Answer:
<u>The area of the circular garden is 28.3 square feet</u>
Step-by-step explanation:
Let's recall that the area of a circle is π * r², therefore if the diameter of the circular garden is 6 feet, the area is:
Diameter = 6 feet ⇒ radius = (6/2) = 3 feet
Area of the circular garden = π * 3²
Area of the circular garden = 3.1416 * 9
Area of the circular garden = 28.2744
<u>Area of the circular garden = 28.3 square feet</u>
(7-1/8) - (1-7/8) = 57/8 -15/8 = 21/4
The slope is 10. For every 1 increase in x, y increases by 10.
Answer:
yp = -x/8
Step-by-step explanation:
Given the differential equation: y′′−8y′=7x+1,
The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)
First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;
y′′−8y′=0
The auxiliary equation will give us;
m²-8m = 0
m(m-8) = 0
m = 0 and m-8 = 0
m1 = 0 and m2 = 8
Since the value of the roots are real and different, the complementary solution (yc) will give us
yc = Ae^m1x + Be^m2x
yc = Ae^0+Be^8x
yc = A+Be^8x
To get yp we will differentiate yc twice and substitute the answers into the original DE
yp = Ax+B (using the method of undetermined coefficients
y'p = A
y"p = 0
Substituting the differentials into the general DE to get the constants we have;
0-8A = 7x+1
Comparing coefficients
-8A = 1
A = -1/8
B = 0
yp = -1/8x+0
yp = -x/8 (particular integral)
y = yc+yp
y = A+Be^8x-x/8
