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vaieri [72.5K]
3 years ago
13

How to find the general solution to y"'+2y"-4y'-8y=0?

Mathematics
1 answer:
S_A_V [24]3 years ago
8 0
y'''+2y''-4y'-8y=0

has characteristic equation

r^3+2r^2-4r-8=r^2(r+2)-4(r+2)=(r^2-4)(r+2)=(r-2)(r+2)^2=0

which has roots at r=\pm2. The negative root has multiplicity 2. So the general solution is

y=C_1e^{2x}+C_2e^{-2x}+C_3xe^{-2x}
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-4+6y=16<br> Change to slope (intercept)
hichkok12 [17]
*here is step by step*
(Remember to add the 'x' to the slope)

-4x+6y=16

6y=4x+16

y= 4/6x + 2.66

The complete answer is:
y= 2/3x + 2.66
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3 years ago
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2 years ago
Trucks that travel on highways have to stop at various locations to be weighed and inspected for safe brakes and light systems.
IrinaVladis [17]

Answer:

The reuired probability is 0.756

Step-by-step explanation:

Let the number of trucks be 'N'

1) Trucks on interstate highway N'= 76% of N =0.76N

2) Truck on intra-state highway N''= 24% of N = 0.24N

i) Number of trucks flagged on intrastate highway  = 3.4% of N'' = \frac{3.4}{100}\times 0.24N=0.00816N

ii)  Number of trucks flagged on interstate highway  = 0.7% of N' = \frac{0.7}{100}\times 0.76N=0.00532N

Part a)

The probability that the truck is an interstate truck and is not flagged for safety is P(E)=P_{1}\times (1-P_{2})

where

P_{1} is the probability that the truck chosen is on interstate

P_{2} is the probability that the truck chosen on interstate is flagged

\therefore P(E)=0.76\times (1-0.00532)=0.756

5 0
3 years ago
What is the value of   ?
azamat
Sure! So this is ready as "the cube root of 125". This basically means, "what number cubed can get me 125?"
Let's go through our options.
We can rule out D, as D cubed would be unreasonably big.
We can also rule out C, because 375 cubed is easily over 10000, you know this even if you haven't computed it all, just compute the 300 cubed.
We can rule out B, too. 41 squared is already over 125, therefore it can't be the answer.
Therefore our answer is A, 5. We can check that by cubing 5, and that indeed gets us 125.
Hope this helps!
4 0
3 years ago
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<span>the vertical line test is a visual way to determine if a curve is a graph of a function or not.</span>
6 0
3 years ago
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