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1 year ago

The radius of a quarter circle is 3 what is the quarter circle's perimeter?

Mathematics

1 answer:

slava [35]1 year ago

6 0

Answer:

21.42

Step-by-step explanation:

Imagine it as a full circle. 3 x 4 will give you the diameter of a full circle, which is 12. circumference = pi x diameter. so 12 pi (we can work that out later). now for the quater circle, divide it by 4, so 3 pi. Then you have the 2 extra edges which are both 2r, so 6 each. finally, you have 3 pi plus 12 which = 21.42

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A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

⇒ $2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}$

⇒ $\frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}$ ...as $\frac{d(500)}{dt}= 0$

⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

3 0

3 years ago

PLEASE HURRY IM TAKING A EXAM!!!!What is the equation of a line that is perpendicular to y=2x+4 and passes through the point (4,

Marat540 [252]

Answer:

what are the answers available or does it not show?

6 0

3 years ago

What is the equation of the horizontal line that passes through the point (-2, -1)

diamong [38]

Answer:

y= -1

Step-by-step explanation:

A horizontal line would mean that it has no slope, since the line is not decreasing or increasing. The horizontal line drawn through (0, -1) would pass through (-2, -1), since they share the same y coordinate.

5 0

3 years ago

A signalized intersection has a cycle length of 60 seconds and an effective red time of 25 seconds. The effective green time is

alexandr402 [8]

Answer:

effective green time = 35 seconds

Step-by-step explanation:

given data

cycle length = 60 seconds

effective red time = 25 seconds

solution

we get here effective green time that is express as

effective green time = cycle length - effective red time ...........................1

put here value and we will get

effective green time = 60 seconds - 25 seconds

effective green time = 35 seconds

3 0

3 years ago

if a trip between work and home takes 15 minutes each way, how much time will be spent in a 5-day work week traveling back and f

Trava [24]

Hello there! Since the person goes there and back, we need to multipy 15(2)=30. 30(5)=150; therefore, the person spends 150 minutes. I hope I helped!

4 0

3 years ago

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