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Zina [86]
3 years ago
9

15, Evaluate 6 choose 4.

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
4 0

Answer:  The required result is 15.

Step-by-step explanation:  We are given to evaluate the following :

"6 choose 4".

Since we are to choose 4 from 6, so we have to use the combination of 6 different things chosen 4 at a time.

We know that

the formula for the combination of n different things chosen r at a time is given by

^nC_r=\dfrac{n!}{r!(n-r)!}.

For the given situation, n = 6  and  r = 4.

Therefore, we get

^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6!}{4!2!}=\dfrac{6\times5\times4!}{4!\times2\times1}=15.

Thus, the required result is 15.

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Picture provided help!
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Answer:

A -60i - 14j

Step-by-step explanation:

u = -9i + 8j

v = 7i + 5j

2u = 2(-9i + 8j) = -18i + 16j

6v = 6(7i + 5j) = 42i + 30j

2u - 6v

(-18i + 16j) - (42i + 30j)

(-18i - 42i) + (16j-30j)

-60i - 14j

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A child lies on the ground and looks up at the top of a 17-ft tree nearby. The child is 14 ft away from the tree. What is the an
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3 years ago
A pair of tow trucks are pulling on a trailer that is stuck
Varvara68 [4.7K]

Answer:

R=10,244 Lb

Step-by-step explanation:

In order to solve this problem, we can start by drawing the situation. (See attached picture).

We can look at the forces applied by the trucks as vectors, so in this case, in order to find the resultant force, we can add the two vectors. You can do so by drawing one force after the other and join the start of the first force with the end of the second force to form a triangle. The missing side will be the resultant force. In that triangle I drew there, the inner angle will be found by subtracting 180°-110°=70°

In this case we can find the resultant force by using the law of cosines:

A^{2}=B^{2}+C^{2}-2AB cos \alpha

so we can use the data given by the problem:

R^{2}=T_{1}^{2}+T_{2}^{2}-2T_{1}T_{2} cos \alpha

so we can solve this for R, so we get:

R=\sqrt{T_{1}^{2}+T_{2}^{2}-2T_{1}T_{2} cos \alpha}

now we can substitute:

R=\sqrt{(10,000Lb)^{2}+(7,500Lb)^{2}-2(10,000Lb)(7,500Lb) cos (70^{0})}

which yields:

R=10,244Lb

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