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3 years ago

Evaluate x+16, when x=8

Mathematics

1 answer:

Hatshy [7]3 years ago

7 0

Answer:

Step-by-step explanation:

x + 16

8 + 16

= 24

You just plug in 8 in the x place. Hope this helps, thank you !!

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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

Which number is greatest?

user100 [1]

Answer:

$6.23 \times 10 {}^{12}$

Step-by-step explanation:

$6 .23\times 10 {}^{12}$

$6.23 \times 1000000000000 \\ 6230000000000$

7 0

3 years ago

Read 2 more answers

if it is friday then letica family will have pizza for dinner. if letica family has pizza for dinner, letica will song at the di

stiv31 [10]

Answer:

the first statement

Step-by-step explanation:

it's the first one because on the second one the family members name is letica and the family is letica so it cant be both

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3 years ago

Are these lines perpendicular?<br> yes<br> no

liberstina [14]

Answer:

Step-by-step explanation:

perpendicular means that they intersect at a 90° angle

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2 years ago

Kit bought a soft drink and a sandwich for $9.00. What was the price of each of the sandwich cost 3.5 times as much as the drink

Rainbow [258]

Sandwich cost $7.70 and the soda costs $2.20.

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3 years ago