a. For what values of k does the function y = cos(kt) satisfy the differential equation 25y'' = −16y?
b. For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution.

Answers

Answer 1

Answer:

Step-by-step explanation:

Given y = coskt

y' = -ksinkt

y'' = -k²coskt

Substitute this y'' into the expression 25y'' = −16y

25(-k²coskt) = -16(coskt)

25k²coskt = 16(coskt)

25k² = 16

k² = 16/25

k = ±√16/25

k = ±4/5

b) from the DE 25y'' = −16y

Rearrange

25y''+16y = 0

Expressing using auxiliary equation

25m² + 16 = 0

25m² = -16

m² = -16/25

m = ±4/5 I

m = 0+4/5 I

Since the auxiliary root is complex number

The solution to the DE will be expressed as;

y = Asinmt + Bsinmt

Since k = m

y = Asinkt+Bsinkt where A and B are constants


Related Questions

use the simplified ratio to find the equivalent ratio with a denominator of 140​

Answers

Answer:

x

__

140

Step-by-step explanation:

all i could get sorry

The number of pages that Armando, Billy, Robert, and Joel can read in a day is shown below.
Armando read 15% of his 46-page book.
Billy read 11% of his 72-page book.
Robert read 12% of his 68-page book.
Joel read 14% of his 69-page book.

Who can read the greatest number of pages in a day?


a Armando
b Joel
c Billy
d Robert

Answers

B Joel hope this helps

Answer: B. Joel

hope this helps :}

A bag contains 5 blue, 3 red, 6 green, 9 orange, and 20 black marbles. What is the ratio of number of blue marbles to the number of marbles that are orange or green?

Answers

Answer:

What you are looking for is the ratio which is 5/9

Step-by-step explanation:

all you had to do was add them together

Answer:

Step-by-step explanation:

5 to 9

In 10 minutes a heart can beat 700 time at this rate in how many minutes will a heart beat 140 time

Answers

2 minutes because 10/700 divide by 10 1/70 so 70 bpm 140/70= 2

Answer: i believe the answer is 2 minutes

Step-by-step explanation:

Ms Liu has $40 to buy water and popcorn at the movie theater. Popcorn costs $8 per bag and water costs 3$ per bottle. write an algebraic expression that will be used to find the amount of money left when Ms. Liu 3 bags of popcorn and 4 bottles of water.

Answers

Answer:

S = 1 bag of popcorn

Y = 1 water

Step-by-step explanation:

S x 3 + Y x 4 = R

40 - R = (The Answer)

The difference of two integers is 1. The product of the integers is 30. What
are the integers?

Answers

[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]

Let us take ,

First integer be x .Second integer be y .

Also let us consider x > y .

According to first Condition :-

⇒ x - y = 1.

⇒ x = y + 1. .............(i)

According to second Condition :-

⇒ x × y = 30 .

⇒ ( y + 1 )y = 30 . [ From (i) ]

⇒ y² + y = 30.

⇒ y² + y - 30 = 0 .

⇒ y² + 6y - 5y -30 = 0.

⇒ y ( y + 6 ) -5 ( y + 6 ) = 0 .

⇒ ( y + 6 ) ( y - 5 ) = 0 .

[tex]\red{\bf \longmapsto y = 5 , (-6)}[/tex]

Here y can sustain both values 5 and minus 6 as y is an integer.

So , x = -6 , 5 .

Hence possible answers are ,

[tex]\boxed{\purple{\bf x = -6 , y = -5 }}[/tex]

[tex]\qquad\qquad\qquad \bf Or [/tex]

[tex]\boxed{\purple{\bf x = 6 , y = 5 }}[/tex]

.

(x+5) (x+4) give me the answers quick please​

Answers

[tex] \red { \orange {\boxed {\boxed{Answers}}}}[/tex]

[tex] = (x + 5)(x + 4)[/tex]

[tex] = {x}^{2} + 4x + 5x + 20[/tex]

[tex] = {x}^{2} + 9x + 20[/tex]

Ns. Moore drove 200 miles in February. She drove 8 times as many miles in March as she did in January. How many mailed did Ms. Moore drive in March

Answers

Answer:

25

Step-by-step explanation:

200 divided by 8

Solve for V and simplify.
2v+6=13v-4v+62

Answers

V = -8

Explanation:

Hansel's age is one less than three times Gretel's age. The sum of their ages is 43.

Answers

Answer: Hansel is 32

Step-by-step explanation: 11x3-1=32, 32+11=43

What’s the y intercept

Answers

The y intercept is where the function intersects the y-axis.

Answer:

y-intercpet is In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

Is 35 - square of 40 greater than 6 pi?

Answers

Answer:

yes

Step-by-step explanation:

Four college friends (one is named Cathy) were all accepted to a graduate school.

Answers

Answer:

Wow that is great

Step-by-step explanation:

is there a question? uhhhmmmmm

Steven put together 2,494 pieces of a puzzle. About how many pieces did he put together?

Answers

Answer:

2,494

Step-by-step explanation:

if he put 2,494pieces together you repeated the same question

The equation of a circle is (x−2)2+(y+6)2=100. Find the equation of a circle that is externally tangent to the given circle and has a center at (14, 3).

