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GarryVolchara [31]

3 years ago

8

What unit of measure would you use to measure length of piece of paper?

1 answer:

GenaCL600 [577]3 years ago

4 0

Typically, you would use inches.

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A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago

Help me please thank

pickupchik [31]

37 students get at most 67 scores.

The numbers 60-67 represent the lower quartile (lowest 25%). 25% of 60 is 15 not 30. Therefore it is incorrect.

7 0

3 years ago

Read 2 more answers

Find the rule. Solve for n.<br> Х Y<br> 3 5<br> 4 7<br> n 11<br> 8 15

fredd [130]

Answer:

6

Step-by-step explanation:

This looks like a linear function.

From the first two points, we get the equation to be y=2x-1.

So to find n, 11=2n-1.

12=2n

n=6

6 0

2 years ago

If f(x)=3x-7, find f(5). *

tatiyna

Answer:

f(5) = 8

Step-by-step explanation:

3(5)-7

15-7

8

6 0

3 years ago

Read 2 more answers

Solve the equation -3(x - 1) + 7x = 27

Lady_Fox [76]

The answer is X=6 !!!!!!

6 0

3 years ago

Read 2 more answers