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3 years ago

The graph below shows an airplane's speed over a period of time. Describe the events.

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

The airplane gains speed when it takes off. Then it begins to lose speed at the same rate. The plane then stays at the same speed the rest of the time.

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A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can cost

Advocard [28]

Answer:

Radius = 1.12 inches and Height = 4.06 inches

Step-by-step explanation:

A soup can is in the shape of a right circular cylinder.

Let the radius of the can is 'r' and height of the can is 'h'.

It has been given that the can is made up of two materials.

Material used for side of the can costs $0.015 and material used for the lids costs $0.027.

Surface area of the can is represented by

S = 2πr² + 2πrh ( surface area of the lids + surface are of the curved surface)

Now the function that represents the cost to construct the can will be

C = 2πr²(0.027) + 2πrh(0.015)

C = 0.054πr² + 0.03πrh ---------(1)

Volume of the can = Volume of a cylinder = πr²h

16 = πr²h

$h=\frac{16}{\pi r^{2}}$ -------(2)

Now we place the value of h in the equation (1) from equation (2)

$C=0.054\pi r^{2}+0.03\pi r(\frac{16}{\pi r^{2}})$

$C=0.054\pi r^{2}+0.03(\frac{16}{r})$

$C=0.054\pi r^{2}+(\frac{0.48}{r})$

Now we will take the derivative of the cost C with respect to r to get the value of r to get the value to construct the can.

$C'=0.108\pi r-(\frac{0.48}{r^{2} })$

Now for C' = 0

$0.108\pi r-(\frac{0.48}{r^{2} })=0$

$0.108\pi r=(\frac{0.48}{r^{2} })$

$r^{3}=\frac{0.48}{0.108\pi }$

r³ = 1.415

r = 1.12 inch

and h = $\frac{16}{\pi (1.12)^{2}}$

h = 4.06 inches

Let's check the whether the cost is minimum or maximum.

We take the second derivative of the function.

$C"=0.108+\frac{0.48}{r^{3}}$ which is positive which represents that for r = 1.12 inch cost to construct the can will be minimum.

Therefore, to minimize the cost of the can dimensions of the can should be

Radius = 1.12 inches and Height = 4.06 inches

5 0

3 years ago

Which shape is always an isosceles triangle?

Lady_Fox [76]

Only triangles , there isosceles if they both have two congruent sides & angles !

8 0

3 years ago

Please help!!!!!!! im so confused lol

pav-90 [236]

Answer:

a : c = 7 : 10

Step-by-step explanation:

The two ratios (a : b and b : c) both have b in common, so to work out what a : c is, we can use b to 'bridge' the two ratios together.

However, in a : b, b is 4. But in b : c, b is 2. We need to make sure b is the same in both ratios before we can combine the ratios together. The easiest way to do this is to multiply b : c by 2 to get b : c = 4 : 10. Now b is 4 in both ratios.

So now, we can combine the two ratios together to get a : b : c = 7 : 4 : 10. Since we only want a : c though, we can just drop the b and get a : c = 7 : 10. No simplifying is necessary since the ratio is already in its simplest form.

Hope that helps! :)

5 0

2 years ago

Lois is riding in the country. after riding her bike at a constant speed for 4 hours, she finds that she traveled a distance of

never [62]

She is going 13 miles an hour or 52 divided by 4

7 0

3 years ago

Read 2 more answers

A number x is greater than 0. write the word sentence as an inequality

IgorLugansk [536]

9514 1404 393

Answer:

x > 0

Step-by-step explanation:

The only thing that needs translation to symbols is "greater than". Your "word sentence" already uses the symbols x and 0. The symbol for greater than is >. Your inequality is ...

x > 0

8 0

3 years ago