I would say 90 degrees. I say this because triangles always will equal 180 so 60 + 30 = 90 and 180 - 90 = 90 degrees!!
Maybe its right. Maybe its wrong!
Answer:
The inner function is
.
The outer function is
.
![\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20y%5E%7B%5Cprime%7D%20%3D%20%5Csec%5E%7B2%7D%28u%29%2A%5Cpi%20%3D%20%5Cpi%5Csec%5E%7B2%7D%7B%5Cpi%20x%7D)
Step-by-step explanation:
The inner function is the one we apply the outer function to.
So
![y = \tan{\pi x}](https://tex.z-dn.net/?f=y%20%3D%20%5Ctan%7B%5Cpi%20x%7D)
We apply the outer function tangent to
.
So, the inner function is
.
The outer function is
.
The derivative of a compositve function
in which
is given by the following function.
![y^{\prime} = f^{\prime}(u)*g^{\prime}(x)](https://tex.z-dn.net/?f=y%5E%7B%5Cprime%7D%20%3D%20f%5E%7B%5Cprime%7D%28u%29%2Ag%5E%7B%5Cprime%7D%28x%29)
So
![f(u) = \tan{u}](https://tex.z-dn.net/?f=f%28u%29%20%3D%20%5Ctan%7Bu%7D)
![f^{\prime}(u) = \sec^{2}{u}](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28u%29%20%3D%20%5Csec%5E%7B2%7D%7Bu%7D)
![u = g(x) = \pi x](https://tex.z-dn.net/?f=u%20%3D%20g%28x%29%20%3D%20%5Cpi%20x)
![g^{\prime}(x) = \pi](https://tex.z-dn.net/?f=g%5E%7B%5Cprime%7D%28x%29%20%3D%20%5Cpi)
So
![y^{\prime} = f^{\prime}(u)*g^{\prime}(x)](https://tex.z-dn.net/?f=y%5E%7B%5Cprime%7D%20%3D%20f%5E%7B%5Cprime%7D%28u%29%2Ag%5E%7B%5Cprime%7D%28x%29)
![\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20y%5E%7B%5Cprime%7D%20%3D%20%5Csec%5E%7B2%7D%28u%29%2A%5Cpi%20%3D%20%5Cpi%5Csec%5E%7B2%7D%7B%5Cpi%20x%7D)
1.A) Any number x multiplied by
will be less than the original x.
1.B)
= 1, so B
= 1.5, so F
The rest are similar.
2) There are 4 quarts in a gallon, so calculate the number for 2 gallons.
3) 4 ÷
is the same as 4 × 6
4) Follow PEMDAS rules, Parenthesis first, division and multiplication next, then finally addition.
10235
I just typed it in a calculator
the answer is in the above image
Answer:
- 150π ft²
- 10π ft.
Step-by-step explanation:
Area of the sector :
![Area (sector) = \pi r^{2} \times \frac{\theta}{360^{o}}](https://tex.z-dn.net/?f=Area%20%28sector%29%20%3D%20%5Cpi%20r%5E%7B2%7D%20%5Ctimes%20%5Cfrac%7B%5Ctheta%7D%7B360%5E%7Bo%7D%7D)
Finding the area given r = 30 ft. and θ = 60° :
⇒ Area = π × (30)² × 60/360
⇒ Area = π × 900/6
⇒ Area = 150π ft²
===========================================================
Length of the arc :
![Length (arc) =2 \pi r} \times \frac{\theta}{360^{o}}](https://tex.z-dn.net/?f=Length%20%28arc%29%20%3D2%20%5Cpi%20r%7D%20%5Ctimes%20%5Cfrac%7B%5Ctheta%7D%7B360%5E%7Bo%7D%7D)
Finding the arc length given r = 30 ft. and θ = 60° :
⇒ Arc Length = 2 × π × 30 × 60/360
⇒ Arc Length = 60/6 × π
⇒ Arc Length = 10π ft.