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2 years ago

A carousel with a 40-foot radius makes 2 rpms. What is the linear speed of the carousel?

Mathematics

1 answer:

elena-s [515]2 years ago

7 0

I believe its

40*2*1/2*pi meters per second

which is just

<h2><u><em>40pi meters per second</em></u></h2>

if you need it simplified, its

<h2><u><em>125.66370meters per second</em></u></h2>

You might be interested in

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

nadezda [96]

Answer:

Step-by-step explanation:

We have volume of cone as

$V=\frac{1}{3} \pi r^2 h$

and for a cone always r/h = constant

Given that r' = rate of change of radius = -7 inches/sec

(Negative sign because decresing)

V' =- 948 in^3/sec

Radius = 99 inches and volume = 525 inches

Height at this instant = $\frac{525}{\frac{1}{3} \pi (99)^2} \\=\frac{0.1607}{\pi}$

Let us differentiate the volume equation with respect to t using product rule

$V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\$

$-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14 + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514$

Rate of change of height = 0.08514 in/sec

8 0

3 years ago

Let's say the probability of you winning a game of checkers and a game of chess against your friend is 20%. The probability of y

GREYUIT [131]

The probability of winning a game of checkers against your friend is 67%.

<h3>What is the probability of winning a game of checkers against my friend?</h3>

Probability can be described as the process of determining the chances of an event happening. The chances that an event would occur has a value that lies between 0 and 1. A value of 0 is given when the event does not occur and a value of 1 if the event occurs.

The probability of winning a game of checkers = probability of winning both games / probability of winning a game of chess

20% / 30% = 67%

To learn more about probability, please check: brainly.com/question/26321175

8 0

2 years ago

10.3.23

Helga [31]

Answer:

The probability that a high school member selected at random is on the swim team is $\frac{9}{40} = 0.225$

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: High school student.

Event B: Is on the swin team.

Probability of selecting a high school student:

Of the 1500 students, 200 are on high school. So

$P(A) = \frac{200}{1500}$

Probability of selecting a high school student who swims:

Of the 1500 students, 45 are high school students who swim. So

$P(A \cap B) = \frac{45}{1500}$

What is the probability that a high school member selected at random is on the swim team?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{45}{1500}}{\frac{200}{1500}} = \frac{45}{200} = \frac{9}{40} = 0.225$

The probability that a high school member selected at random is on the swim team is $\frac{9}{40} = 0.225$

4 0

3 years ago

For each sentence below, find the value of x that makes each sentence true.

vitfil [10]

<u>ANSWER</u>

1. $x=\frac{1}{2}$

2. $x=1$

<u>QUESTION 1</u>

The first sentence is $(5^{\frac{1}{5}})^5=25^x$ .

Recall that;

$(a^m)^n=a^{mn}$

We simplify the left hand side by applying this property to get;

$5^{\frac{1}{5}\times 5}=25^x$ .

$\Rightarrow 5^{1}=25^x$ .

We now rewrite the right hand side too in an index form to obtain;

$\Rightarrow 5^{1}=5^{2x}$

We now equate the exponents to get;

$\Rightarrow 1=2x$ .

$\Rightarrow \frac{1}{2}=x$

$\Rightarrow x=\frac{1}{2}$ .

<u>QUESTION 2</u>

The second sentence is $(8^{\frac{1}{3}})^2=4^x$

We simplify the left hand side first to get;

$(2^{3\times \frac{1}{3}})^2=4^x$

$2^2=4^x$

We now rewrite the left hand side too in index form to obtain;

$2^2=2^{2x}$

We equate the exponents to get;

$2=2x$

This implies that;

$1=x$

$x=1$

4 0

3 years ago

The domain of a function is the set of all negative numbers. Which quadrant could the function be located in? Select two that ap

Marina86 [1]

Answer:

Step-by-step explanation:

5 0

3 years ago