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weqwewe [10]
4 years ago
10

You are planning to make an open rectangular box from aa 4141​-in.-by-8181​-in. piece of cardboard by cutting congruent squares

from the corners and folding up the sides. What are the dimensions of the box of largest volume you can make this​ way, and what is its​ volume
Mathematics
1 answer:
marissa [1.9K]4 years ago
3 0

Answer:

13058.83 cubic inches

Step-by-step explanation:

Given that a rectangular box is having dimensions as 41x81 inches.

Let x be the side of square cut from all the four corners.

The open box made would have height as x and length 41-2x with width 81-2x

Volume =

V(x) = x(41-2x)(81-2x)\\V(x) =x(3321-244x+4x^2)\\V(x) = 3321x-244x^2+4x^3\\V'(x) = 3321-488x+12x^2\\V"(x) = -488+24x\\

Equate first derivative to 0

We get applicable root as x = 8.642

Max volume = 13058.83 cubic inches

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avanturin [10]

Answer:

First and Second Derivative Tests. First identifies critical points. The second determines behavior around the point.

  • Concave up is a minimum
  • Concave down is a maximum

Step-by-step explanation:

The extreme points of a function are called the maximum and/or minimums. AT these points, the function (or y-values) are at their highest or lowest. These points are often the peaks and valleys of a function on a graph. You can determine if a function has max or min using the first and second derivative tests. The first determines critical points of the function. The second determines behavior around a point. If the value is positive then the function is concave up. It forms a valley and the point is a minimum. If the value is negative then the function is concave down. It forms a peak which has a maximum.

7 0
3 years ago
Solve the equation. What is the value of x?<br><br> x minus 6.8 = 356.3
koban [17]

Answer:

the answer is 363.1 i used a calculater to find the answer. so 356.3+ 6.8 = 363.1 so x=363.1

Step-by-step explanation:

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3 years ago
Josie 10.50 per hour many hours would she have worked once she got 175
spayn [35]
16 or 17 is the estimated answer
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To make 6 apples pie, you need 2 pounds of apples. How many pounds of apples do you need to make 10 apple pies?
Bezzdna [24]
For every 6 apple pie, you need 2 pounds of apples.
So, how many pounds of apples do you need for 10 apple pies?
Well, first to figure out this question we first need to make a conversion factor.
I see in the fraction 6/3 we can simplify that to 2/1. Now we got our conversion factor.
We need to invert the fraction in order for the pie unit to cancel out.
1/2 * 10 = 5

You will need 5 pounds of apples to make 10 apple pies.

4 0
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The answer is the first option

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