Solve whats in the parentheses first
5k+25+4<21+6k
5k+29<21+6k
plug in a number in k for both sides
5(1)+29<21+6(1)
5+29<21+6
34<27
5(2)+29<21+6(2)
10+29<21+12
39<33
so 5(k+5)+4 is greater than 21+6k
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:
z = 137°
Step-by-step explanation:
Hope this helps
The equation is y = 63/x
And y = 3 when x=21
Step-by-step explanation:
When y varies inversely with x, The inverse proportion is given by:
y ∝1/x
When the proportionality symbol is removed, a constant of proportionality is introduced
Putting y = 7 and x = 9
So,
Putting x =21
Hence,
The equation is y = 63/x
And y = 3 when x=21
Keywords: Proportion, variables
Learn more about proportion at:
#LearnwithBrainly
