Answer:
PY = 8
Step-by-step explanation:
Lets run down the other three to show why they're wrong
<em>MY=8</em>
By P.T, that's wrong (PERPENDICULAR)
<em>PM=MY </em>
We can't prove that with the given
XY=42
Again, by P.T., this is false
BTW: You can prove PY=8 by proving XMP congruent to YMP by SAS
The final answer should be
2x^3 - 2x^2 + 4x + 5
hope this helps!
Answer:
Second option 1.6x10^14
Step-by-step explanation:
x*y' + y = 8x
y' + y/x = 8 .... divide everything by x
dy/dx + y/x = 8
dy/dx + (1/x)*y = 8
We have something in the form
y' + P(x)*y = Q(x)
which is a first order ODE
The integrating factor is
Multiply both sides by the integrating factor (x) and we get the following:
dy/dx + (1/x)*y = 8
x*dy/dx + x*(1/x)*y = x*8
x*dy/dx + y = 8x
y + x*dy/dx = 8x
Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).
Since (xy)' turns into y + x*dy/dx, and vice versa, this means
y + x*dy/dx = 8x turns into (xy)' = 8x
Integrating both sides with respect to x leads to
xy = 4x^2 + C
y = (4x^2 + C)/x
y = (4x^2)/x + C/x
y = 4x + Cx^(-1)
where C is a constant. In this case, C = -5 leads to a solution
y = 4x - 5x^(-1)
you can check this answer by deriving both sides with respect to x
dy/dx = 4 + 5x^(-2)
Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.
Answer:
1500 ft²
Step-by-step explanation:
The sum of two adjacent sides of the pasture is half the perimeter (160 ft/2 = 80 ft), so the side adjacent to the 50 ft side will be 80 ft - 50 ft = 30 ft.
The product of adjacent sides of a rectangle gives the area of the rectangle. That area will be ...
area = (50 ft)(30 ft) = 1500 ft²