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2 years ago

If A varies direct as a square of R. Find the % increase in A if R is increase by 20%.

Mathematics

1 answer:

katen-ka-za [31]2 years ago

4 0

Answer:

20%

Step-by-step explanation:

A=R^2

120/100

=1.2

1.2R= new value of R

original of R=R

A^1/2=R

change/origionalx100%

(1.2A^1/2-A^1/2)

-------------------- x 100%

A^1/2

A^1/2 (1.2-1)

--------------- x100%

A^1/2

0.2

---- x100

0.2x100

=20%

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anygoal [31]

Answer:

Step-by-step explanation:

1) lets get rid of the parentheses, we dont really need them:

−22 −4 + 8+ 52 + 2 − 25

Following order of operations we need to work from left to right

-22-4=-26

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34+2=36

36-25=11

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3 years ago

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3 years ago

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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

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
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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

Sep 08, 2:59:48 PM

Anuta_ua [19.1K]

Answer:

5c + 1.3d - 6.3

Step-by-step explanation:

$5c-(-1.3d-6.3)\\\\\boxed{5c+1.3d-6.3}\\\\\left \{ {{-1*-1.3d=1.3d} \atop {-1*6.3=-6.3}} \right.$

Hope this helps.

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2 years ago

The theoretical probability of spinning a 1 is

balandron [24]

Answer:

Step-by-step explanation:

That depends on how many sections there are. If there are 2 sections, then it will be a 50/50 chance it lands on 1 if there are 3 sections then it would be 1/3 or for 4, 1/4, and for 5, 1/5, etc.

6 0

2 years ago

If A varies direct as a square of R. Find the % increase in A if R is increase by 20%.​

If A varies direct as a square of R. Find the % increase in A if R is increase by 20%.