A would be (-3, 6).
B would be (-6, 3).
Anytime something is asking you to reflect off of the Y-axis, you put the original but flipped. Also, your answer will always be straight across vertically.
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
Answer:
12,548 rounded to the nearest thousand is 13,000 and 4,685 rounded to the nearest thousand is 5,000
Step-by-step explanation:
The figure is a trapezoid (or trapezium), and the exact length of the trapezoid is 5 units
<h3>How to determine the length?</h3>
The figure is a trapezoid with the following parameters:
Area = 107.95
Base= 12
Height = 12.7
Length = x
The area of a trapezoid is:
Area = 0.5 * (Base + Length) * Height
So, we have:
0.5 * (12 + Length) * 12.7 = 107.95
Evaluate the product
(12 + Length) * 6.35 = 107.95
Divide both sides by 6.35
12 + Length = 17
Subtract 12 from both sides
Length = 5
Hence, the length of the trapezoid is 5 units
Read more about areas at:
brainly.com/question/24487155
#SPJ1
Answer:
b. (-1, 5)
Step-by-step explanation:
Since the first equation is already solved for y, we can use substitution.
Substitute y in the second equation with 3x + 8.
5x + 2y = 5
5x + 2(3x + 8) = 5
5x + 6x + 16 = 5
11x = -11
x = -11/11
x = -1
Now substitute x in the first original equation by -1 and solve for y.
y = 3x + 8
y = 3(-1) + 8
y = -3 + 8
y = 5
Answer: (-1, 5)
