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oee [108]
3 years ago
11

Is this triangle congruent?

Mathematics
1 answer:
Sladkaya [172]3 years ago
6 0
Yes you can tell the at
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Consider the differential equationy′′+3y′−10y=0.(a) Find the general solution to this differential equation.(b) Now solve the in
RSB [31]

Answer:

Y= 2e^(5t)

Step-by-step explanation:

Taking Laplace of the given differential equation:

s^2+3s-10=0

s^2+5s-2s-10=0

s(s+5)-2(s+5) =0

(s-2) (s+5) =0

s=2, s=-5

Hence, the general solution will be:

Y=Ae^(-2t)+ Be^(5t)………………………………(D)

Put t = 0 in equation (D)

Y (0) =A+B

2 =A+B……………………………………… (i)

Now take derivative of (D) with respect to "t", we get:

Y=-2Ae^(-2t)+5Be^(5t)   ....................... (E)

Put t = 0 in equation (E) we get:

Y’ (0) = -2A+5B

10  = -2A+5B ……………………………………(ii)

2(i) + (ii) =>

2A+2B=4 .....................(iii)

-2A+5B=10 .................(iv)

Solving (iii) and (iv)

7B=14

B=2

Now put B=2 in (i)

A=2-2

A=0

By putting the values of A and B in equation (D)

Y= 2e^(5t)

6 0
3 years ago
A simple random sample of 60 items resulted in a sample mean of 65. The population standard deviation is 14. a. Compute the 95%
bazaltina [42]

Answer:

The 95% confidence interval for the population mean is between 61.5 and 68.5.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96*\frac{14}{\sqrt{60}} = 3.5

The lower end of the interval is the sample mean subtracted by M. So it is 65 - 3.5 = 61.5

The upper end of the interval is the sample mean added to M. So it is 65 + 3.5 = 68.5

The 95% confidence interval for the population mean is between 61.5 and 68.5.

6 0
3 years ago
Read 2 more answers
What is the solution to y=-x-6 and y=x-4
xz_007 [3.2K]

Answer:

(-1,-5)

Step-by-step explanation:

Solve by substitution

7 0
2 years ago
I need help plz !!!!!!!
morpeh [17]

0: 3000

5: 500

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5 0
3 years ago
−3/4+1 and 1/4<br><br> please help me :] thanks!
USPshnik [31]

^                                        ^

I Give this guy Brainliest I

v                                       v

7 0
3 years ago
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