Answer:
The answer should be: r ≈ 8.21
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
Absolute value is simply the non-negative version of the number regardless of its symbol
So for the absolute value of 20? the answer is just 20.
For reference, the absolute value of -20 is also just 20.
Hope the explanation helps :)
We need to see the rest of the question...
A quadrilateral is a kite if the diagonals are:
i) perpendicular
ii) bisect each other
iii) not equal ( together with conditions i and ii this would make the quadrilateral a square)
Another definition of the kite is :
a quadrilateral with 2 pairs of equal adjacent sides.
Let's check the choices one by one:
A. <span>∠M is a right angle and MK bisects ∠LMJ.
according to these, ML and MJ may well be not equal...
</span><span>B. LM = JM = 3 and JK = LK = √17.
</span>
this makes the quadrilateral a kite.
<span>C. MK intersects LJ at its midpoint
</span>
if they are not perpendicular, the quadrilateral is not a kite.
<span>D. The slope of MK is –1 and the slope of LJ is 1.
this only means that MK and LJ are perpendicular, but not whether they bisect each other,
Answer: only B</span>
