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babymother [125]
2 years ago
13

The volume of a stack of identical circular drink coasters, each 1 centimeter thick, can be found using the function v(r)=8(3.14

)(r)^2, where r is the radius of a coaster. What does the constant 8 in the function represent?
Mathematics
2 answers:
Vladimir79 [104]2 years ago
8 0

The volume of a stack of identical circular drink coasters, each 1 centimeter thick, can be found using the function v(r)=8(3.14)(r)^2, where r is the radius of a coaster. What does the constant 8 in the function represent?

The constant 8 represents the height of the stack and hence the number of coasters.

Gnesinka [82]2 years ago
5 0

Answer:

It represents the number of coasters.

Step-by-step explanation:

The formula for finding the volume of a cylinder is

V = πr²h

If you we take π =3.14 and h = 1 cm, as given in the question, then we can rewrite the formula for the volume of one coaster as

V = 3.14 * r²

But the formula in this question is

V(r) = 8*3.14 * r² so this means that there are 8 coasters here hence the formula for one coaster being multiplied by 8.

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8.1g of sugar is needed for every cake made. How much sugar is needed for 6 cakes?
Lerok [7]

Answer:

48.6

Step-by-step explanation:

If you use 8.1g of sugar for 1 cake then 6 cakes will be 48.6g of sugar

Just do 8.1*6 and you will get 48.6

8 0
2 years ago
Triangle H N K is shown. Angle H N K is 90 degrees. The length of hypotenuse H K is n, the length of H N is 12, and the length o
Mazyrski [523]

Answer:

13

Step-by-step explanation:

From the question, we are given a triangle HNK with an angle of 90°

The length of hypotenuse H K is n,

the length of HN is 12

the length of N K is 6.

From the above values, obtained in the question, we can see that this is a right angled triangle.

We are asked to find the length of the hypotenuse.

We can use Pythagoras Theorem of solve for this.

c² = a² + b²

where c = HK = n

a = NK = 6

b = HN = 12

c² = 6² + 12²

c² = 36 + 144

c² = 180

c = √180

c = 13.416407865

Approximately to the nearest whole number = 13

Therefore the value of HK = n = 13

We can also use Law of Cosines as given in the question to solve for this.

a² = b² + c² - 2ac × Cos A

where c = HK = n

a = NK = 6

b = HN = 12

Hence

c² = a² + b² - 2ab × Cos C

c = √ (a² + b² - 2ab × Cos C)

Where C = 90

c = √ 6² + 12² - 2 × 6 × 12 × Cos 90

c = 13.42

Approximately to the nearest whole number ≈ 13

Therefore the value of HK = n = 13

8 0
1 year ago
Simplify fully12xy24xy​
Darina [25.2K]

Answer:

288xy

Step-by-step explanation:

First, you multiply 12 by 24 and you get 288. Next, you can't forget the variables, so you add those to the end and get, 288xy.

5 0
2 years ago
Martin chose two of the cards below. When he found the quotient of the numbers, his answer was -16/9. Write the division problem
Sveta_85 [38]

Answer:

The required division problem he must solve is:

\frac{2}{3} \div \frac{-3}{8} =\frac{2}{3}\times\frac{-8}{3}=\frac{-16}{9}

Step-by-step explanation:

Consider the provided information.

Martin chose two of the cards below. When he found the quotient of the numbers, his answer was -16/9.

As we know that the quotient of the number is a negative number.

Therefore, the sign of both numbers must be different,

Thus we can concluded he must select \frac{2}{3} as one of the card, so that product is a negative number.

Let the selected card be x.

\frac{2}{3} \div x =\frac{-16}{9}\\\\x=\frac{2}{3}\div\frac{-16}{9}\\\\x=\frac{2}{3}\times\frac{-9}{16}\\\\x=\frac{-3}{8}

Hence, the two cards should be \frac{2}{3} and \frac{-3}{8}

The required division problem he must solve is:

\frac{2}{3} \div \frac{-3}{8} =\frac{2}{3}\times\frac{-8}{3}=\frac{-16}{9}

3 0
1 year ago
The lifetime of a cheap light bulb is an exponential random variable with mean 36 hours. Suppose that 16 light bulbs are tested
photoshop1234 [79]

Answer:

P(T

Step-by-step explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

P(X=x)=\lambda e^{-\lambda x}, x>0

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

X \sim Exp(\lambda=\frac{1}{16})

Or equivalently:

X \sim Exp(\mu=16)

Solution to the problem

For this case we are interested in the total T, and we can find the mean and deviation for this like this:

\bar X =\frac{\sum_{i=1}^n X_i}{n}=\frac{T}{n}

If we solve for T we got:

T= n\bar X

And the expected value is given by:

E(T) = n E(\bar X)= n \mu= 16*36=576

And we can find the variance like this:

Var(T) = Var(n\bar X)=n^2 Var(\bar X)= n^2 *\frac{\sigma^2}{n}=n \sigma^2

And then the deviation is given by:

Sd(T)= \sqrt{n} \sigma=\sqrt{16} *36=144

And the distribution for the total is:

T\sim N(n\mu, \sqrt{n}\sigma)

And we want to find this probability:

P(T< 600)

And we can use the z score formula given by:

z=\frac{T- \mu_T}{\sigma_T}

And replacing we got this:

P(T

6 0
2 years ago
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