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kvasek [131]
3 years ago
14

Quick Fix Inc. repairs bikes. The company’s revenue is modeled by the function R(h)=220h−160 for every h hours spent repairing b

ikes. The company’s overhead cost is modeled by the function C(h)=20h^2−400.
After how many hours does the company break even?
Mathematics
1 answer:
alisha [4.7K]3 years ago
6 0
The break-even point is when revenue, R(h) is the same as cost, C(h).
R(h)=C(h)
220h-160 = 20h²-400
Gather all the variables on one side by subtracting 220h:
220h-160-220h = 20h²-400-220h
-160=20h²-220h-400 (we can move these around so long as we take their respective signs with them)
We want our quadratic equation to equal 0 to solve it, so add 160 to both sides:
-160+160=20h²-220h-400+160
0=20h²-220h-240
All 3 terms of this quadratic are divisible by 20, we can factor 20 out:
0 = 20(h² - 11h - 12)
The quadratic that is left is easily factorable.  We want factors of -12 that sum to -11; that would give us -12*1, because -12+1 = -11.  Thus we have
0 = 20(h - 12)(h + 1)
Using the zero product property, we know that one of the factors must be 0 in order for the product to be 0.  20 ≠ 0, so it must be either h-12 or h+1:
h-12 = 0
Add 12 to both sides:
h - 12 + 12 = 0 + 12
h = 12

h+1 = 0
Subtract 1 from both sides:
h + 1 - 1 = 0 - 1
h = -1

Since a negative number of hours is not realistic, the answer must be h = 12 hours.
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Find the sum of the first 47 terms of the following series, to the nearest integer.
topjm [15]

Answer:

The sum of the first 47 terms of the given series = 6016

Step-by-step explanation:

Given the sequence

13, 18, 23, ...

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

18-13=5,\:\quad \:23-18=5

As the difference between all the adjacent terms is the same.

so

d=5

a_1=13

Arithmetic sequence sum formula

n\left(a_1+\frac{d\left(n-1\right)}{2}\right)

Put the values

d=5

a_1=13

n=47

=47\left(13+\frac{5\left(47-1\right)}{2}\right)

=47\left(13+\frac{5\left(47-1\right)}{2}\right)

=47\left(13+115\right)

=47\cdot \:128

=6016

Thus, the sum of the first 47 terms of the given series = 6016

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elixir [45]

Answer:

A parallelogram is made within the shape below by what

Step-by-step explanation:

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2 years ago
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Answer:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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