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iogann1982 [59]
3 years ago
7

A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per hour and the sides of the square a

re decreasing at a rate of 5 meters per hour. When the radius is 4 meters, and the sides are 23 meters, then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is square meters per hour.
Mathematics
1 answer:
slavikrds [6]3 years ago
3 0

Answer:

<h2>305.408m^2/hour</h2>

Step-by-step explanation:

Let r = radius of circle

     s = length of a side of the square

 

dr/dt = -3m/hour

  ds/dt = 5m/hour

we know that

area of square= s^2

area of circle=πr^2

Let A be the area of outside

A = (area of square) - (area of circle)

          = s^2 - πr^2

dA/dt=?

when r = 4 and s = 23

 substituting we have

dA/dt = 2s(ds/dt) - 2πr(dr/dt)

             =2(23)(5) - 2π(4)(-3)

            = (230 + 24π) m^2/hour

            = (230 + 75.408) m^2/hour

            = 305.408m^2/hour

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Answer:

C.  In the given expression -9 + p < 15 , the value of p <  24.

Step-by-step explanation:

Here, the given expression is :

-9 + p < 15

Now, solving for the value of p.

If equals are added to both sides of inequality, the inequality remains unchanged.

Now, -9 + p < 15

⇒  -9 + p  + 9 < 15  + 9                                  (adding +9 on both sides)

or,  p <  24

Hence, in the given expression -9 + p < 15  the value of  p <  24.

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3 years ago
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3 years ago
You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the larg
katovenus [111]
Problema Solution

You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?

Answer provided by our tutors

Make a drawing and denote:


x = half of the length of the enclosure


2x = the length of the enclosure


y = the width of the enclosure


P = 800 ft the perimeter


The perimeter of the two enclosures can be expressed P = 4x + 2y thus


4x + 3y = 800


Solving for y:

........

click here to see all the equation solution steps

........

y = 800/3 - 4x/3


The area of the two enclosure is A = 2xy.


Substituting y = 800/3 - 4x/3 in A = 2xy we get


A = 2x(800/3 - 4x/3)


A =1600x/3 - 8x^2/3


We need to find the x for which the parabolic function A = (- 8/3)x^2 + (1600/3)x has maximum: 


x max = -b/2a, a = (-8/3), b = 1600/3


x max = (-1600/3)/(2*(-8/3))


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3 years ago
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Answer:

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Step-by-step explanation:

The binomial probability parameters given are;

The probability that the pitcher throwing a strike, p = 0.675

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The binomial probability is given as follows;

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Therefore, the probability that the pitcher throws 19 strikes out of 29 pitches is found as follows;

The probability that exactly 19 of them are strikes is given as follows;

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