Compute the magnitude and direction of the sum of the two vectors: 170N of force at 87° and 100N of force at 46°.

F = 254.08N Θ = 72.03°

Step-by-step explanation:

First of all we find the resolution in both x and y axis

∑Fx = 170cos87 + 100cos46 = 78.36N

∑Fy = 170sin87 + 100sin46 = 241.70N

To find the resultant vector we use pythagorean theorem

F = √(∑Fx)² + ∑(Fy)²

F = √(78.36² + 241.70²)

F = √(64559.1796)

F = 254.08N

the angle between both force can be obtained using

tanθ = ∑Fy / ∑Fx

tanθ = 241.70 / 78.36

tanθ = 3.084

Θ = tan⁻ 3.084

Θ = 72.03°

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

add 5 subtract 1

step-by-step explanation: