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3 years ago

Myles doesn't want to spend more than $11,000 per month on gate keepers. He hires 12 gate keepers who work an

Mathematics

1 answer:

ss7ja [257]3 years ago

6 0

Answer:

$13.09 for an hourly rate

Step-by-step explanation:

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A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0

3 years ago

Ma.clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?

k0ka [10]

The answer to this question is 17

8 0

3 years ago

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The leader of the team wants to do everything him or herself. They have a very big ego and are difficult to work with. What is t

Aleks [24]

Answer:

This is a hardbut I think the awnser is C

Step-by-step explanation:

This usually happens when a person think that the others are incapable of actullay figuring out he problems .

6 0

3 years ago

What is the measure of the angle formed by the minute hand and the hour hand of a clock when the clock shows 3:00?

FrozenT [24]

Answer: 90 degree angle

if im wrong let me know please

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3 years ago

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Which is the rate of change for the interval between 2 and 6 on the x-axis?

nadezda [96]

Answer:

Step-by-step explanation:

I think you misses attaching the photo, so please have a look at my photo for your better understanding.

We know the formula for rate of change of the parabola line:

$\frac{f(b)- f(a)}{b-a}$

Given here:

a= 2 => f(a) = 2

b=6 => f(b) = 2

Substitute all the values into the function, we have:

$\frac{14-2}{6-2} = 3$

So the rate of change is 3

7 0

3 years ago

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