Step 1: learn to draw a free-body diagram. Read your school notes or look up a web site on the subject.
Step 2: Denote the angle of the ramp with the horizontal as theta=tan^(-1)(20/30)=33.69 degrees (approx.)
Step 3: denote the mass of the object as m=100 lb-mass.
Step 4: find force due to mass and gravity = -100g = -100 lb-force. (downwards), denoted by the vector F=(0,-100) lb-force.
Step 5: resolve force along incline:
Force parallel to incline = F1 = -100(cos(theta))
=-83.21 lb-force (negative => down the incline)
Step 6: resolve force perpendicular to incline
= F2 = -100(sin(theta)
=-55.47 lb-f (-ve =>into the incline)
By the way, this question is not calculus 3, but more mechanics, or physics. You have a better chance of getting answers if posted under "physics".
For starters,
tan(2θ) = sin(2θ) / cos(2θ)
and we can expand the sine and cosine using the double angle formulas,
sin(2θ) = 2 sin(θ) cos(θ)
cos(2θ) = 1 - 2sin^2(θ)
To find sin(2θ), use the Pythagorean identity to compute cos(θ). With θ between 0 and π/2, we know cos(θ) > 0, so
cos^2(θ) + sin^2(θ) = 1
==> cos(θ) = √(1 - sin^2(θ)) = 4/5
We already know sin(θ), so we can plug everything in:
sin(2θ) = 2 * 3/5 * 4/5 = 24/25
cos(2θ) = 1 - 2 * (3/5)^2 = 7/25
==> tan(2θ) = (24/25) / (7/25) = 24/7
Answer:
Brand A is the better buy
Step-by-step explanation:
bag Which is the better buy?
Step one
Brand A: $5 for 80 pounds of sand
Let us find the unit cost
Unit cost =5/80
=$0.0625 per pound
Brand B: $14 for 175 pound
The unit cost is
=14/175
=$0.08 per pound
Answer:
angle x is an exterior angle of the triangle
