Answer:
100 tickets were sold.
Step-by-step explanation:
If she bought 20 tickets and had a 20 percent chance of winning that means there were 100 sold tickets because 20 percent of 100 would be the 20 tickets she purchased.
No they cannot be simplified together from what I know
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.
Remark
I'm going to assume you are in the Northern Hemisphere.
Answer
A looks like you are beginning in Winter. The temperature is down quite a bit. That would be about October where I live. B is spring because the temperature is rising but not at it's peak. That would be about April May here.
C is summer. Glorious warm summer. June July and August.
D is autumn. The temperature is falling and it is just about at it's low peak again.
Answer:
77,000
Step-by-step explanation:
If 72,000 is 150% of direct labor, then direct labor is 48,000 (72000/1.5)
direct labor 48000
overhead. 72000
total. 120,000
total costs: 197,000
less total above: 120,000
=material costs. 77,000
