Using the given formula, we solve for r:
\(\displaystyle{V}=π{r}²{h}\)

Divide both sides by πh \(\displaystyle\frac{{V}}{

Divide both sides by πh \(\displaystyle\frac{{V}}{

Question

asked 2021-01-06

A cylinder has a surface area of 748 cm² and a radius of 7 cm. Estimate the volume of the cylinder to the nearest whole number.

asked 2020-11-01

Scientists are working with a sample of cobalt-56 in their laboratory. They begin with a sample that has 60 mg of cobalt-56, and they measure that after 31 days, the mass of cobalt-56 sample is 45.43 mg. Recall that the differential equation which models exponential decay is \(\frac{dm}{dt}=-km\) and the solution of that differential equation if \(m(t)=m_0e^{-kt}\), where \(m_0\) is the initial mass and k is the relative decay rate.

a) Use the information provided to compute the relative decay rate k. Show your calculation (do not just cit a formula).

b) Use the information provided to determine the half-life of cobalt-56. Give your answer in days and round to the second decimal place. Show your calculation (do not just cite a formula).

c) To the nearest day, how many days will it take for the initial sample of 60mg of cobalt-56 to decay to just 10mg of cobalt-56?

d) What will be the rate at which the mass is decaying when the sample has 50mg of cobalt-56? Make sure to indicate the appropriate units and round your answer to three decimal places.

a) Use the information provided to compute the relative decay rate k. Show your calculation (do not just cit a formula).

b) Use the information provided to determine the half-life of cobalt-56. Give your answer in days and round to the second decimal place. Show your calculation (do not just cite a formula).

c) To the nearest day, how many days will it take for the initial sample of 60mg of cobalt-56 to decay to just 10mg of cobalt-56?

d) What will be the rate at which the mass is decaying when the sample has 50mg of cobalt-56? Make sure to indicate the appropriate units and round your answer to three decimal places.

asked 2020-11-22

Scientists are working with a sample of cobalt-56 in their laboratory. They begin with a sample that has 60 mg of cobalt-56, and they measure that after 31 days, the mass of cobalt-56 sample is 45.43 mg. Recall that the differential equation which models exponential decay is \(\displaystyle{\frac{{{d}{m}}}{{{\left.{d}{t}\right.}}}}=-{k}{m}\) and the solution of that differential equation if \(\displaystyle{m}{\left({t}\right)}={m}_{{0}}{e}^{{-{k}{t}}}\), where \(\displaystyle{m}_{{0}}\) is the initial mass and k is the relative decay rate.

a) Use the information provided to compute the relative decay rate k. Show your calculation (do not just cit a formula).

b) Use the information provided to determine the half-life of cobalt-56. Give your answer in days and round to the second decimal place. Show your calculation (do not just cite a formula).

c) To the nearest day, how many days will it take for the initial sample of 60mg of cobalt-56 to decay to just 10mg of cobalt-56?

d) What will be the rate at which the mass is decaying when the sample has 50mg of cobalt-56? Make sure to indicate the appropriate units and round your answer to three decimal places.

a) Use the information provided to compute the relative decay rate k. Show your calculation (do not just cit a formula).

b) Use the information provided to determine the half-life of cobalt-56. Give your answer in days and round to the second decimal place. Show your calculation (do not just cite a formula).

c) To the nearest day, how many days will it take for the initial sample of 60mg of cobalt-56 to decay to just 10mg of cobalt-56?

d) What will be the rate at which the mass is decaying when the sample has 50mg of cobalt-56? Make sure to indicate the appropriate units and round your answer to three decimal places.

asked 2021-02-21

A sphere and a cone have the same volume, and each has a radius of 6 centimeters. What is the height of the cone?

asked 2021-02-25

A plane intersects the center of a spere with a volume of about 11.3 m3. What is the area of the cross-section? Round to the nearest tenth.

asked 2021-03-09

The volume of a sphere is 5,572.45 in^3. To the nearest inch, what is the radius of the sphere?

asked 2020-12-29

Marks will be awarded for accuracy in the rounding of final answers where you are asked to round. To ensure that you receive these marks, take care in keeping more decimals in your intermediate steps than what the question is asking you to round your final answer to.

A fair 7 -sided die with the numbers 1 trough 7 is rolled five times. Express each of your answers as a decimal rounded to 3 decimal places.

(a) What is the probability that exactly one 3 is rolled?

(b) What is the probability that at least one 3 is rolled?

(c) What is the probability that exactly four of the rolls show an even number?

A fair 7 -sided die with the numbers 1 trough 7 is rolled five times. Express each of your answers as a decimal rounded to 3 decimal places.

(a) What is the probability that exactly one 3 is rolled?

(b) What is the probability that at least one 3 is rolled?

(c) What is the probability that exactly four of the rolls show an even number?

asked 2021-02-10

A games shop sells marbles
in clear plastic cylinders.
Four marbles fit across the
diameter of the cylinder, and
10 marbles fit from the base
to the top of the cylinder.
Each marble has a diameter
of 2cm2cm. What is the area of
the plastic that is needed to
nake one cylinder?

asked 2021-03-18

Soda is sold in aluminum cans that measure 4.83 inches in height and 2.6 inches in diameter. Use 3.14 for. What is the volume?

asked 2021-01-15

The height of the cone 19 ft and the radius is 9 ft, what is the volume?