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What is the slope of the line that passes through the points (2, –3) and (–2, 5)?

Evgen [1.6K]

The answer is b) 1/2

3 0

3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

3 years ago

True or False?

almond37 [142]

#1

That is false..one could have side lengths of 9 and 1, and the other could have side lengths of 3. Both the areas would be 9, but the figures would not be congruent.

#2

That is true, they must both have the same side length to have the same perimeter, therefore they will also have the same area.

8 0

3 years ago

Sean tried to drink as fast as he could. He drank the slushy at a constant rate. There were originally 275 milliliters of slushy

Artist 52 [7]

The rate at which Sean drank the slushy is 5 milliliters per second.

The time it would take to drink all the slushy is 55 seconds.

<h3>How fast did Sean drink?</h3>

In order to determine the speed at which the slushy was drank, divide the slushy drank in 13 seconds by 13 seconds.

Speed = slushy drank in 13 seconds / time

(275 - 210) / 13

65 / 13 = 5 milliliters per second

Time it would take to drink all the slushy =total milliliters of the slushy / speed

275 / 5 = 55 seconds.

To learn more about average speed, please check: brainly.com/question/21734785

#SPJ1

3 0

1 year ago

Expand and simplify 2(5x - 1) – (2x - 5)

horrorfan [7]

Answer:

2(5x - 1) – (2x - 5)

=2(5x−1)−2x+5

=10x−2−2x+5

=(10x−2x)+(−2+5)

=8x+3

Step-by-step explanation:

3 0

3 years ago