If v lies in the first quadrant and makes an angle π/3 with the positive x-axis and |v| = 8, find v in component form.
1 answer:
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The product of 8 and 5/7 is 5.7
<u>Step-by-step explanation:</u>
The given product is .
<u>In the product, two terms are given :</u>
- The first term 8 is a whole number.
- The second term 5/7 is a fraction.
1) So, to find the product of the first term and the second term, one method is to simplify the fraction into decimal number and then perform multiplication operation.
2) Either you can multiply the two terms in the first step and then the division operation is performed at the final step.
<u>First method :</u>
<u><em>Step 1 :</em></u> Convert the fraction into decimal
⇒ 5/7 = 0.71
<u><em>Step 2 :</em></u> Multiply the result with the other term.
⇒ 8 × 0.71
⇒ 5.68 (approximately 5.7)
<u>Second method :</u>
<u><em>Step 1 :</em></u> Multiply both the terms
⇒ 8 ×(5/7) = 40/7
<u><em>Step 2 :</em></u> divide 40 by 7
⇒ 40÷ 7 = 5.7
Therefore, the product of 8 and 5/7 is 5.7
The
formula , where r! is 1*2*3*...r
is the formula which gives us the total number of ways of forming groups of r objects, out of n objects.
for example, given 10 objects, there are C(10,6) ways of forming groups of 6, out of the 10 objects.
<span>The sample space S in our problem is as follows: </span>
triples selected from 5 freshmen, 4 sophomores, and 4 juniors, so that at least 1 freshman is selected.
The selection of 1 freshman can be done in 5 ways. The selection of the remaining 2 out of 4 freshmen (one is already chosen), 4 sophomores, and 4 juniors can be done in C(12, 2) many ways.
So there are in total, 5*66= 330 possible triples.
n(S)=330
The event E "selecting 2 freshmen and 1 junior" can occur in :
many ways.
so n(E)=40
P(E)=n(E)/n(S)=40/330=0.12
Answer: 0.12