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3 years ago

HELP ME PLS W 23 AND 24

Mathematics

1 answer:

n200080 [17]3 years ago

8 0

Answer:

23 is 1/25

24 is -3

Step-by-step explanation:

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g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur

sdas [7]

Answer:

The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

Step-by-step explanation:

A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

Recall that the volume for a cylinder is given by:

$\displaystyle V = \pi r^2h$

Substitute:

$\displaystyle (300) = \pi r^2 h$

Solve for h:

$\displaystyle \frac{300}{\pi r^2} = h$

Recall that the surface area of a cylinder is given by:

$\displaystyle A = 2\pi r^2 + 2\pi rh$

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

First, substitute for h.

$\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r} \end{aligned}$

Find its derivative:

$\displaystyle A' = 4\pi r - \frac{600}{r^2}$

Solve for its zero(s):

$\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}$

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

$\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}$

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

7 0

2 years ago

If a 200 N net force acts on a 500 grams car, what will the acceleration of the car be?

ladessa [460]

Answer:

The acceleration of the car will be 400 m/s².

Step-by-step explanation:

The acceleration of the car can be found using Newton second law:

$F = ma$

Where:

F: is the net force = 200 N

m: is the mass = 500 g

a: is the acceleration =?

Then, the acceleration will be:

$a = \frac{F}{m} = \frac{200 N}{500 g*\frac{1 kg}{1000 g}} = 400 m/s^{2}$

Therefore, the acceleration of the car will be 400 m/s².

I hope it helps you!

4 0

2 years ago

Which expression is equivalent to -3 (2m - 1) - n?

Semenov [28]

Answer:

−6−m+3

Explanation

-3 (2m - 1) - n?

Distribute

−3(2−1)−

−6+3−

Rearange

−6+3−

−6−m+3

7 0

2 years ago

Find X and Y. I really need help on this. It’s confusing.

stepan [7]

Step-by-step explanation:

7x-2 ) + (١١x -34)

so u will get the answer

after getting it u can easy get y

4 0

2 years ago

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Steve is replacing the carpet in his square shaped living room. Which formula should Steve use to calculate the amount of carpet

Ray Of Light [21]

He would need to find the area of the room (area of the rectangle) by multiplying the length of the room by the width of the room.

6 0

2 years ago