Physics, 26.02.2020 21:05 giovannymarvez16

How many di↵erent strings can be made from the letters in the work PEPPERCORN when all the letters are used? How may of the strings start and end with the letter P? How many strings have 3 consecutive Ps?

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Answer from: evafaith

Answer

a. 151,200 ways b. 10,080 ways c. 10,080 ways

Explanation:

a. How many different strings can be made from the letters in the work PEPPERCORN when all the letters are used?

Since there are 10 letters in the word PEPPERCORN, there are 10! ways of arranging them. Since we have 3 P's, there are 3! ways of arranging them . We have 2 E's, there are 2! ways of arranging them. We have 2 R's, there are 2! ways of arranging them. We have 1 O, there are ! ways of arranging them. We have 1 C, there are 1! ways of arranging them. We have 1 N, there are 1! ways of arranging them. So there are

$\frac{10!}{3!2!2!1!1!1!} = 151,200 ways$ of arranging the word

b. How may of the strings start and end with the letter P?

If the strings start and end with P, then we have 8 letters left including 1 P.

Since there are 8 letters left in the word PEPPERCORN, there are 8! ways of arranging them. Since we have 1 P, there are 1! ways of arranging them . We have 2 E's, there are 2! ways of arranging them. We have 2 R's, there are 2! ways of arranging them. We have 1 O, there are ! ways of arranging them. We have 1 C, there are 1! ways of arranging them. We have 1 N, there are 1! ways of arranging them. So there are

$\frac{8!}{2!2!1!1!1!1!} = 10,080 ways$ of arranging the word

c. How many strings have 3 consecutive Ps?

There are 8 different ways of arranging the P's consecutively. We are then left with 7 letters. Since there are 7 letters left in the word PEPPERCORN, there are 7! ways of arranging them. We have 2 E's, there are 2! ways of arranging them. We have 2 R's, there are 2! ways of arranging them. We have 1 O, there are ! ways of arranging them. We have 1 C, there are 1! ways of arranging them. We have 1 N, there are 1! ways of arranging them. So there are

$\frac{8!}{2!2!1!1!1!1!} = 10,080 ways$ of arranging the word

Answer from: Quest

Full change in the electric plus system

Answer from: Quest

W= fd
where f is an applied force and d is the distance over which it is applied. when a parachuting skydiver is at constant velocity, he is experiencing "terminal velocity", the point at which his acceleration down is canceled out by air resistance. that means that the resisting force of the air is equal to his weight, but in the opposite direction. with this, we can solve for the work done by the force.
w = fd
w = (92.0)(9.81 m/s^2) (325)
w= 2.93 x 10^5 j
the value for work in this case is positive because it is pushing up on the skydiver, who has a downward force of gravity.
therefore the answer is 2.93 x 10^5 j

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