F ( x ) = k * x²
f ( 4 ) = 96
96 = k * 4²
96 = 16 k
k = 96 : 16
k = 6
f ( 2 ) = 6 * 2² = 6 * 4 = 24
Answer: D ) 24
The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.
Solution:
<u>Note that:</u>
- 2πrh + 2πr² = Area of cylinder formula
- Radius = 4 m
- Height = 8 m
<u>Finding the surface area:</u>
- 2πrh + 2πr²
- => 2(π)(4)(8) + 2(π)(4²)
- => 64π + 2(π)(16)
- => 64π + 32π
- => 96π m²
Im guessing that it's 4 because it said round it to the ones place and 3 is in the ones place and 8 is grater that five so 4 should be you answer
