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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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2 years ago
DOES ANYONE KNOW HOW TO DO THIS???
Anna11 [10]

Answer:

Cost of a pound of chocolate chips: $3.5

Cost of a pound of walnuts: $1.25

Step-by-step explanation:

x - cost of a pound of chocolate chips

y - cost of a pound of walnuts

We create two equations based on the information we have:

3x+2y=13

8x+4y=33

The whole point of these problems os to get rid of x or y. In this question, we can do this by multiplying both sides of the first equation by 2, and then subtracting it from the second equation:

8x+4y=33

6x+4y=26

2x=7

x=3.5

Then we change x for 3.5 in the first equation:

3×3.5+2y=13

10.5+2y=13

2y=2.5

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Hope this helps!

4 0
2 years ago
A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the sma
RSB [31]

Answer:

A.

Step-by-step explanation:

<em>NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.</em>

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

y=2(x+3)

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

y=3x+5

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

y=2(x+3)\\y=2x+6\\-2x+y=6

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

-2x+y=6\\2x-y=-6

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

y=3x+5\\-3x+y=5\\3x-y=-5

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.

7 0
3 years ago
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5 0
2 years ago
Which equation represents the line with a slope of 5/6 that passes through the point (-2, 1)?
andreyandreev [35.5K]

Answer:

Step-by-step explanation:

Slope m = 5/6

The points (-2,1)

So; y1 = 1 and x1 = -2

The equation is y - y1 = m(x - x1)

y - 1 = 5/6(x + 2)

Multiply each term by 6

6y - 6 = 5(x + 2)

6y - 6 = 5x + 10

6y = 5x + 10 + 6

6y = 5x + 16

- 5x + 6y = 16

Multiplying by minus

5x - 6y = -16

5 0
3 years ago
Read 2 more answers
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