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hram777 [196]
3 years ago
9

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=-29x^2+1388x-10040
Mathematics
1 answer:
kenny6666 [7]3 years ago
5 0

Given:

The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation

y=-29x^2+1388x-10040

To find:

The maximum amount of profit the company can make, to the nearest dollar.

Solution:

If a quadratic equation is f(x)=ax^2+bx+c, then the vertex is

Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)

If a>0, then vertex is the minimum point and if a<0, then the vertex is the maximum point.

We have,

y=-29x^2+1388x-10040

Here, a=-29,b=1388, c=-10040. Clearly, a<0. So, the vertex is the point of maxima.

-\dfrac{b}{2a}=-\dfrac{1388}{2(-29)}

-\dfrac{b}{2a}=-\dfrac{1388}{-58}

-\dfrac{b}{2a}\approx 23.931

Putting x=23.931 in the given equation, we get

y=-29(23.931)^2+1388(23.931)-10040

y=-16608.09+33216.228-10040

y=6568.138

The vertex is at (23.931,6568.138).

Therefore, the maximum profit is $6568.138 when x=23.931.

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Answer:

Step-by-step explanation:

The continuous compound formula is

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y=3624e^{(.03)(2)}\\y=3624e^{.06}\\y=3624(1.061836547)\\y=3848.09

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8 0
3 years ago
There are 3 people pulling on an object, the first person pulls with a force of 226 newtons at a direction of 145 degrees the se
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Answer:

R=883.74N

Step-by-step explanation:

From the question we are told that:

Force 1 F_1=226N

Force 2 F_2=331N

Force 3 F_3=377N

Direction 1  \theta_1=145 degrees \approx 35 \textdegree (2nd qudrant)

Direction 2 \theta_2=303 degrees \approx 57 \textdegree (3rd qudrant)

Direction 3 \theta_3=77 degrees

Generally Resolving forces to X axis is mathematically given by

 \sum f_x=337cos77+331cos57+226sin35

 \sum f_x=351.596N

Generally Resolving forces to Y axis is mathematically given by

 \sum f_y=337sin77+331sin57+226cos35

 \sum f_x=810.788N

Generally the equation for Resultant force R is mathematically given by

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 R=\sqrt{351.596^2+810.788^2}

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7 0
3 years ago
Solve for the value of v: V+27=117
Fudgin [204]
V+27=117
Subtract 27 to 117:
v=90
7 0
2 years ago
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Find the volume of a right circular cone that has a height of 8.9 ft and a base with a
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1186.16

Step-by-step explanation:

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2 years ago
Find the sum of the arithmetic series given ai = 45, an = 85, and n = 5.
seraphim [82]

Answer:

C. 325.

Step-by-step explanation:

The last term a5 = 85

a1 = 45

Sum of n terms = n/2 (a1 + l)

So here we have n = 5, a1 = 45 and the last term l = 85

= (5/2)(45 + 85)

= 5/2 * 130

= 325.

5 0
3 years ago
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