's on each side)

6 - 8x = -2x - 24

(pass -2x on the other side (adding))

6 - 6x = -24

(pass the 6 to the other side (subtracting))

- 6x = - 30

(divide by -6 on both sides)

x = 5

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1 and one - twelfth
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Plug in 44
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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

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

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3 years ago

Sweater:regular price 50$ sale price ,42.50

Marina CMI [18]

The discount is $7.5 if the discount is what you are looking for.
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3 years ago

A coin will be tossed three times, and each toss will be recorded as heads (H) or tails (T). Give the sample space describing al

cricket20 [7]

Answer:

Sample space:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Third toss is heads:

{HHT, HTT, THT, TTT}

First toss is heads, second tails and third heads:

{HTH}

Explanation:

In order to find the sample space we need to write all the possible outcomes from tossing the coin three times.You can start by writting all the possible outcomes for the first toss being a head and finish with all the possible outcomes for the first toss being Tails. The number of elements in the sample space can be found by multiplying the possible outcomes of each toss together, so 2*2*2=8

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For the third toss being heads we will have one restriction this time. Which is that the third toss is Tails. You can take the elements from the sample space where the third element is a tails. In this case, the number of elements can be calculated by multiplying the possible outcomes for only the first two tosses 2*2=4

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For first toss is heads, second tails and third heads there is only one possible way for you to get this outcome so there is only one element to this set.

{HTH}

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2 years ago