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3 years ago

I NEED AN ANSWER PLZZZZZZZZZZZZZ

Mathematics

1 answer:

Marina86 [1]3 years ago

6 0

Answer:

I think it might be B

i hope this helps!

(if B is wrong then it is definitely C)

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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

4 years ago

Necesito ayuda por fis

svet-max [94.6K]

Answer:

pues que es en que necesitas ayuda

Step-by-step explanation:

dime namas comentame y te ayudo

3 0

3 years ago

Which of the following is a step in constructing angle bisectors using a compass and straight edge? a Construct a copy of the li

motikmotik

Answer:

start with a line segment to divide into equal parts

Step-by-step explanation:

that's the first step you take before you make the angle bisector because there's no point in doing the other steps before that

8 0

3 years ago

Read 2 more answers

The current in a simple electric circuit varies inversely as the resistance. If the current is 20amps when the resistance is 5 o

IrinaVladis [17]

Answer:

0.5amps

Step-by-step explanation:

I is inversely proportional to resistance

I = k/R

k = I/ R

k = 20/5

k = 4

This means that, I = 4/R

So, when R = 8ohms,

I = 4/8

=0.5amps

3 0

3 years ago

The sum of x and 6.5 is 11.9. Find<br> he value of x.

pashok25 [27]

Answer:

5.4

Step-by-step explanation:

Sum = 11.9

One decimal = 6/5

x = 11.9 - 6.5

= 5.4

Therefore x is 5.4 :)

8 0

3 years ago