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2 years ago

If Gary bikes at an average speed of 6 miles per hour, how many hours will it take him to bike 84 miles?

Mathematics

2 answers:

Anna [14]2 years ago

7 0

Step-by-step explanation:

No of hours =84 ÷ 6 = 14 hours

Option C is the correct answer

murzikaleks [220]2 years ago

4 0

The answer is c; 14 hours

do 84 divided by 6 and you will get 14

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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

Express in simplest radical form. V100

Elanso [62]

Answer:

I think it is 10.

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Subtract 3x^2+8x3x 2 +8x from -9x^2+3x-8−9x 2 +3x−8

r-ruslan [8.4K]

Answer:

oogla boogla

Step-by-step explanation:

5 0

3 years ago

Look at picture (15 point)

NNADVOKAT [17]

Answer:

Option C is the correct option

Step by step explanation

$\sqrt{ \frac{22 {x}^{6} }{11 {x}^{4} } }$

Reduce the fraction with 11

$\sqrt{ \frac{2 {x}^{6} }{ {x}^{4} } }$

Simplify the expression

$\sqrt{2 {x}^{6 - 4} }$

$\sqrt{2 \: {x}^{2} }$

Simplify the radical expression

$x \sqrt{2}$

Hope this helps...

Good luck on your assignment..

3 0

2 years ago

Pls help i will mark brainliest!:) thank you!;D

pashok25 [27]

<h2>ANSWER</h2>

Here the two points given on the graph A and B

To find : The distance in between the two points we know distance in between two point on a graph 

= 

 $\sqrt{ {(x2 - x1)}^{2} } + \sqrt{ {(y2 - y1)}^{2} }$ 

The Point A = (0,0)

The point B = (3,6)

so the distance in between points A and B 

 $\sqrt{ {(0 - 0)}^{2} } + \sqrt{ {(6 - 3)}^{2} }$ 

 $\sqrt{ {3}^{2} }$ 

 $3$ 

So 3.0 is the distance

Hope it helps

7 0

2 years ago