Answer:
The minimum cost of installing the cable is $156.
Step-by-step explanation:
We have an optimization problem.
We have to minimize the cost of the cable.
We will use the variable x to express the the length of cable CP and PM, accordingly to the attache picture.
The length of the cable that goes from C to P (let's call it CP) is x.
Then, the length of the cable that goes from P to M (PM) can be calcualted usign the Pithagorean theorem:
The cost function Y is:
To optimize this cost funtion we have to derive and equal to 0:
![\dfrac{dY}{dx}=0\\\\\\\dfrac{dY}{dx}=4+5(\dfrac{1}{2})((33-x)^2+9^2)^{-1/2} *(-2)(33-x)\\\\\\\dfrac{dY}{dx}=4+5\dfrac{x-33}{\sqrt{(33-x)^2+81}}=0\\\\\\\dfrac{x-33}{\sqrt{(33-x)^2+81}}=-\dfrac{4}{5}\\\\\\(x-33)=-\dfrac{4}{5}\sqrt{(33-x)^2+81}\\\\\\(x-33)^2=(-\dfrac{4}{5})^2[(x-33)^2+81]\\\\\\(x-33)^2=\dfrac{16}{25}(x-33)^2+\dfrac{1296}{25}\\\\\\\dfrac{25-16}{25} (x-33)^2=\dfrac{1296}{25}\\\\\\9(x-33)^2=1296\\\\\\x-33=\sqrt{\dfrac{1296}{9}}=\sqrt{144}=\pm12\\\\\\x=33\pm12\\\\\\x_1=33-12=21\\\\x_2=33+12=45](https://tex.z-dn.net/?f=%5Cdfrac%7BdY%7D%7Bdx%7D%3D0%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdY%7D%7Bdx%7D%3D4%2B5%28%5Cdfrac%7B1%7D%7B2%7D%29%28%2833-x%29%5E2%2B9%5E2%29%5E%7B-1%2F2%7D%20%2A%28-2%29%2833-x%29%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdY%7D%7Bdx%7D%3D4%2B5%5Cdfrac%7Bx-33%7D%7B%5Csqrt%7B%2833-x%29%5E2%2B81%7D%7D%3D0%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bx-33%7D%7B%5Csqrt%7B%2833-x%29%5E2%2B81%7D%7D%3D-%5Cdfrac%7B4%7D%7B5%7D%5C%5C%5C%5C%5C%5C%28x-33%29%3D-%5Cdfrac%7B4%7D%7B5%7D%5Csqrt%7B%2833-x%29%5E2%2B81%7D%5C%5C%5C%5C%5C%5C%28x-33%29%5E2%3D%28-%5Cdfrac%7B4%7D%7B5%7D%29%5E2%5B%28x-33%29%5E2%2B81%5D%5C%5C%5C%5C%5C%5C%28x-33%29%5E2%3D%5Cdfrac%7B16%7D%7B25%7D%28x-33%29%5E2%2B%5Cdfrac%7B1296%7D%7B25%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7B25-16%7D%7B25%7D%20%28x-33%29%5E2%3D%5Cdfrac%7B1296%7D%7B25%7D%5C%5C%5C%5C%5C%5C9%28x-33%29%5E2%3D1296%5C%5C%5C%5C%5C%5Cx-33%3D%5Csqrt%7B%5Cdfrac%7B1296%7D%7B9%7D%7D%3D%5Csqrt%7B144%7D%3D%5Cpm12%5C%5C%5C%5C%5C%5Cx%3D33%5Cpm12%5C%5C%5C%5C%5C%5Cx_1%3D33-12%3D21%5C%5C%5C%5Cx_2%3D33%2B12%3D45)
The valid solution is x=21, as x can not phisically larger than 33.
The cost then becomes:
Answer: It flies 165 miles in 5 hours
Step-by-step explanation:
396/12 = 33
It flies 33 miles every hour.
33 * 5 = 165
Answer:
Area = 1/2 b x h
18 = 1/2 ((x) x 4x)
18 =1/2 4x^2
36 = 4x^2
36/4 = x^2
9 = x ^2
x = 3
Base = 3 m
Height = 4 x base = 4 x 3 = 12 m
Step-by-step explanation:
ANSWER:
Let width be x, then length be 2x – 2
Now, Area of rectangle = L × B
- x(2x – 2) = 40
- 2x² – 2x – 40 = 0
- 2(x² – x – 20) = 0
- x² – x – 20
- x² –5x + 4x – 20 = 0
- x(x – 5) + 4(x – 5) = 0
- (x + 4)(x – 5) = 0
- x = – 4; 5
Hence, width can't be negative.
So width = 5in.
And Length = 2 × 5 – 2
So, <u>Correct choice</u> - [D] Length is 8 in, Width is 5 in.
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Mayor axis vertical = 14
Minor axis = 10
Center = (-7, 3)
Formula
Mayor axis = 2a
Minor axis = 2b
Process
2a = 14 2b = 10
a = 7 b = 5
h = -7 k = 3
Substitution
