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?

Question 184347: 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?

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 edjones(8007) (Show Source): You can put this solution on YOUR website!
A =6V^(2/3)
6V^(2/3)=12
v^(2/3)=2 divide each side by 6
v^2=2^3 cube each side
v=2^(3/2)ft^3 Take sqrt of each side.
=sqrt(8)
=sqrt(4*2)
=2sqrt(2)
.
Let n=winston's time
willie's time=n+1
In 1 hr winston can do 1/n of the job.
In 1 hr willie can do 1/(n+1) of the job
Together they can do 1/2 the job in 1 hr
1/n + 1/(n+1) = 1/2
2(n+1)+2n=n(n+1) Multiply each side by the LCM 2n(n+1)
2n+2+2n=n^2+n
4n+2=n^2+n
n^2-3n-2=0 subtract the left side from the right.
n=3.56...hrs winston's time. (see below)
4.56...hrs willie's time.
.
I don't think you copied the 3rd question corectly because as written it gives a minimum not a maximum.
.
Ed
.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=17 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.56155281280883, -0.56155281280883. Here's your graph:

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