SOLUTION: -/ = sqrt 1. 7+ -/(2x - 1) = 10 2.4(x - 9)^1/3 =8 3. -/(2x - 1) = x - 8 4. (4x + 3)^2/3 = (16x + 44)^1/3 5. A circular table is to be made that will have a

Algebra ->  Rational-functions -> SOLUTION: -/ = sqrt 1. 7+ -/(2x - 1) = 10 2.4(x - 9)^1/3 =8 3. -/(2x - 1) = x - 8 4. (4x + 3)^2/3 = (16x + 44)^1/3 5. A circular table is to be made that will have a      Log On


   

Question 263760: -/ = sqrt
1. 7+ -/(2x - 1) = 10
2.4(x - 9)^1/3 =8
3. -/(2x - 1) = x - 8
4. (4x + 3)^2/3 = (16x + 44)^1/3
5. A circular table is to be made that will have a top covered with material that costs $3.50 per square foot. The covering is to cost no more than $60. What is the maximum radius for the top of the table? (1 point)
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
-/ = sqrt
1. 7+ -/(2x - 1) = 10
Multiply everything by (2x-1)
7(2x-1)+(2x-1)=10(2x-1)
14x-7+2x-1=20x-10
16x-8=20x-10
-8=4x-10
2=4x
1/2=x

3. -/(2x - 1) = x - 8
Multiply everything by (2x-1)
(2x-1)=(x-8)(2x-1)
2x-1=2x^2 -17x -9
0=2x^2 -19x -8
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-19x%2B-8+=+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=%28-19%29%5E2-4%2A2%2A-8=425.

Discriminant d=425 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--19%2B-sqrt%28+425+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+425+%29%29%2F2%5C2+=+9.90388203202208
x%5B2%5D+=+%28-%28-19%29-sqrt%28+425+%29%29%2F2%5C2+=+-0.403882032022076

Quadratic expression 2x%5E2%2B-19x%2B-8 can be factored:
2x%5E2%2B-19x%2B-8+=+2%28x-9.90388203202208%29%2A%28x--0.403882032022076%29
Again, the answer is: 9.90388203202208, -0.403882032022076. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-19%2Ax%2B-8+%29