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3 years ago

Y''-4y=cosx find general solution.

Mathematics

1 answer:

Anastasy [175]3 years ago

8 0

Answer:

Step-by-step explanation:

$y''-4y=cosx$

The auxialary equation and solutions are as follows:

$m^2-4=0\\m=2,-2$

General solution is

$y=Ae^{2x} +Be^{-2x}$

Right side =cosx

Particular Integral

= $\frac{cosx}{-1-4} =\frac{-cosx}{5}$

Hence full solution is

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Two more than four times a number is three

klio [65]

Answer:

1/4 is the number

a.k.a. 0.25

Step-by-step explanation:

Replace the words "a number" with x

4x + 2 = 3

Then, simplify

4x = 1

x = 1/4

5 0

3 years ago

Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after t seconds is given by E(t)=2600−50t.

lesya692 [45]

Answer:

Part 1) The equation tells us that Terry started at an elevation of 2,600 ft

Part 2) The elevation is decreasing by 50 feet each second

Step-by-step explanation:

we have

$E(t)=2,600-50t$

where

E(t) is Terry's elevation in feet

t is the time in seconds

Part 1) Find the E intercept of the equation

The E-intercept is the value of E when the value of t is equal to zero

For t=0

substitute

$E(0)=2,600-50(0)$

$E(0)=2,600\ ft$

therefore

The equation tells us that Terry started at an elevation of 2,600 ft

Part 2) Find the slope of the equation

we have

$E(t)=2,600-50t$

This is the equation of the line into slope intercept form

The slope m is equal to

$m=-50\ ft/sec$

The slope is negative, because is decreasing

therefore

The elevation is decreasing by 50 feet each second

6 0

3 years ago

Rachel solved 50 problems of her Homework correctly and scored 62.5%. How many problems were there in the Homework?

maria [59]

Answer:

Step-by-step explanation:

50 problems/x total = 62.5%

50/62.5=0.8 problem for each percent

0.8 * 100 percent = 80 problems

3 0

3 years ago

Read 2 more answers

Jennifer is saving money to buy a bike. The bike costs $223. She has $124 saved, and each week she adds $11 to her savings.

Elan Coil [88]

233-124 is 109.

109/11 is nearly 10.

answer is 10 weeks

4 0

3 years ago

For each of the following, determine the interest rate per compounding period. 1) 12% per year, compounded weekly b) 8% per year

Zarrin [17]

Using compound interest, the rates per compounding period are given as follows:

a) 0.1273 = 12.73%.

b) 0.0833 = 8.33%

c) 0.0617 = 6.17%

<h3>What is compound interest?</h3>

The amount of money earned, in compound interest, after t years, is given by:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

In which:

A(t) is the amount of money after t years.

P is the principal(the initial sum of money).

r is the interest rate(as a decimal value).

n is the number of times that interest is compounded per year.

The <u>interest rate per compounding period</u> is given as follows:

$\left(1 + \frac{r}{n}\right)^n - 1$

For item a, the parameters are:

r = 0.12, n = 52.

Hence:

$\left(1 + \frac{0.12}{52}\right)^{52} - 1 = 0.1273$

For item b, the parameters are:

r = 0.08, n = 104.

Hence:

$\left(1 + \frac{0.08}{104}\right)^{104} - 1 = 0.0833$

For item c, the parameters are:

r = 0.06, n = 12.

Hence:

$\left(1 + \frac{0.06}{12}\right)^{12} - 1 = 0.0617$

More can be learned about compound interest at brainly.com/question/25781328

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8 0

2 years ago