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blsea [12.9K]
3 years ago
6

The power P required to do a fixed amount of work varies inversely as the time t. If a power of 15 J/h is required to do a fixed

amount of work in 2 hours, what is the power required to do the same work in 1 hour?
Mathematics
2 answers:
Ann [662]3 years ago
6 0

Answer: the power required to do the same work in 1 hour is 30 j/h

Step-by-step explanation:

If two variables vary inversely, an increase in one of the variables causes a decrease in the other variable and vice versa.

The power P required to do a fixed amount of work varies inversely as the time t. If we introduce a constant of variation, k, the expression would be

P = k/t

If a power of 15 J/h is required to do a fixed amount of work in 2 hours, it means that

15 = k/2

k = 15 × 2 = 30

The equation becomes

P = 30/t

Therefore, the power required to do the same work in 1 hour is

P = 30/1 = 30 j/h

Ira Lisetskai [31]3 years ago
4 0

Answer:

7.5

Step-by-step explanation:

if 2h =15j/h

then 1h=1/2 *15

=7.5

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Step-by-step explanation:

Consider the provided information.

A coin is flipped eight times where each flip comes up either heads or tails.

Part (a) How many possible outcomes are there in total?

Each time we flip a coin it comes up either heads or tail.

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Part (b) contain exactly three heads?

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According to the definition of combination: \binom{n}{r}=\frac{n!}{r!(n-r)!}

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Hence, there are 56 possible outcomes contain exactly three heads.

Part (c) contain at least three heads?

For 3 heads: \binom{8}{3}=\frac{8!}{3!(5)!}=56

For 4 heads: \binom{8}{4}=\frac{8!}{4!(4)!}=70

For 5 heads: \binom{8}{5}=\frac{8!}{5!(3)!}=56

For 6 heads: \binom{8}{6}=\frac{8!}{6!(2)!}=28

For 7 heads: \binom{8}{7}=\frac{8!}{7!(1)!}=8

For 8 heads: \binom{8}{8}=1

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56+70+56+28+8+1=219

Hence, the possible outcomes contain at least three heads is 219.

Part (d) contain the same number of heads and tails?

Same number of heads and tails means that the value of r=4.

Therefore,

\binom{8}{4}=\frac{8!}{4!(4)!}=70

Hence, the possible outcomes contain the same number of heads and tails are 70.

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