Answer:
h = 10sin(π15t)+35
Step-by-step explanation:
The height of the blade as a function f time can be written in the following way:
h = Asin(xt) + B, where:
B represets the initial height of the blade above the ground.
A represents the amplitud of length of the blade.
x represents the period.
The initial height is 35 ft, therefore, B = 35ft.
The amplotud of lenth of the blade is 10ft, therefore A = 10.
The period is two rotations every minute, therefore the period should be 60/4 = 15. Then x = 15π
Finally the equation that can be used to model h is:
h = 10sin(π15t)+35
Answer:

Step-by-step explanation:
=> 5x-4+2(x-4) = 16
Expanding the brackets
=> 5x-4+2x-8 = 16
Combining like terms
=> 5x+2x-4-8 = 16
=> 7x - 12 = 16
Adding 12 to both sides
=> 7x = 16+12
=> 7x = 28
Dividing both sides by 7
=> x = 4
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take

, so that

and we're left with the ODE linear in

:

Now suppose

has a power series expansion



Then the ODE can be written as


![\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%5Cge2%7D%5Cbigg%5Bn%28n-1%29a_n-%28n-1%29a_%7Bn-1%7D%5Cbigg%5Dx%5E%7Bn-2%7D%3D0)
All the coefficients of the series vanish, and setting

in the power series forms for

and

tell us that

and

, so we get the recurrence

We can solve explicitly for

quite easily:

and so on. Continuing in this way we end up with

so that the solution to the ODE is

We also require the solution to satisfy

, which we can do easily by adding and subtracting a constant as needed:
Answer:
d
Step-by-step explanation:
formula for area of a triangle is base * width * 1/2