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NARA [144]
3 years ago
8

The circumference of a circle is

Mathematics
1 answer:
EleoNora [17]3 years ago
8 0

Answer:

C=2πr

Step-by-step explanation:

The circumference is the total distance around the circle.

C=πd but d = 2r.

:.C=2πr.

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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 <em>h: </em>

\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 <em>h</em>.

\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
3 years ago
If you flip a coin and roll a 6-sided die, what is the probability that you will flip a tails and roll at least a 2?
Finger [1]

Step-by-step explanation:

Flipping a tails and rolling at least a tail are 2 independent events: they don't affect each other. So, to get the probability of both happening, we just need to multiply the probability of one by the probability of the other. he probability of rolling at least a 2 is 5/6.

4 0
3 years ago
Luke's water bottle holds 2,150 milliliters. He drinks 3.5 bottles of water each day. How many milliliters of water does he drin
sashaice [31]

Answer:

7525 milliliters

Step-by-step explanation:

because if you multiply 2150 by 3.5 you will get that number

4 0
2 years ago
What is the median of the data set? 15, 19, 20, 22, 26, 30, 31
Paladinen [302]

Answer:

C. 22

Step-by-step explanation:

The median is the middle number of the set if the numbers are in order from least to greatest.

This set of numbers is in order, so the median is the middle number = 22

7 0
3 years ago
A researcher computes r = 0.45 using a sample of 18 participants. Is this Pearson correlation coefficient significant for a two-
Eduardwww [97]

Answer with explanation:

Given : The computed r -value = 0.45

Sample size : n=18

Degree of freedom : df=n-2=18-2=16

Now, the critical value for Pearson correlation coefficient  for a two-tailed test at a .05 level of significance will be :

r_c=0.468   ( by critical correlation coefficient table)

Since , r>r_c i.e. 0.45>0.468 , then we say that his Pearson correlation coefficient is not significant for a two-tailed test at a .05 level of significance.

3 0
3 years ago
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