This is a question of resolving the forces in question into horizontal and vertical and then finding the action of the resultant force.
The first force acts at an angle less than 90° and thus its resolved forces are positive. The second force acts at angle larger than 90° and is incident and thus its horizontal value is positive while its vertical value is negative.
Therefore;
For force of 300 N at 30°;
Horizontal value = 300*Cos 30 = 259.81 N
Vertical value = 300*Sin 30 = 150 N
For 150 N at 135°;
Horizontal value = 150*Cos (180-135) = 106.07 N
Vertical value = -150*Sin (180-135) = -106.07 N
Then,
Resultant horizontal value = 259.81+106.07 = 365.88 N
Resultant vertical value = 150-106.07 = 43.93 N
Therefore,
Resultant force, v = Sqrt (365.88^2+43.93^2) = 368.51 N
Angle of action measured from horizontal = tan ^-1(43.93/365.88) 6.85°
Then,
v = 368.51 N at 6.85° from horizontal
Length multiplied by Width is Area, or A = L x W. 5/9 x 7/8 is your answer.
Answer:
50.8°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between side lengths and trig functions for a right triangle. Here, you are given the short side and the hypotenuse, and asked for the largest acute angle.
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The short side is adjacent to the largest acute angle, so the relevant relation is ...
Cos = Adjacent/Hypotenuse
cos(β) = (2√6)/(2√15) = √0.4
The angle measure is found using the inverse cosine function:
β = arccos(√0.4) ≈ 50.8°
The larger acute angle is about 50.8°.
Please, use "^" to denote exponentiation. Your 2x2 should be written as 2x^2.
Your relationships are then f(x,y)=2x^2+3y^2-4x-2
and x^2 + y^2 <span>≤ 16
Please note that the 2nd relationship represents a circle of radius 4 whose entire interior has been shaded.
Graph this. Then, rewrite f(x,y) in the form f(x,y) = 2x^2 - 4x + 3y^2 -2. Can you identify the shape of the curve in the xy plane representing this function? You'll need to find the points (x,y) in which the graph of f(x,y) intersects the shaded circle x^2 + y^2 </span><span>≤ 16.
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Think: what do "extreme values of f"
