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2 years ago

Which equation represents the sentence? Four more than a number is half the number.

1 answer:

5 0

A. n+4=n/2

B. cannot be the answer because it is subtracting instead of adding.

C. cannot be the answer because half of the number is supposed to go after the equal sign.

D. cannot be the answer because the half of the number part did not go before adding the number. Also, it's subtracting instead of adding.

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Let v = (v1, v2) be a vector in R2. Show that (v2, −v1) is orthogonal to v, and use this fact to find two unit vectors orthogona

andrey2020 [161]

Answer:

a. v.v' = v₁v₂ - v₁v₂ = 0 b. (20, -21)/29 and (-20,21)/29

Step-by-step explanation:

a. For two vectors a, b to be orthogonal, their dot product is zero. That is a.b = 0.

Given v = (v₁, v₂) = v₁i + v₂j and v' = (v₂, -v₁) = v₂i - v₁j, we need to show that v.v' = 0

So, v.v' = (v₁i + v₂j).(v₂i - v₁j)

= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)

= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

i.i = 1, i.j = 0, j.i = 0 and j.j = 1

So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

= v₁v₂ × 1 - v₁v₁ × 0 + v₂v₂ × 0 - v₂v₁ × 1

= v₁v₂ - v₂v₁

= v₁v₂ - v₁v₂ = 0

So, v.v' = 0

b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).

So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.

A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29

8 0

2 years ago

Rotations. Please help me

densk [106]

See the attached picture.

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2 years ago

121 is increased to 321 percent of change

valina [46]

Answer: This is the percentage increase.

Step-by-step explanation:

265.28925619834706%

7 0

3 years ago

One evening in snowed in several towns the number of inches of snow received are shown in the list below

Yuri [45]

Answer:

Please find the required line chart created with MS Excel

Step-by-step explanation:

Question:

The given data are;

3/4, 1 1/2, 2, 1 1/4, 3/4, 2, 1 1/2, 1 1/4, 1 1/2, 1/2, 1

In the question, it is required to create a line plot to represent the data

The given data can be sorted in ascending order in decimal form as follows;

0.5, 0.75, 0.75, 1, 1.25, 1.25, 1.5, 1.5, 1.5, 2

The line chart created with MS Excel is attached.

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3 years ago

What is the value x in 8+6y=9

Rashid [163]

Answer:

Do you mean y? if you did it should be 1/6 or 1.666666 repeating.

Step-by-step explanation:

I needed the 6y to = 1 so I did the inverse of it by and got 1 so y should = 1/6

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3 years ago