1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pentagon [3]
4 years ago
14

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form

the general solution. (please explain your work)
y(4) - y =0 , {e^x,e^-x,cosx,sinx}
Mathematics
1 answer:
Zina [86]4 years ago
4 0

Answer:

  y =C₁eˣ + C₂e⁻ˣ  + C₃ cos x + C₄ sin x

Step-by-step explanation:

given,

y⁽⁴⁾ - y = 0

( D⁴ - 1 ) y = 0..............(1)

writing characteristics equation

m⁴ -1  =  0

(m² - 1)(m² +1) = 0

(m - 1)(m+1)(m²+1) = 0

hence, roots of the equation comes out to be

              = 1, -1, ± i

so the general solution will be

  y =C₁eˣ + C₂e⁻ˣ  + C₃ cos x + C₄ sin x

You might be interested in
Your weekly base salary is $150. You earn $20 for each phone you taht you sell. The company policy is that as a part-time employ
Eduardwww [97]

Answer:

You can sell at least 40 phones each week.

Step-by-step explanation:

Given that:

Weekly base salary = $150

Earning on each phone = $20

Maximum amount that can be earned each week = $950

Let,

m be the number of phones.

20m + 150 ≤ 950

20m ≤ 950 - 150

20m ≤ 800

Dividing both sides by 20

\frac{20m}{20}\leq \frac{800}{20}

m ≤ 40

Hence,

You can sell at least 40 phones each week.

6 0
3 years ago
An automobile manufacturer wants to assess a new style of visual display to see if it changes the amount of reported eye-strain
finlep [7]

Answer:

Standard error = 0.34

t-statistic = 11.18

Step-by-step explanation:

Given Data:

Mean difference d = 3.8

Standard deviation S.D = 1.36

Number of people = 16

The appropriate test are:

1. Standard error

2. T- statistic

1. Calculating the standard error using the formula;

Standard error = S.D/√n

                         = 1.36/√16

                          = 1.36/4

                           = 0.34

2. Calculating the t-statistic using the formula;

t-statistic = d/(S.D/√n)

              = 3.8/(1.36/√16)

              = 3.8/(1.36/4)

              = 3.8/0.34

               = 11.18

7 0
4 years ago
Which equation represent a line parralel to y=4x+1 and passes through (1,7)?
Alecsey [184]

Answer:

y=4x+3

Step-by-step explanation:

3 plus 4 is 7, 0 plus 1 is 1, so yeah, same slope and y-intercept is in a spot so the next point on the line is (1,7)

6 0
3 years ago
Read 2 more answers
-6d=-42 can you help me solve please
eduard

Given the equation :

-6d=-42

So, to find d , divide both sides by ( -6 )

So,

\begin{gathered} \frac{-6d}{-6}=\frac{-42}{-6} \\  \\ d=7 \end{gathered}

Note: when we divide two negative numbers, the result will be a positive number

5 0
1 year ago
the area of a rectangle is 54 cm. the length is 2 cm more than a x and the width is 5 cm less than twice of x. solve for x. roun
xxMikexx [17]
Well, you have to set up an equation. You should know that length×width will give you the area. length=2cm more than x (x+2) width=5cm less than twice of x (2x-5) so, the equation is (x+2)×(2x-5)=54 Now, just solve for x.
8 0
3 years ago
Other questions:
  • The Fosters bought a car in 2003 for $38,799. In 2012 they decided they wanted to sell the car. If the value of the car is decre
    15·1 answer
  • When we get a p-value that is very large, we may conclude that:
    5·1 answer
  • What are the properties of addition?
    8·1 answer
  • ∠1and ​∠2​ are a linear pair, and ​∠2​ and ​∠3​ are vertical angles. m∠1=(3y+10)∘ and ​m∠3=(5y−30)∘. What is m∠2?
    7·1 answer
  • 2. Darlene read 5/8 of a 56-page book. How many pages did Darlene read?
    11·2 answers
  • choose the answer that best represents the situation described below. casey is taking pictures outdoors. she knows that the late
    11·1 answer
  • What is the domain of the function ?
    10·1 answer
  • Kids filled up a swimming pool with 5000 gallons of water. The water leaked out at 2 gallons per minute. Write a linear equation
    6·1 answer
  • 4. A comprehensive study conducted by the National Institute of Child Health and Human Development tracked more than 1,000 child
    5·1 answer
  • Change the order from least to greatest
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!