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3 years ago

If v1 = (2,-5) and v2 = (4,-3), then the angle between the two vectors is _________. Round your answer to two decimal places.

1 answer:

3 0

The angle between two vectors is given by:
cos (x) = (v1.v2) / (lv1l * lv2l)
We have then:
v1.v2 = (2, -5). (4, -3)
v1.v2 = (2 * 4) + (-5 * (- 3))
v1.v2 = 8 + 15
v1.v2 = 23
We look for the vector module:
lv1l = root ((2) ^ 2 + (-5) ^ 2)
lv1l = 5.385164807
lv2l = root ((4) ^ 2 + (-3) ^ 2)
lv2l = 5
Substituting values:
cos (x) = (23) / ((5.385164807) * (5))
x = acos ((23) / ((5.385164807) * (5)))
x = 31.33 degrees
Answer:
The angle between the two vectors is:
x = 31.33 degrees

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To write a decimal in word form, we write out the words we would say as we read the decimal. When we read a decimal, we read the whole number before the decimal. This is "two." The decimal is read as "and." After this, we read the digits behind the decimal as a group; 51 would be read as "fifty-one", and since 1 is in the hundredths place, it is "fifty-one hundredths."

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3 years ago

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Step-by-step explanation:

We can set up the following equation:

$\frac{80}{100} = \frac{36}{N}$

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Let's first multiply both sides by $N$ :

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Finally, let's divide both sides by $80$ :

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Step-by-step explanation:

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3 years ago

A school is taking a field trip with 195 students and 10 adults. Each bus can hold at most 40 students. We need to determine the

Alex777 [14]

Answer:

$40n>195+10$

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Step-by-step explanation:

The equality must satisfy the following:

A total of 195 students and 10 adults with 40 students per bus at most.

If the students it can take is at most 40, we must consider the adults as well. This maximum excludes the adults so therefore the actual amount of students must be less the 40 to allow adults on the bus as well.

$40n>195+10$

We can solve for n:

$40n>205$

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