Please explain how to solve these.
Solve and check for extraneous solutions.
1. (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?
Solve and check for extraneous solutions.
1. (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?
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1. one way...
start by raising each side to the third power to get
(4x+3)² = (16x+44)
expand left side to get
16x² + 24x + 9 = 16x + 44
subtract 16x and 44 from both sides to get
16x² + 8x - 35 = 0
factor to get
(4x - 5)(4x + 7) = 0
so either 4x - 5 = 0 or 4x + 7 = 0 <---by zero product rule
so x = 5/4 or x = -7/4
[substitute each into original problem to determine if there are extraneous roots (-7/4 is extraneous)]
the only 'real' solution is x = 5/4
2. about 2.3 feet.
Area of table top is π∙r² and max cost is $60. $60/$3.5 ≈ 17.14, so 17.14 is appx. the most square feet you can have.
solve π∙r² = 17.14 for r to get answer
good luck
start by raising each side to the third power to get
(4x+3)² = (16x+44)
expand left side to get
16x² + 24x + 9 = 16x + 44
subtract 16x and 44 from both sides to get
16x² + 8x - 35 = 0
factor to get
(4x - 5)(4x + 7) = 0
so either 4x - 5 = 0 or 4x + 7 = 0 <---by zero product rule
so x = 5/4 or x = -7/4
[substitute each into original problem to determine if there are extraneous roots (-7/4 is extraneous)]
the only 'real' solution is x = 5/4
2. about 2.3 feet.
Area of table top is π∙r² and max cost is $60. $60/$3.5 ≈ 17.14, so 17.14 is appx. the most square feet you can have.
solve π∙r² = 17.14 for r to get answer
good luck