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Gelneren [198K]
2 years ago
7

What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out

squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give one decimal place in your final answer. (10 points)
Mathematics
1 answer:
Romashka-Z-Leto [24]2 years ago
5 0

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides 12-2x and 16-2x, and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

(12-2x)(16-2x)x = 4x^3-56x^2+192x

The derivative of this function is

12x^2-112x+192

and it equals zero if and only if

12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}

If we evaluate the volume function at these points, we have

f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)

So, the maximum volume is given if you cut a square with side length

x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7

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50 is one tenth of what number?
Stella [2.4K]

Answer:

500

Step-by-step explanation:

Well you find one tenth of a number by dividing it by 10

So to do the opposite, you can do 50*10 which is 500

Or if you really wanted to you could go through each option dividing them all by 10 till you got 50

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3 years ago
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Safara wants to rent a bicycle the graph shows the cost for renting a bicycle for different lengths of time. What is the slope o
enot [183]

The slope of the line will be equal to 30.

Slope of a line may be defined as the steepness of a curve. Slope of line can be positive, negative or zero. Slope of a line is used to determine the equation of the line which is given as y = mx + b where m is the slope, b is y intercept and x and y are independent and dependent variables respectively. The slope of a line on points (x₁, y₁) and (x₂, y₂) is given by the formula, m = y₂ - y₁/x₂ - x₁.

According to the question the value of points is (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 60).

Now, the slope can be calculated as

m = (60 - 0)/(2 - 0)

=> m = 60/2

=> m = 30 which is the required slope.

Learn more about Slope at:

brainly.com/question/6531433

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11 months ago
The table below represents a linear function f(x) and the equation represents a function g(x):
PIT_PIT [208]

Answer:

Step-by-step explanation:

Listen bro or girl I have a question answer it for me and i will answer it for you deal

5 0
2 years ago
No links need help ASAP
Alexandra [31]

Answer:

4, 2

Step-by-step explanation:

The formulas for 180 clockwise and counterclockwise wise is -x,-y since both of them are negative they would become positive because -x * -x = + same with y.

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Can someone help me pls
BartSMP [9]

Answer:

30.4

Step-by-step explanation:

if you want the basic perimeter just add up all the sides

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