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3 years ago

A circular garden has a diameter of 9 feet. How many feet of trim are

1 answer:

4 0

Needing to find the circumference of a circle you you find that you need to use the equation C=2 π R
C= 28.26
this is how much fence they would need around the garden approximately.

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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

If I was asked to think of a number and multiply it by 2, I could

finlep [7]

Answer:

4(2x-3)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

6 times the sum of a number and 7 is 18

lutik1710 [3]

The simplest way to find this number is to add your two known values (7 and 6) which should be 13. Now you should subtract it from 18. (18-13). That should equal to 5, which is your answer.

5 0

3 years ago

Read 2 more answers

I needddddddd helppppppp.

Setler [38]

Answer:

129

Step-by-step explanation:

34+17 = 51

180 - 51 = 129

4 0

3 years ago

Suppose that two teams are playing a series of games, each of which is independently won by team A with probability p and by tea

Lady_Fox [76]

Answer:

4 games played = 1/56

5 games played = 5/56

6 games played = 15/56

7 games played = 35/56

Step-by-step explanation:

The probability of each time winning is 0.5

So there are a couple of ways the series could go.

Team A could win all first 4 matches. We can depict this as A-A-A-A
Team A could win 4, while having lost 1. Lets depict this a A-B-A-A-A
Team A could win 4, while having lost 2. A-B-B-A-A-A
Team A could win 4, while having lost 3. A-B-B-B-A-A-A

These 4 possibilities could be repeated with B winning as well. It should be noted that these are the only ways for the series to end. We find the number of permutations of each possibility above to find their probability.

I advise you to study 'how to permute identical objects' for this.

These permutations are stated below:

1. 4!/4! = 1

2. $\frac{5!}{4! * 1!}$ = 5

3 $\frac{6!}{4! * 2!}$ = 15

4 $\frac{7!}{4! * 3!}$ = 35

These are they ways A or B could win. The total is 1+5+15+35 = 56. The answer given thus reflects the possibilities.

4 0

4 years ago