Determine the magnitude of the vector sum v = v1 + v2 and the angle θx which v makes with the positive x-axis. complete both graphical and algebraic solutions.

Let  θ be the angle V1 makes with x axis and θ2

√√√To start, we have  

Tan θ = 3/6=1/2

From there, do some quick manipulation to find sin θ1 and cosθ1  

So we have v1= (9 cos θ1and 9 sin θ1)=(8.05,4.02)

Now, v2 makes an angle of 1800- 630=1170=θ2with x axis so we have  

V2=(12 cosθ2,12sinθ2)=(-5.45,10.69)

From there, we have  

V=v1+v2=(2.60,14.71)

Now it’s a simply a matter of finding /v/=  √2.602+14.712

=14.9

Θx=arctan(14.71/2.6)=80°

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d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.