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2 years ago

If a cone has a radius of 6 cm and the height of 18 cm what is it's volume ?

Mathematics

1 answer:

VLD [36.1K]2 years ago

4 0

The volume is V≈678.58cm³

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A fair die is rolled repeatedly. find the expected number of rolls until all 6 faces appear.

Makovka662 [10]

Each face has a chance of 1/6
So you beed 6 rolls

8 0

3 years ago

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca

Hitman42 [59]

Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

$\frac{dQ}{dt} = -rt$

Which has the following solution:

$Q(t) = Q(0)e^{-rt}$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that $Q(6) = (1-0.03)Q(0) = 0.97Q(0)$ . We use this to find r.

$Q(t) = Q(0)e^{-rt}$

$0.97Q(0) = Q(0)e^{-6r}$

$e^{-6r} = 0.97$

$\ln{e^{-6r}} = \ln{0.97}$

$-6r = \ln{0.97}$

$r = -\frac{\ln{0.97}}{6}$

$r = 0.0051$

$Q(t) = Q(0)e^{-0.0051t}$

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.0051t}$

$0.5Q(0) = Q(0)e^{-0.0051t}$

$e^{-0.0051t} = 0.5$

$\ln{e^{-0.0051t}} = \ln{0.5}$

$-0.0051t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0051}$

$t = 135.9$

The half-life of the radioactive substance is 135.9 hours.

6 0

2 years ago

400ml of squash is made by mixing 50ml of cordial with water. what fraction of the drink is water?

olga55 [171]

7/8 of that drink is water because 50 ml is 1/8 of 400 so the other 7/8 is water

8 0

2 years ago

What is 17x-2xy+3x+10xy

BlackZzzverrR [31]

The answer is 14x + 8xy

8 0

3 years ago

Read 2 more answers

If x is 6, What is X+4

hichkok12 [17]

Answer:

x = 10

Step-by-step explanation:

We know x = 6

asked: x + 4

Plus it in =>

6 + 4

=> 10

8 0

3 years ago