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Tpy6a [65]
3 years ago
12

The radius of the circle is increasing at a rate of 2 meters per minute and the sides of the square are increasing at a rate of

1 meter per minute. When the radius is 6 meters, and the sides are 24 meters, then how fast is the AREA outside the circle but inside the square changing?
Mathematics
1 answer:
Lunna [17]3 years ago
6 0

Answer:

Change in area=24\pi-48

Step-by-step explanation:

Let s will be the side of square and r will be the radius of circle.

Then two given conditions are

1)dr/dt=2 m/s

2)ds/dt=1 m/s

Area enclosed=(Area of square)-(Area of circle)

Area of square=s^{2}

Area of circle=\pi r^{2}

Area enclosed=(\pi  r^{2})-s^{2}

dA/dt=2\pir(dr/dt)-2s(ds/dt)

At s=24,and r=6

dA/dt=2(\pi)(6)(2)-2(24)(1)

Change in area=24\pi-48

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Simplify:

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Subtract 3.65X from each side:

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ludmilkaskok [199]

Answer:

x = 3/4

Step-by-step explanation:

Step 1: Write equation

5x - 2(x + 1) = 1/4

Step 2: Solve for <em>x</em>

  1. <u>Distribute -2:</u> 5x - 2x - 2 = 1/4
  2. <u>Combine like terms:</u> 3x - 2 = 1/4
  3. <u>Add 2 to both sides:</u> 3x = 9/4
  4. <u>Divide both sides by 3:</u> x = 3/4

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

5(3/4) - 2(3/4 + 1) = 1/4

15/4 - 2(7/4) = 1/4

15/4 - 14/4 = 1/4

1/4 = 1/4

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Answer:

The graph i the attached figure

Step-by-step explanation:

we have

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The solution of the inequality A is the shaded area above the dotted line y=2x-5

The slope of the dotted line is positive

The x- intercept of the dotted line is the point (2.5,0)

The y- intercept of the dotted line is the point (0,-5)

y < -3x -----> inequality B

The solution of the inequality B is the shaded area below the dotted line y=-3x

The slope of the dotted line is negative

The x- intercept of the dotted line is the point (0,0)

The y- intercept of the dotted line is the point (0,0)

The solution of the system of inequalities is the shaded area between the two dotted lines

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