Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
Answer: 1/8
Step-by-step explanation:
-1/4 = -2/8
3/8 + (-2/8) = 3/8 - 2/8
3/8 - 2/8 = 1/8
Hope I helped!!
Answer:
The length of the rectangle (l) = 10 cm
The width of the rectangle (w) = 7 cm
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Let 'x' be the length of the rectangle
Given that the width is 3 feet shorter than the length
The width of the rectangle = x -3
Area of the rectangle = length × width
<u><em>Step(ii):-</em></u>
Area of the rectangle = length × width
= x ( x-3)
Given that the area of the rectangle = 70 square feet
x ( x-3) = 70
⇒ x² - 3x - 70 =0
⇒ x² - 10 x + 7 x - 70 =0
⇒ x (x -10) +7( x-10) =0
⇒ ( x+7) ( x-10) = 0
⇒ x =-7 and x=10
<u><em>Final answer:</em></u>-
we choose x=10
The length of the rectangle (l) = 10 cm
The width of the rectangle (w) = 7 cm
Answer:
0.375
Step-by-step explanation:
0.125 x 3 = 0.375
Answer:
15 miles in 75 minutes
-I don’t know what a tape diagram is so sorry I can’t answer that part-