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kobusy [5.1K]
3 years ago
7

What is (-2,2) multiplied by 2.5 and (2,1) multiplied by 2.5

Mathematics
1 answer:
Anestetic [448]3 years ago
5 0
(-2, 2) multiplied by 2.5 is given by 2.5(-2, 2) = (-5, 5)

while (2, 1) multiplied by 2.5 is given by 2.5(2, 1) = (5, 2.5)
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Answer:

It is A

Step-by-step explanation:

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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
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(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

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(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 \\ &#10;y = (3 + 2\cos\theta) \sin \theta

Differentiating with respect to theta

\begin{aligned}&#10;\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\&#10;&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\&#10;\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}&#10;&= 2/3&#10;\end{aligned}

2/3 is the slope

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"</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
By selling a cow for Rs 144, there is a profit of the same percentage as its cost price. Find the cost price.​
hjlf

Answer:

Step-by-step explanation:

<h2><u>☼︎</u><u>Answer:</u></h2>

The cost price of cow = Rs.80

Explanation:

<h2><u>☼︎</u><u>Given :-</u></h2>

  • By selling a cow for Rs 144, there is a profit of the same percentage as its cost price.
<h2><u>☼︎</u><u>T</u><u>o Find</u><u>:</u><u>-</u></h2>

  • The cost price.
<h2 /><h2 /><h2><u>☼︎</u><u>L</u><u>e</u><u>t</u><u>:</u><u>-</u></h2>

  • The cost price of cow = Rs.x

<h2><u>☼︎</u><u>Solution :-</u></h2>

\sf x + x \: of \: x\%= 144 \\ \\ \sf \implies x + \frac{x \times x}{100} = 144 \\ \\ \sf \implies {x}^{2} + 100x - 14400 = 0 \\ \\ \sf \implies x(x - 80) + 180(x - 80) = 0 \\ \\ \sf \implies x + 180 = 0 \\ \\ \sf \implies x = - 180 \\ \\ \sf \therefore \:  {\boxed{ \sf \pink{x = 80}}}

<h2><u>Hence: </u></h2>

The cost price of cow =<u>R</u><u>s</u><u>8</u><u>0</u>

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4x, 8, 20

X/6, 1/3, 5/6

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