Question 171659: My Prof. had a review for our final, but she wasn't able to complete all of the questions so here are the ones I need help with understanding! Thank you!
8. A rectangular pen for your pet is being built using 120 feet of fencing.
a. What dimensions give an area of 875 sq. feet?
b. What dimensions give a maximum area?
9. Use a sign pattern to solve 2x^3-x^2-3x is greater than or equal to 0. Give the solution in interval notation.
10. Sketch the graph of a rational function. f(x)=2x-3/x+1
You must include the following:
a. Any vertical or horizontal
asymptotes drawn with a
dashed line and labeled.
b. the x and y intercepts
plotted and labeled.
11. Write the complete factored form of f(x)=x^3-3x^2+9x-27.
12. Solve for x algebraically and check your soluionts.
square root of 1-x=x+5
13. Give the 20th term of the sequence: -2, 1, 4, 7,…………..
Find the sum of the first 20 terms.
14. Find the formula for the geometric sequence.
- 2, 6, -18, 54, -162………………..
Find the sum of the first 10 terms of the sequence.
15. Solve using the properties of logarithms.
log(base 3)x+log(base 2)(x-1)=log(base 3)6
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 8. A rectangular pen for your pet is being built using 120 feet of fencing.
a. What dimensions give an area of 875 sq. feet?
120 = 2L+2W
60 = L + W
L = 60-W
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Area = LW = w(60-W) = 60W-W^2
875 = 60W-W^2
solve for W and then solve for L
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b. What dimensions give a maximum area?
Area = 60W-W^2
max occurs when W = -b/2a = -60/(2(-1) = 30
Then L = 60-30 = 30
Max area when W = L = 30
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9. Use a sign pattern to solve 2x^3-x^2-3x is >= 0. Give the solution in interval notation.
Solve the EQUALITY: 2x^3-x^2-3x = 0
x(2x^2-x-3) = 0
x(2x^2-3x+2x-3)=0
x(x(2x-3)+(2x-3))= 0
x((2x-3)(x+1) = 0
x = 0, or x = 3/2, or x = -1
----
Draw a number line and plot -1, 0 and 3/2 on it
Check test points in the resulting 4 intervals to see where the solutions
for the INEQUALITY lie.
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10. Sketch the graph of a rational function. f(x)=(2x-3)/(x+1)
You must include the following:
a. Any vertical or horizontal
VA: x=-1
HA: y = 2x/x = 2
asymptotes drawn with a
dashed line and labeled.
-------------
b. the x and y intercepts
x-intercept: Let y = 0 and solve for x : x = 3/2
y-intercept: Let x = 0, and solve for y: y = -3/1 = -3
plotted and labeled.
-------------------------------------
11. Write the complete factored form of f(x)=x^3-3x^2+9x-27.
f(x) = (x-3)^3
---------------------
12. Solve for x algebraically and check your soluionts.
square root of 1-x=x+5
sqrt(1-x) = x+5
1-x = x^2+10x+25
x^2 + 11x +24 = 0
(x+3)(x+8) = 0
x = -3 or x = -8
---
Checking:
x = -1 ?
sqrt(-2) = 4
extraneous
----------------
x = -8 ?
sqrt(-9) = 3
extraneous
---------------
Conclusion: No solutions.
===============================
Cheers,
Stan H.
13. Give the 20th term of the sequence: -2, 1, 4, 7,…………..
Find the sum of the first 20 terms.
14. Find the formula for the geometric sequence.
- 2, 6, -18, 54, -162………………..
Find the sum of the first 10 terms of the sequence.
15. Solve using the properties of logarithms.
log(base 3)x+log(base 2)(x-1)=log(base 3)6
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