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babunello [35]
3 years ago
9

Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What

is the approximate area of the paper remaining after the circles have been cut out?
Mathematics
1 answer:
aivan3 [116]3 years ago
3 0
Okay, so if your rectangle is 16 by 8, that means that the circle diameter of 8 because that would be outside of the card's width,
the area of the rectangle is 16 x 8 or 128 
the radius of the circle would be 4 (because 1/2 of the diameter is radius)
we know that the equation of the circle PIr^2, so the area of the circle is 16PI
then, the remaining area would be calculated by 128-16PI 
This comes out to be approximately 77.73 
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Step 1: Simplify both sides of the equation.

8(x−3)+7=2x(4−17)

(8)(x)+(8)(−3)+7=2x(4−17)(Distribute)

8x+−24+7=−26x

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8x−17=−26x

Step 2: Add 26x to both sides.

8x−17+26x=−26x+26x

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Step 3: Add 17 to both sides.

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Step 4: Divide both sides by 34.

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3 0
2 years ago
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3 0
3 years ago
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drek231 [11]
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3 years ago
The Ace Novelty company produces two souvenirs: Type A and Type B. The number of Type A souvenirs, x, and the number of Type B s
Molodets [167]

Answer:

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Step-by-step explanation:

The method of Lagrange multipliers can solve this quickly. For objective function f(x, y) and constraint function g(x, y)=0 we can set the partial derivatives of the Lagrangian to zero to find the values of the variables at the extreme of interest.

These functions are ...

  f(x,y)=4x+2y\\g(x,y)=2x^2+y-4

The Lagrangian is ...

  \mathcal{L}(x,y,\lambda)=f(x,y)+\lambda g(x,y)\\\\\text{and the partial derivatives are ...}\\\\\dfrac{\partial \mathcal{L}}{\partial x}=\dfrac{\partial f}{\partial x}+\lambda\dfrac{\partial g}{\partial x}=4+\lambda (4x)=0\ \implies\ x=\dfrac{-1}{\lambda}\\\\\dfrac{\partial \mathcal{L}}{\partial y}=\dfrac{\partial f}{\partial y}+\lambda\dfrac{\partial g}{\partial y}=2+\lambda (1)=0\ \implies\ \lambda=-2

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Since x and y are in thousands, maximum profit is to be had when the company produces ...

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3 0
3 years ago
What 0.003 a tenth of i need a real answer
Andrej [43]
3000th is the answer.
If I get it wrong, I apologize. I didn't exactly understand your grammar..
5 0
3 years ago
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