What is the image point of (-6,-9)(−6,−9) after a translation left 1 unit and down 5 units?

A water tank is in the shape of a right circular cone as shown above. The diameter of the cone is 10 feet, and the height is 15

Vsevolod [243]

Answer:

The rate at which the height of the water tank is changing is approximately 0.4244 ft/hour

Step-by-step explanation:

The given parameters are;

The diameter of the cone = 10 feet

The height of the cone = 15 feet

The rate at which water is leaking from the tank, (dV/dt) = 12 ft³/h

The volume of water in the tank = 27·π cubic feet

The volume V of a right circular cone with radius r and height h = 1/3×π×r²×h

The rate of change of the volume, dV, with time dt is given as follows;

The radius of the cone when the volume of the water in the tank is 27·π cubic feet is given as follows;

1/3×π×r²×h = 27·π ft³

The ratio of the height to the radius of the cone is h/r = 15/5 = 3

h/r = 3

∴ r =h/3

The volume of the cone, V = 1/3×π×r²×h = 1/3×π×(h/3)²×h = 1/27×π×h³ = h³/27×π

dV/dt = dV/dh × dh/dt

Which gives;

12 = d(h³/27×π)/dh × dh/dt = π×h²/9 × dh/dt

dh/dt = 12/(π×h²/9)

At 27·π ft³ = 1/27×π×h³ ft³, we have;

27 = 1/27×h³

27² = h³

h = ∛27² = 9

∴ dh/dt = 12/(π×h²/9) = 12/(π×9²/9) = 12/(π×9) = 4/(3·π) ≈ 0.4244 ft/hour

The rate at which the height of the water tank is changing ≈ 0.4244 ft/hour.

6 0

3 years ago

A doctor is interested in people who have experienced an unexplained episode of vitamin D intoxication. She took a SRS of size 1

Mila [183]

Answer:

(a) (2.573, 3.167) is the 99% confidence interval for $\mu$ the true mean calcium level of the population of people who experienced an unexplained episode of vitamin D intoxication.

(b) There is a 99% probability that the average calcium level of all people who have experienced an unexplained episode of vitamin D intoxication is in the interval.

Step-by-step explanation:

If we have a random sample of size n from a normal distribution with mean $\mu$ and standard deviation $\sigma$ , then we know that $\bar{X}$ is normally distributed with mean $\mu$ and standard deviation $\sigma/n$ . Therefore we can use $(\bar{X}-\mu)/\frac{\sigma}{\sqrt{n}}$ as a pivotal quantity.

We have a sample size of n = 12. The sample mean is $\bar{x}$ = 2.87 mmol/l and the standard deviation is $\sigma = 0.40$ . The confidence interval is given by $\bar{x}\pm z_{\alpha/2}(\frac{\sigma}{\sqrt{n}})$ where $z_{\alpha/2}$ is the $\alpha/2$ th quantile of the standard normal distribution. As we want the 99% confidence interval, we have that $\alpha = 0.01$ and the confidence interval is $2.87\pm z_{0.005}(\frac{0.40}{\sqrt{12}})$ where $z_{0.005}$ is the 0.5th quantile of the standard normal distribution, i.e., $z_{0.005} = -2.5758$ . Then, we have $2.87\pm (-2.5758)(\frac{0.40}{\sqrt{12}})$ and the 99% confidence interval is given by (2.573, 3.167)

(b) We found a 99% confidence interval for the true mean calcium level of the population of people who experienced an unexplained episode of vitamin D intoxication. Therefore, there is a 99% probability that the average calcium level of all people who have experienced an unexplained episode of vitamin D intoxication is in the interval.

8 0

3 years ago

Help please!!! 10 points

Sever21 [200]

Answer:

the y intercept is 0

Step-by-step explanation:

y=5x

there is a 0 as y inter

8 0

4 years ago

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