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il63 [147K]
2 years ago
6

What’s the number of pretzels that must be sold if the equation is P(x)=-4x^2+3200x-100

Mathematics
1 answer:
cupoosta [38]2 years ago
7 0

The number of pretzels that must be sold to maximize the profit is 400.

<h3>What is the number of pretzels to be sold in the quadratic equation?</h3>

The number of pretzels to be sold can be determined by taking the derivative of the quadratic equation.

Given that:

P(x) = -4x^2+3200x-100

P'(x) = -8x + 3200

P''(x) = -8

At the critical point;

P'(x) = 0

Thus;

8x = 3200

x = 3200/8

x = 400

P''(400) = -8

P'' (400) < 0

Therefore, at x = 400, P(x) will be maximum.

Learn more about calculating the derivative of a quadratic equation here:

brainly.com/question/13759985

#SPJ1

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Two numbers whose sum is 44 and whose product is a maximum
Mashcka [7]

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x)                    Remove the brackets

Max = 44x - x^2                   Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x )               Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done  is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.


4 0
3 years ago
Can someone please help me with this
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Step-by-step explanation:

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Hector has a floor plan showing his new house. On the floor plan, his bedroom is 3 inches wide and 3 1 2 inches long. The scale
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     Hector has a floor plan showing his new house. On the floor plan, his bedroom is 3 inches wide and 3 1 2 inches long. The scale of the floor plan is 1 4 inch = 1 foot. What is the actual length of Hector’s room? A) 13 feet B) 14 feet C) 15 feet D) 16 feet <span> 1/4 inch = 1 foot
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