(-4k^4 + 14 + 3k^2) + (-3k^4

In each of Problems 5 through 10, verify that each given function is a solution of the differential equation.

WARRIOR [948]

Answer:

For First Solution: $y_1(t)=e^t$

$y_1(t)=e^t$ is the solution of equation y''-y=0.

For 2nd Solution: $y_2(t)=cosht$

$y_2(t)=cosht$ is the solution of equation y''-y=0.

Step-by-step explanation:

For First Solution: $y_1(t)=e^t$

In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

$y_1(t)=e^t$

First order derivative:

$y'_1(t)=e^t$

2nd order Derivative:

$y''_1(t)=e^t$

Put Them in equation y''-y=0

e^t-e^t=0

0=0

Hence $y_1(t)=e^t$ is the solution of equation y''-y=0.

For 2nd Solution:

$y_2(t)=cosht$

In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

$y_2(t)=cosht$

First order derivative:

$y'_2(t)=sinht$

2nd order Derivative:

$y''_2(t)=cosht$

Put Them in equation y''-y=0

cosht-cosht=0

0=0

Hence $y_2(t)=cosht$ is the solution of equation y''-y=0.

3 0

2 years ago

John took all his money from his savings account. He spent $110 on a radio and 4/11 of what was left on presents for his friend

svp [43]

Answer:

$1210

Step-by-step explanation:

Let x be total amount

First John spent $110 on a radio and 4/11 of what was left on presents for his friends so he was left with

$\frac{7}{11}(x-110)=\frac{7}{11}x-70$

Then he put 2/5 of his remaining money into a checking account

$\frac{3}{5}\left(\frac{7}{11}x-70\right)$

Rest he donated to charity

$420=\frac{3}{5}\left(\frac{7}{11}x-70\right)\\\Rightarrow \left(\frac{7}{11}x-70\right)=\frac{2100}{3}\\\Rightarrow \frac{7}{11}x-70=700\\\Rightarrow \frac{7}{11}x=770\\\Rightarrow x=1210$

Hence total amount of money John originally had was $1210

8 0

2 years ago

Matt and Shirley, working together, can rake the yard in 10 hours. Working alone, Shirley takes twice as long as Matt. How long

AysviL [449]

5 hours is the answer

4 0

2 years ago

For a normally distributed random variable x with m = 75 and s = 4, find the probability that 69 < x < 79 Use the table to

nalin [4]

10-14-19-12-14-18-10-15-15

6 0

2 years ago

What is the smallest positive multiple of $32$?

Artemon [7]

Answer:

2 is the smallest positive multiple of $32$

explanation:

hope it helps, btw i dont have step-by-step explanation becuase i already have a answer. 

its you're choice if you're going to copy my answer. correct me if im wrong naman. 

3 0

1 year ago

(-4k^4 + 14 + 3k^2) + (-3k^4 - 14k^2 -8)