If f(x)=x^2-5x and g(x)=8-x^3, evaluate the following:
1 answer:
Answer:
a. -25
b. -52
c. 54
d. 8/7 = 1 1/7
Step-by-step explanation:
Evaluate each of the functions for each of the variable values and compute the composite as defined.
a. (f+g)(3) = f(3) + g(3) = 3^2 -5·3 + 8 -3^3 = -25
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b. (g -f)(4) = g(4) -f(4) = 8 -4^3 -(4^2 -5·4) = 8 -64 -16 +20 = -52
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c. (f*g)(-1) = f(-1) · g(-1) = ((-1)^2 -5(-1)) · (8 -(-1)^3) = 6·9 = 54
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d. (g/f)(-2) = (8 -(-2)^3)/((-2)^2 -5(-2)) = (8+8)/(4+10) = 16/14 = 8/7
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<em>Comment on approach to the problem</em>
When there are a number of evaluations of the same function with different values of the variable, it can be convenient to let a calculator or spreadsheet do those for you.
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Answer:
The walk will cost $8164.
Step-by-step explanation:
Given:
Diameter of the circular pond (D) = 24 yd
Width of the gravel path (x) = 2 yd
Cost per yard of the path = $50
Now, radius of the circular pond is half of the diameter and is given as:
Now, area of the pond is given as:
Area of the complete path including the pond area is given as:
Now, area of the gravel path can be obtained by subtracting the pond area from the total outer area. This gives,
Now, using unitary method,
Cost of 1 square yard of path = $50
∴ Cost of 163.28 square yard of path = 50 × 163.28 = $8164
Hence, the walk will cost $8164.