Question 1(Multiple Choice Worth 2 points)

Mathematics

2 answers:

adelina 88 [10]3 years ago

8 0

Answer:

5. $, \sqrt{73}$

6.132.47 pounds at 121.87°

Step-by-step explanation:

Question 1

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>

Question 2

Add the two vectors together:

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

u + v = <-6,-4>

Question 3

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.

$u=$

Question 4

Multiply both components of the vector by 8:

$8u=$

Question 5

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:

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

Question 6

See attached image.

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