SOLUTION: 114. Surface area of a cube. The formula A =6V^2/3 gives the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet? 94

Algebra ->  Radicals -> SOLUTION: 114. Surface area of a cube. The formula A =6V^2/3 gives the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet? 94      Log On


   

Question 184247: 114. Surface area of a cube. The formula A =6V^2/3 gives
the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet?
94. Find all real or imaginary solutions to each equation.
49x^2+9=42x
98. x-1/x+2= 2x-3/x+4


110. Winston works faster. Winston can mow his dad’s lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
114. Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by P(x)=-0+2x^2+300x-200 . What is the profit if 500 are sold? For what value of x will the profit be at a maximum?



Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
114. Surface area of a cube. The formula A =6V^2/3 gives
the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet?
I'll take your word for the formula.
A =6V^2/3
A^3 = 216V^2
V^2 = A^3/216
V^2 = 1728/216 = 8
V = sqrt(8) = 2sqrt(2) cubic feet
---------------------------------
94. Find all real or imaginary solutions to each equation.
49x^2+9=42x
49x^2 - 42x + 9 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 49x%5E2%2B-42x%2B9+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-42%29%5E2-4%2A49%2A9=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-42%29%29%2F2%5C49.
Expression can be factored: 49x%5E2%2B-42x%2B9+=+%28x-0.428571428571429%29%2A%28x-0.428571428571429%29

Again, the answer is: 0.428571428571429, 0.428571428571429. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+49%2Ax%5E2%2B-42%2Ax%2B9+%29

x = 3/7
--------------
98. x-1/x+2= 2x-3/x+4

110. Winston works faster. Winston can mow his dad’s lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
114. Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by P(x)=-0+2x^2+300x-200 . What is the profit if 500 are sold? For what value of x will the profit be at a maximum?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
114. Surface area of a cube. The formula A =6V^2/3 gives the surface area of
a cube in terms of its volume V.
What is the volume of a cube with surface area 12 square feet?
write it:
6V%5E%282%2F3%29 = 12
divide both sides by
V%5E%282%2F3%29 = 12%2F6
V%5E%282%2F3%29 = 2
Cube both sides and you have
V^2 = 8
V = sqrt%288%29
v = 2.828 cu/ft
:
:
94. Find all real or imaginary solutions to each equation.
49x^2 + 9 = 42x
49x^2 - 42x + 9 = 0
(7x-3)(7x-3) = 0
7x = 3
x = 3%2F7
:
98. %28%28x-1%29%29%2F%28%28x%2B2%29%29 = %28%282x-3%29%29%2F%28%28x%2B4%29%29
Cross multiply
(x-1)(x+4) = (x+2)(2x-3)
FOIL
x^2 + 3x - 4 = 2x^2 + x - 6
combine on the right
0 = 2x^2 - x^2 + x - 3x - 6 + 4
x^2 - 2x - 2 = 0
Solve this using the quadratic formula: a=1; b=-2; c=-2
You should get: x = 2.732 and x = -.732
:
:
110. Winston works faster. Winston can mow his dad’s lawn in 1 hour less
than it takes his brother Willie. If they take 2 hours to mow it when
working together, then how long would it take Winston working alone?
:
let x = W's mowing time working alone
then
(x+1) = brother's time working alone
:
Let the completed job = 1
:
2%2Fx + 2%2F%28%28x%2B1%29%29 = 1
Multiply eq by x(x+1), results
2(x+1) + 2x = x(x+1)
2x + 2 + 2x = x^2 + x
4x + 2 = x^2 + x
0 = x^2 + x - 4x - 2
x^2 - 3x - 2 = 0; a quadratic equation
Use the quadratic formula to solve this a=1; b=-3; c=-2
Positive solution: x=3.56 hrs W working alone
:
:
114. Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by P(x)=-0+2x^2+300x-200 . What is the profit if 500 are sold?
:
Assume you mean
P(x)=-.2x^2+300x-200
substitute 500 for x
P(x)=-.2(500^2) + 300(500) - 200
P(x)=-.2(250000) + 150000 - 200
P(x)=-50000 + 150000 - 200
P(x)= $99,800 profit
:
For what value of x will the profit be at a maximum?
Use the axis of symmetry formula: x = -b/(2a); in this eq: a=-.2; b=300
x = -300%2F%282%2A-.2%29
x = -300%2F%28-.4%29
x = 750 unit for max profit