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
irina [24]
3 years ago
9

Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+16y=0. Separate your answers by co

mmas. isn't the answer just ±4?
Mathematics
1 answer:
ziro4ka [17]3 years ago
5 0

Answer:

0, 4, -4 and they may want you to mention formally all the kt multiples of \pi.

Step-by-step explanation:

Let's do the second derivative of the function: y(t)=sin(k\,t)

y'(t) =k\,cos(k\,t)\\y"(t)=-k^2\,sin(kt)

So now we want:

y"+16\,y'=0\\-k^2\,sin(kt)+\,16\,sin(kt)=0\\sin(kt)\,(16-k^2)=0\\

Then we have to include the zeros of the binomial (16-k^2) which as you say are +4 and -4, and also the zeros of sin(kt), which include all those values of

kt=0\,,\,\pi\,\,,\,2\pi\, ,\,etc.

So an extra one that they may want you to include is k = 0

You might be interested in
Three students are arguing over who can run the fastest. Student A says that she can run 2/3 mile in six minutes. Student B says
Liula [17]

Answer:

student A- can run 2/3 mile in six minutes

1/9 mile/min

student B- can run 1/2 mile in 4 minutes

Speed=1/8 mile/min

student C- can run 4/5 mile in 8 minutes

speed=1/10 mile/min

Step-by-step explanation:

5 0
3 years ago
Which of the following numbers is closest to the product of 48.9x21.2
Marina CMI [18]
The answer is C because 48.9 multiplied by 21.2 is 1036.68
3 0
3 years ago
Which expression means 7 more than a number?
Kisachek [45]
The answer is B 

- <span>"More" means added to, or addition. So 7 more than 'A number' is: </span><span>d + 7</span>
4 0
4 years ago
Evaluate the numerical expression. − 1 3 − (− 4 9 )
notka56 [123]
Two negatives make a positive so, -13 - (-49) equals -13 + 49, or 49-13, they are all the same thing, all equal to 36. 
6 0
4 years ago
SOMEONE PLEASE HELP WILL MARK BRAINLIEST
Mashutka [201]

Radical form for 112 would be 4{7 and then I think you can just search up how to reduce the 4 to 7 i don’t have the symbol btw
4 0
3 years ago
Other questions:
  • At a peanut butter factory, the daily production cost, C, for j jars of peanut butter is modeled by the graph below. What are th
    10·2 answers
  • The sum of two numbers is -3 and their difference is 9 find the numbers​
    14·1 answer
  • Explaining How to S
    14·1 answer
  • Emily's graduation picnic costs $3 for every attendee. At most how many attendees can there be if Emily budgets a total of $18 f
    10·2 answers
  • Explain what it means to solve a system of equations
    13·1 answer
  • You are standing outside of a circle at point A. You know that you are 12 ft from a tangent point of the circle. You also know t
    14·1 answer
  • So if 15 + 5 is 20 and 30 + 30 is 60 then what is 9 + 12 x 15 plus if red is blue are purple then what is 2 + 5 = ? (Red = 1 (Or
    6·1 answer
  • Please help me with this!<br> •<br> •<br> •
    8·1 answer
  • 3^4 expanded form please help
    9·2 answers
  • On Rhombus WXYZ,if W is located at (-5,-2) and Y is located at (3,-2), what is the slope of XZ?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!