Answers

Answer:

(x-14)^2+(y-3)^2=9

Step-by-step explanation:

equation of a circle is (x-h)^2+(y-h)^2=r^2

so center is (14,3) and is tangent externally means

(x-14)^2+(y-3)2=3^2

(x-14)^2+(y-3)^2=9 answer

The equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]

The standard formula for finding the equation of a circle is expressed as:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where

(a, b) is the centre

r is the radius

Given the center at (14, 3)

If the equation of a circle is externally tangent to the given circle and has a center at (14, 3), then the radius will be 3

Substitute the radius and the centre into the expression above to have:

[tex](x-14)^2 + (y-3)^2=3^2\\(x-14)^2 + (y-3)^2=9[/tex]

Hence the equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]

Learn more here: https://brainly.com/question/24217736

The photo below is the reduced form of a 16-by-20-inch print. What is the scale factor being used to reduce te
4 in
5 in

Answers

Answer:

Option (B)

Step-by-step explanation:

Photo given in the picture has dimensions as,

Length = 4 in.

Width = 5 in.

This photo is the reduced form of a photo having dimension 16 by 20 inch print.

Since scale factor of an image is given by,

Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the original picture}}[/tex]

                    = [tex]\frac{4}{16}[/tex]

                    = [tex]\frac{1}{4}[/tex]

Therefore, scale factor used to reduce the picture is [tex]\frac{1}{4}[/tex].

Option (B). will be the correct option.

Answer:

it's 4

Step-by-step explanation:

it's 1:4 cause 16/4 is 4 so the scale factor is 4

Donavon and three friends go to a fair. They each spend 1/2 of their money on rides. ​ Then, they each spend​ $3 on food. At the end of the​ day, Donavon and his friends have a total of​ $8 remaining. How much money did each person bring to the​ fair? Complete the work to find the value of x.

(Type integers or​ fractions as the answer.) like top to down

Answers

Answer:

$22

Step-by-step explanation:

Hi here is the explanation

We just do the opposite of the question

We just add the values

So 3+8=11

Now multiply. Since when we have the total and we spent haslf of it, we divide, so now we multiply by reciprocal, the opposite

11*2=22 (2 is the reciprocal)

Now let’s see we did it right

22*1/2=11

Now let’s subtract to find the remaining

11-3=8

As you can see, we are right as they had $8 left.

Hope it helps

Hope you mark me brainliest!

Bart drives 45 miles in 30 minutes. If he drove 3 hours in total at the same rate how far did he go! How many minutes did Bart drive in total!

Answers

Answer:

270 miles and 180 minutes

Step-by-step explanation:

whay is called when there is a difference between what one expects to happen and what actually happens
O metaphor
O symbolism
O personification
O irony​

Answers

Answer:

I do believe it is irony

A taxi cab in Myrtle Beach charges $2 per mile and $1 for every person. If a taxi cab ride for two people costs $12 how far will the cab travel?​

Answers

Answer:

5 miles

Subtract the 1 dollar for each person from 12. You get ten, and divide ten by two, which is 5

Grace is measured for her annual check up. She is 28 1/5 inches tall. Last year she was 25 3/5 inches tall. How much did she grow in one year?

Answers

Answer:

2 3/5 inches in a year

Step-by-step explanation:

28 1/5 - 25 3/5 = 141/5 - 128/5 = 13/5 = 10/5 + 3/5 = 2 + 3/5 = 2 3/5

What value of x is in the solution set of 8x -6 > 12 + 2x?
-1
0
3
5

Answers

Answer:

x:5

Step-by-step explanation:

The value of 'x' in the solution set is 5 Option D

How to determine the value of x

From the equation

8x -6 > 12 + 2x

Collect like terms

8x - 2x >  12 + 6

6 x > 18

Make 'x' subject of formula

x > 18/6

x >  3

If x is greater than 3, then x is 5

Therefore, the value of 'x' in the solution set is 5. Option D

Learn more about inequalities here:

https://brainly.com/question/24372553

#SPJ9

please help!! I'm really confused

Answers

Answer:

Point a is correct.

Step-by-step explanation:

hope I helped.


PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((

Answers

Answer:

-4.9

Step-by-step explanation:

The answer is -4.9 because:

1) As the number line increases, the numbers are also increasing even though  it seems like they are decreasing.

2) The number that comes right after -5 is -4.9

Hope this helps! :D

the product of -3 and t is greater then 11

Answers

Answer:

t ≤ 4

Step-by-step explanation:

3 X 4 = 12  or any number greater than 4

what is 5 divided by 1 4/7

Answers


3.18 is the answer i believe !

As you can see, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3.

How many squares should he use for the sixth stage?​

Answers

Answer:

21 squares

Step-by-step explanation:

1 = 1

2 = 3

3 = 6

The pattern follows squares use in the previous stage + new stage = squares use the new stage

Squares used in stage 2 = Squares used in stage 1 + stage 2

= 1 + 2

= 3 squares

Squares used in stage 3 = Squares used in stage 2 + stage 3

= 3 + 3

= 6 squares

Squares used in stage 4 = Squares used in stage 3 + stage 4

= 6 + 4

= 10 squares

Squares used in stage 5 = Squares used in stage 4 + stage 5

= 10 + 5

= 15 squares

Squares used in stage 6 = Squares used in stage 5 + stage 6

= 15 + 6

= 21 squares

4 = 10

5 = 15

6 = 21

The volume of a cube is 27 in.. How long is each side? Each side of the cube is____in. long.​

Answers

Answer:

the volume is 27 and to get a volume of a cube it will be side cubed meaningit will be side x side x side so to get the length of one side we will look for the cube root of 27 by using factor tree and the cube root will be 3

you must take medicine in 4 equal doses each day. each days medicine come in a single container and measure 3 1/5 tablespoons. how much medicine is in each dose

Answers

1.2 tablespoons in each dose

I mark as brainliest ​

Answers

Answer:

The answer is D

Step-by-step explanation:

you might get confused with A but its D because D is separating 4 + 3 from 3 wich we are multiplying  and A is not. so the answer is D

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