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Nutka1998 [239]
3 years ago
6

When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units

Mathematics
2 answers:
alexira [117]3 years ago
5 0

Answer:

r=1/π

Step-by-step explanation:

Area of the circle is defined as:

Area = πr²

Derivating both sides

\frac{dA}{dr}=2πr

\frac{dA}{dt}  =  \frac{dA}{dr} x \frac{dr}{dt}  =  2πr\frac{dr}{dt}

If area of an expanding circle is increasing twice as fast as its radius in linear units. then we have : \frac{dA}{dt}  =2\frac{dr}{dt}

Therefore,

2πr \frac{dr}{dt}  =  2  \frac{dr}{dt}

r=1/π

Ber [7]3 years ago
4 0

Answer:

r = 1/π

Step-by-step explanation:

Here we have

Area of a circle given as

Area = πr²

Where:

r = Radius of the circle

When the area of the circle is expanding twice as fast s the radius we have

\frac{dA}{dt} =2 \times  \frac{dr}{dt}

However,

\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt} and

\frac{dA}{dr} = \frac{d\pi r^2}{dr} = 2\pi r

Therefore, we have

\frac{dA}{dt} =2 \times  \frac{dr}{dt} = 2\pi r \times  \frac{dr}{dt}

Cancelling like terms

1= \pi r

Therefore, r = \frac{1}{\pi }.

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Dmitrij [34]

Answer:

Ok, the probability of winning is:

For the first draw, we have 13 diamonds in a 52 card deck, the probability of drawing a diamond is:

p1 = 13/52

for the second draw we have 12 diamonds and 51 cards in the deck, now the probability is:

p2 = 12/51

the total probability is equal to the product of the individual probabilities, this is:

P = p1*p2= (13/52)*(12/51) = 0.059

now, the expected value can be calculated as follows.

EV = (P1*X1 + P2*X2)

where P1 is the probabilty of event 1, and X1 is the event 1,

In this case X1 is the event of winning $29, then P1 = 0.059

X2 will be the event of loosing $4, so P2 = 1 - 0.059 = 0.941

Then the expected value for 1 round of the game is:

EV = (0.059*$29 - 0.941*$4) = -$2.05

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4 0
3 years ago
How do I solve this properly?
o-na [289]

Answer:

x \geq 4

Step-by-step explanation:

4x^2 - 64 \geq 0 ; move 64 over

4x^2 \geq 64 ; divide by 4

x^2 \geq 16 ; take square root of both sides

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6 0
3 years ago
Dan is 18 years old. In 6 years he will be 4/5 the age of his brother Nick. How old will
attashe74 [19]
4 times 6 is equal to 24 so I did the same to 5 ( because 4/5) and then I got 30 so.
In six years he will be 24 and his brother will be 30 but in 4 years his brother Nick will be 28.
3 0
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Y =a/x make x the subject​
aniked [119]

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Step-by-step explanation:

6 0
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Jill arranges quarters in stacks of increasing powers of 2, starting with the zeroth power (20). If she ends up with six stacks,
Ratling [72]
Stack 1 : 2^0 = 1 quarter.
Stack 2 : 2^1 = 2 quarters.
Stack 3: 2^2 = 4 quarters.
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Stack 6: 2^5 = 32 quarters.
1 + 2 + 4 + 8 + 16 + 32 = 63
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8 0
3 years ago
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