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faltersainse [42]
3 years ago
7

An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed company as p(x) = x3 − 4x2 + 5x − 2

0, where p is in hundreds of dollars and x is number of years the company has been in business. In which year (x) will the entrepreneur break even?
a)year 1
b)year 2
c)year 3
d)year 4
Mathematics
2 answers:
nikitadnepr [17]3 years ago
7 0
To "break even" means that the costs are equal to the money made, so profit would have to be 0. Therefore, we can rewrite the equation to be
0 = x3 -4x2 +5x -20

From here, all you have to do is factor to be able to solve for the values of x

First, since the first two numbers both have an x2, we can factor that out
x2(x-4) + 5x -20 = 0

The next two can factor out a 5
x2(x-4) + 5(x-4) =0

Since both of these terms share an (x-4), they can be factored to become:
(x-4) (x2 +5) = 0

So now we just solve for x, and get x = 4, and +- (sqrt) 5i

Since 4 is the only answer present in the options (and since 5i is a non-real number), the answer would be 4

ANS: D

Hope this helped ^-^
shtirl [24]3 years ago
5 0

The correct answer is

Year 4

:)


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If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in cm/min) at which the diameter d
grin007 [14]

Answer:

The diameter decreases at a rate of 0.053 cm/min.

Step-by-step explanation:

Surface area of an snowball

The surface area of an snowball has the following equation:

S_{a} = \pi d^2

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Implicit differentiation:

To solve this question, we differentiate the equation for the surface area implictly, in function of t. So

\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}

Surface area decreases at a rate of 3 cm2/min

This means that \frac{dS_{a}}{dt} = -3

Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.

This is \frac{dd}{dt} when d = 9. So

\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}

-3 = 2*9\pi\frac{dd}{dt}

\frac{dd}{dt} = -\frac{3}{18\pi}

\frac{dd}{dt} = -0.053

The diameter decreases at a rate of 0.053 cm/min.

7 0
3 years ago
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Answer:

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Step-by-step explanation:

Given the equation of a line y = x + 4 and equation of a circle as

( x − 3 )² + ( y − 5 )² = 34, if the line and the circle intersect at points A and B, to get this points, we will substitute the equation of the line into that of the circle as shown;

We will have to expand the equation of the circle first before making the substitute.

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Substituting y = x+ 4 into the resulting expression;

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The coordinates of the point of intersection are A(-2, 2) and B(6, 10).

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