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3 years ago

If a humpback whale swam 16.8 miles per hour dor 4.5 hours how far did it swim

Mathematics

1 answer:

fredd [130]3 years ago

8 0

Answer:

easy, it traveled/swam 75.6 miles

Step-by-step explanation:

16.8 x 4.5= 75.6

hope this helps

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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

Mrs. Cazares went shopping for candy for her students. She bought 6 bags of candy. She had a coupon for $6 off her purchase. If

Umnica [9.8K]

Answer:

Step-by-step explanation:

hope you have a great day!

3 0

3 years ago

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A camp leader figures that she needs one tent for every three campers, plus a tent for herself. Define a variable and write an e

Tomtit [17]

3t+1
The t stands for tent, and is being multiplied by 3 because there is always going to be 1 tent for every 3 campers. Plus one, for the camp leader.

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3 years ago

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The image of the point (6, -9) under a translation is (11,-4). Find the coordinates

yaroslaw [1]

Answer:

( - 6 , - 1 )

Step-by-step explanation:

Let's find the rule of that transformation:

1 + = 4 ⇒ = 3

9 + = 10 ⇒ = 1

Thus, the rule of given transformation is ( x + 3 , y + 1 )