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2 years ago

Both circles have the same center. The circumference of the inner circle is 25.12 millimeters.

Mathematics

1 answer:

stira [4]2 years ago

8 0

Answer:

Step-by-step explanation:

let r be radius of inner circle.

2πr=25.12

πr=25.12/2=12.56

3.14r=25.12

r=12.56/3.14=4

outer radius R=4+4=8 mm

reqd. area=πR²-πr²=π(R²-r²)=3.14(8²-4²)=3.14(64-16)=3.14×48= 150.72 mm²

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Solve the equation. -3x +.1 + 10x = x + 4 N olu R X = 18

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Hence after solving the given equation we get x = 13/20.

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3 years ago

A cab company charges according to the following rate chart. Which graph correctly represents the charge, y, in dollars for a ca

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2 years ago

A luxury hotel group purchases a deserted island 3. 5 miles offshore and due south of an endangered bird nesting beach. The near

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Answer:

T.C ( 1.1007 ) = T.C_min = $2252

Step-by-step explanation:

Given:

- Cost of electricity construction over water C_w = $250 / mile

- Cost of electricity construction over ground C_w = $150 / mile

- The distance from hotel island = 3.5 miles

- The distance from beach to power source = 10 miles

Find:

Find the least expensive price for which you can bill the job

Solution:

- This problem requires cost optimization. So we need to develop a cost function as follows

Total Cost = C_w*(distance from island to x) + C_g*( distance from x to power)

- Now calculate the relevant distances using Pythagoras theorem:

Distance from island to x = sqrt ( x^2 + 3.5^2 )

Distance from x to power station = 10 - x

- Input the distances in the cost function:

T.C ( x ) = C_w*sqrt ( x^2 + 3.5^2 ) + C_g*(10 - x )

- Input the relevant rates:

T.C ( x ) = 250*sqrt ( x^2 + 3.5^2 ) + 150*(10 - x )

- Simplify:

T.C ( x ) = 250*sqrt ( x^2 + 12.25 ) + 1500 - 150x

- Next, we will optimize the cost to minimum. We need the distance x that would give us the minimum cost. To minimize the function, set its derivative with respect to x equals to zero.

T.C' ( x ) = 500*x*( x^2 + 12.25 )^( -0.5 ) - 150

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Squaring both sides:

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Simplify and solve:

x = sqrt (110.25 / 91) = 1.1007 miles

- The cost function is minimized at x = 1.1007 miles. We will input this back into our function and evaluate the minimum cost as follows:

T.C ( 1.1007 ) = 250*sqrt ( 1.1007^2 + 12.25 ) + 1500 - 150*1.1007

T.C ( 1.1007 ) = T.C_min = $2252

- So the minimum cost associated with this plan is $2252.

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