Anytime you have a triangle (right triangles are preferred) where at least 2 angle measures and 1 side is known. Or, at least two sides and 1 angle measure.
OR..... 3 sides or three angles are known. So, sines or cosines could be used at almost anytime to find the sides and angles of a triangle!
Answer:
The height of the tent = 3 feet
Step-by-step explanation:
Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 36 feet^3. Syrus isn't sure if the tent will be tall enough for him to sit up inside. The tent is the shape of triangular prism whose length is 6 feet and width is 4 feet. What is the height of the tent?
Given:
Length of the tent = 6 feet
Width of the tent = 4 feet
Volume of the tent = 36
Solution:
Since the ten is in shape of triangular prism, so the volume of traingular prism is given as:
where represents length, represents width and represents height of the prism.
Plugging in the know values of the dimension of the tent and the volume to find the height of the tent.
Simplifying.
\frac{36}{12}=\frac{12h}{12}
3=h
∴ h=3
Thus, the height of the tent = 3 feet
Answer:
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Step-by-step explanation:
Arc length of a parametric curve is:
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
x = t + cos t, dx/dt = 1 − sin t
y = t − sin t, dy/dt = 1 − cos t
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Or, if you wish to simplify:
L = ∫₀²ᵖⁱ √(1 − 2 sin t + sin²t + 1 − 2 cos t + cos²t) dt
L = ∫₀²ᵖⁱ √(3 − 2 sin t − 2 cos t) dt
The answer is C. when you have questions like these, its best to plug in an easy number and test it out.
Say the original radius was 2. That means the area of that sprinkler was 12.56 (if you use the formula Pi(radius)squared.
a number 3 times bigger then 2, is 6. (2 times 3 = 6) There fore, following the same formula as before, you plug that number in and get 113.04 as the area of the new sprinkler.
113.04 divided by 12.56 is 9
Simplified as a decimal could be 0.02
