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

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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)   (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 (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=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 0.428571428571429, 0.428571428571429. Here's your graph:

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)   (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:
= 12
divide both sides by
=
= 2
Cube both sides and you have
V^2 = 8
V =
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 =
:
98. =
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
:
+ = 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 =
x =
x = 750 unit for max profit
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