Where do erasers go for vacation? missing lengths

Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

WINSTONCH [101]

Answer:

a) $y(t) = y_{0}e^{4t} + 2$ . It does not have a steady state

b) $y(t) = y_{0}e^{-4t} + 2$ . It has a steady state.

Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

$y' - 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r - 4 = 0$

$r = 4$

So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

So

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

$-4C = -8$

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

b) $y' +4y = 8$

The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

So

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

6 0

3 years ago

From a point p on level ground, the angle of elevation of the top of a tree is 60°. If the tree is 39m high, how far is its base

zzz [600]

Hello,

tan 60°=√3
d/39=tan 60°==>d=39/√3=39√3/3=13√3=22,516660498... (m)

5 0

4 years ago

A living room has a circular rug. According to a small tag, the rug has a circumference of 6.28 yards. What is the rug's radius?

mezya [45]

Answer:

1 yard

Step-by-step explanation:

the formula for the circumference of a circle is 2 times pi times the radius of the circle. so to find out the radius you divide the circumference by 2 and then by pi.

3 0

3 years ago

Bad gums may mean a bad heart. Researchers discovered that 80% of people who have su ered a heart attack had periodontal disease

saul85 [17]

Answer:

0.069 = 6.9% probability that he or she will have a heart attack

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Does not have periodontal disease

Event B: Has a heart attack.

Probability of not having a periodontal disease:

100 - 80 = 20% of 10%(had a heart attack).

30% of 100-10 = 90%(did not have a heart attack). So

$P(A) = 0.2*0.1 + 0.3*0.9 = 0.29$

Intersection of A and B:

Not having the disease, suffering a heart attack, so 20% of 10%.

$P(A cap B) = 0.2*0.1 = 0.02$

What is the probability that he or she will have a heart attack?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.02}{0.29} = 0.069$

0.069 = 6.9% probability that he or she will have a heart attack

6 0

3 years ago

Help me please if so so will thank you

Whitepunk [10]

I will go less as i write them:

.4 .04 .004 .0004

3 0

3 years ago

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