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3 years ago

Determine whether the relationship between the two quantities in the table is proportional.

Mathematics

1 answer:

arsen [322]3 years ago

6 0

Which two quantities? Please upload a picture or type so we can help you with the best of our abilities!

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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

Paul is three times as old as Mary and Peter is four times as old as Mary,If the sum of their ages is 64, how old are Peter,Paul

uysha [10]

Let Mary's age be x.

Paul is three times as old as Mary, so Paul's age would be 3x.

Peter is four times as old as Mary, so Peter's age would be 4x.

The sum of their ages is 64
⇒ Paul's age+ Peter's age+ Mary's age= 64
⇒ 3x+ 4x+ x= 64
⇒ 8x= 64
⇒ x= 64/8
⇒ x= 8

Paul's age is: 3x= 3*8= 24

Peter's age is: 4x= 4*8= 32

Final answer: Paul is 24 years old.
Peter is 32 years old.
Mary is 8 years old.

Hope this helps~

7 0

3 years ago

Suppose 2 eggs with bacon cost 2.70 . One egg with bacon costs 1.80 . At thesebrates what will bacon alone cost

Leno4ka [110]

If 2 eggs with bacon cost 2.70, and 1 egg with bacon costs 1.80, that means that 1 egg costs 0.90, so when we subtract once more 0.90 we get the price of the bacon alone, which is in this case 0.90.

5 0

2 years ago

-2(bx - 5) = 16 What’s does b and x equal?

horrorfan [7]

To solve this problem you must apply the proccedure shown below:
You have the following equation given in the problem above:
-2(bx - 5) = 16
 When you solve for bx, you have:
-2(bx - 5) = 16
-2bx-10=16
-2bx=26
bx=26/-2
bx=-13

When you solve for b, you obtain:
-2(bx - 5) = 16
-2bx=26
b=-(26/2x)

When yoo solve for x:
2bx=26
x=-(26/2b)

3 0

3 years ago

Please help me thank you

lilavasa [31]

Use the Pythagorean theorem. We have legs with lengths of 15 and 20 miles, now let's solve for the hypotenuse.

$a=15$
$b=20$
$c=?$

$a^2+b^2=c^2$
$15^2+20^2=c^2$
$c^2=400+225=625$
$c=25$

Your answer is 25 miles. Hope this helps! :)

7 0

3 years ago