MAT 117- Week 8–Application Assignment- Due Day 7 (Sunday) Page 1 of 4

NAME:_______

Instructions: In order to complete your Application Assignmentin an organized and efficient manner, please use this template to type your work and answers. Save this template to your computer, complete the problems (showing all work &/or explaining your work in words)and post it as an attachment to your Individual forum.When you save your work, please rename the file with your last name first (i.e. Smith-Wk4AppAssn.docx).

No work = no partial creditNeed to include units of measure in Final Answer!

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1 / The square of a number, decreased by 2, is equal to the negative of that number.
Construct a quadratic equation for that statement, and then solve that equation by factoring to find the answer(s).
Your Solution
Set up the equation:
x2 – 2 = -x
Simplify by adding x:
x2 + x – 2 = 0
Factor:
(x+2)(x-1) = 0
Solving:
x = -2 or 1 / -2 or 1
2 / Suppose that the demand for a certain car accessory is given by the following equation:
D = -3p + 65
where D is the quantity the market will demand, and p is the selling price.
Suppose for that same car accessory, the supply is given by the following equation:
S = -p2 + 36p – 120
Using those two equations, find the equilibrium price. Equilibrium price is the condition where the demand and supply are equal.
Hint: as stated above, the condition of equilibrium: S = D
and you solve for p.
You will need to use the quadratic formula, and report your answer(s) to the nearest penny.
Your Solution
Set supply equal to demand:
-3p + 65 = -p2 + 36p – 120
Move everything to one side:
p2 – 39p + 185 = 0
Quadratic formula:



Using a calculator:
p = $5.53 or $33.47
However, when the price is $33.47, the demand and supply are NEGATIVE, so that answer is a false solution. We discard it. / $5.53
3 / One leg of a right triangle is twice the length of the other. The hypotenuse is 8 m long. Find the length of each leg. Report your answer to the nearest tenth of a meter.
Your Solution
Pythagorean theorem:
x2 + (2x)2 = 82
Expand:
5x2 = 64
Divide by 5:
x2 = 64/5
Square root (the positive one):
x = 3.6 meters / 3.6 meters
4 / The equation: h = -16t2 + 112t gives the height (h) of an arrow shot upward from the ground with an initial velocity of 112 ft/s, where t represents the time after the arrow leaves the ground.
Using that equation, find the height of the arrow after:
(a) 2 seconds
(b) 5 seconds
Your Solution
A:
-16(2)2 + 112(2)
-64 + 224
= 160
B:
-16(5)2 + 112(5)
-400 + 560
= 160 / (a)
160 feet
(b)
160 feet
5 / Suppose that the cost C, in dollars, of producing x chairs in a factory is given by the following equation:
C = 2x2 – 40x + 2400
How many chairs can be produced for $4650?
Your Solution
Set C = 4650:
4650 = 2x2 – 40x + 2400
Subtract 4650:
2x2 – 40x - 2250 = 0
Divide by 2:
x2 – 20x - 1125 = 0
Factor:
(x-45)(x+25) = 0
x = 45 or -25
It can’t be negative… so x = 45 / 45 chairs
6 / Suppose that the profit P in dollars, of producing and selling x appliances is given by P = -3x2 + 240x – 1800.
How many appliances must be produced and sold to achieve a profit of $2535?
Set P = 2535:
2535 = -3x2 + 240x – 1800
Subtract 2535 from both sides:
-3x2 + 240x – 4335 = 0
Divide by -3:
x2 - 80x + 1445 = 0
Quadratic:




x = 27.55 or 52.45 / About 28 or about 52
Finished? I encourage you to go back and check each answer. Did you show all your work? Did you label every answer? Did you use commas where necessary? Did you simplify and/or reduce answers to simplest form? Did you include units of measure in your answer, where applicable?