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grin007 [14]
3 years ago
15

Question 1(Multiple Choice Worth 2 points)

Mathematics
2 answers:
adelina 88 [10]3 years ago
8 0

Answer:

1.

2.

3.

4.

5., \sqrt{73}

6.132.47 pounds at 121.87°

Step-by-step explanation:

<u>Question 1</u>

Find 4u and 3v seperately by simply multiplying the constant with each part of the vector:

4u = <28,-12>

3v = <-27,15>

Then, 4u - 3v =  <55,-27>

<u>Question 2</u>

Add the two vectors together:

u + v = <-3-3,-5+1>

u + v = <-6,-4>

<u>Question 3</u>

Consider vector u as a triangle of which the short sides have lengths of 3 and 4. Using Pythagoras, the length of the vector(the hypotenuse of the triangle) can be calculated as 5. A unit vector has a length of 1 along its hypotenuse. To convert the vector to a unit vector, everything has to be divided by five.

u=

<u>Question 4</u>

Multiply both components of the vector by 8:

8u=

<u>Question 5</u>

Vector PQ has two end points, P=(5,9) and Q=(13,12)

The vector is basically a line drawn between the two points

Thus, the lengths in both the x and y direction can be found by subtracting one from the other:

PQ=<13-5,12-9>

PQ=<8,3>

The magnitude is considered as the hypotenuse of a traingle with short sides of 8 and 3. Using Pythagoras the magnitude can be solved:

L_{pq}^{2} = 8^{2} + 3^{2} \\L_{pq}^{2} = 73\\L_{pq} = \sqrt{73}

<u>Question 6</u>

See attached image.

y_{2} =-150sin(30)=-75\\x_{2} =-150cos(30)=-129.9\\y_{1} =-75sin(30)=-37.5\\x_{1} =75cos(30)=64.95\\\\F_{1}+F_{2}  =\\\\F_{mag} =\sqrt{64.95^{2} +112.5^{2} } \\F_{mag}=132.47\\sin(\alpha )=\frac{112.5}{132.47} \\\alpha =58.13^{o} \\\\180-58.13=121.87^{o}

TEA [102]3 years ago
6 0

Answer:

(55,-23)

Step-by-step explanation:

You multitiply it and then divied it by that number.

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