Answer:
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
Substitute the value of a in the equation
Hence the general solution to the differential equation is
4 – 3(x – y) = –8x + 2
Apply distributive property to left side.
4 - 3x + 3y = -8x + 2
Add 8x to both sides.
4 + 5x + 3y = 2
Subtract 4 from both sides.
5x + 3y = -2
<h3><u>The correct answer is C.</u></h3>
C. 480
Explanation: I’m pretty sure you’re looking for the perimeter. Therefore, since you have a rectangle, you’ll have 4 sides. The measures are 100 by 140 so you’ll put 100 and 140 on the other sides and simply add them up.
Answer:
65 minutes
Step-by-step explanation:
already 16 people in line
total is 81
81 - 16 equals 65
about 5 people every 5 minutes (basically 1 min per person)
so, answer probably 65
Let’s take Sanku as x.
if Madhu is 3 times his age, then he is 3x.
the difference in their age is 14, so
3x - x = 14
2x = 14
x=7
Sanku is 7
Madhu is 21