Answer:
a = 3
Step-by-step explanation:
Since x = 7 is a solution, substitute x = 7 into the equation and solve for a
4(7) - 2(7 + a) = 8 , that is
28 - 2(7 + a) = 8 ( subtract 28 from both sides )
- 2(7 + a) = - 20 ( divide both sides by - 2 )
7 + a = 10 ( subtract 7 from both sides )
a = 3
Answer:
The room dimensions for a minimum cost are: sides of 10 feet and height of 8.75 feet.
Step-by-step explanation:
We have a rectangular room with sides x and height y.
The volume of the room is 875 cubic feet, and can be expressed as:
With this equation we can define y in function of x as:
The cost of wall paint is $0.08 per square foot. We have 4 walls which have an area Aw:
The cost of ceiling paint is $0.14 per square foot. We have only one ceiling with an area:
We can express the total cost of painting as:
To calculate the minimum cost, we derive this function C and equal to zero:
![\dfrac{dC}{dx}=280(-1)\dfrac{1}{x^2}+0.14(2x)=0\\\\\\-\dfrac{280}{x^2}+0.28x=0\\\\\\0.28x=\dfrac{280}{x^2}\\\\\\x^3=\dfrac{280}{0.28}=1000\\\\\\x=\sqrt[3]{1000} =10](https://tex.z-dn.net/?f=%5Cdfrac%7BdC%7D%7Bdx%7D%3D280%28-1%29%5Cdfrac%7B1%7D%7Bx%5E2%7D%2B0.14%282x%29%3D0%5C%5C%5C%5C%5C%5C-%5Cdfrac%7B280%7D%7Bx%5E2%7D%2B0.28x%3D0%5C%5C%5C%5C%5C%5C0.28x%3D%5Cdfrac%7B280%7D%7Bx%5E2%7D%5C%5C%5C%5C%5C%5Cx%5E3%3D%5Cdfrac%7B280%7D%7B0.28%7D%3D1000%5C%5C%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B1000%7D%20%3D10)
The sides of the room have to be x=10 feet.
The height can be calculated as:
The room will have sides of 10 feet and a height of 8.75 feet.
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 180 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 180 is 100%, so we can write it down as 180=100%.
4. We know, that x is 30% of the output value, so we can write it down as x=30%.
5. Now we have two simple equations:
1) 180=100%
2) x=30%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
180/x=100%/30%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 30% of 180
180/x=100/30
(180/x)*x=(100/30)*x - we multiply both sides of the equation by x
180=3.33333333333*x - we divide both sides of the equation by (3.33333333333) to get x
180/3.33333333333=x
54=x
x=54
now we have:
30% of 180=54
