The Jacobian for this transformation is
with determinant 
, hence the area element becomes
Then the integral becomes
where 
is the unit circle,
so that
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
Then
Answer:
x = 115 - p
Step-by-step explanation:
generally in algebra you will use the letter "x" to represent a value you do not know, so it wants an algebraic expression for "p subtracted from 115", this can be rewritten as 115 - p. So the unknown value "x" is equal to 115 - p.
An applicable equation of a vertical parabola in vertex form is:
y-k = a(x-h)^2
Let x=2, y=4, h=-1 and k=-1, where (h,k) is the vertex. Then,
4-(-1) = a(2-[-1])^2, which becomes 5 = a(9). Therefore, a = 5/9, and the
equation of the parabola is
y+1 = (5/9)(x+1)
For this case, the first thing we must do is define a variable.
We have then:
x: unknown number
We now write the equation that models the problem:
From here, we clear the value of x.
We multiply both sides of the equation by 2:
We subtract 30 on both sides of the equation:
Answer:
The value of the unknown number is given by:
