Answer: 24.2° SouthWest
<u>Step-by-step explanation:</u>
First step: DRAW A PICTURE of the vectors from head to tail <em>(see image)</em>
I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.
<u>Perpendicular (x):</u>
cos 35° = adjacent/hypotenuse
cos 35° = x/160
→ x = 160 cos 35°
<u>Angle (θ):</u>
sin θ = opposite/hypotenuse
sin θ = x/320
sin θ = 160 cos 35°/320
θ = arcsin (160 cos 35°/320)
θ = 24.2°
Direction is down (south) and left (west)
We try to factor by maybe grouping
experiment
(x²y³-11x²y)+(6y²-66)
factor
x²y(y²-11)+6(y²-11)
undistribute (y²-11) from each
(x²y+6)(y²-11)
we can force a factor out of the 2nd group in the form of a difference of 2 perfect squares
(x²y+6)(y-√11)(y+√11)
either of those 3 are factors
Answer:
40
Step-by-step explanation:
Answer:
197,8879 N.
Step-by-step explanation:
The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.
The question given says that <em><u>Nancy</u></em> is <em><u>pushing</u></em> the statue with a force of<em><u> 120 N at a 60° angle to the horizontal</u></em> and <em><u>Harry</u></em> is <em><u>pulling</u></em> the statue with a force of <u><em>180 N at a 40° angle with the horizontal</em></u>.
With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.
The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.
F= (120 N cos 60°) + (180 N x cos 40°)
F= 197,8879 N