Find the solution of the differential equation that satisfies the given initial condition.

Find The Solution Of The Differential Equation That Satisfies The Given Initial Condition.

Answers

Answer 1

The first equation is separable:

dy/dx = x/y   ⇒   y dy = x dx

(provided that y ≠ 0)

Integrating both sides yields

1/2 y² = 1/2 x² + C

Given that y(0) = -8, we find

1/2 • (-8)² = 1/2 • 0² + C   ⇒   C = 32

so that the particular solution is

1/2 y² = 1/2 x² + 32

Solving for y explicitly, we have

y² = x² + 64

y = ± √(x² + 64)

but since y(0) is negative, we take the negative solution:

y = - √(x² + 64)

The second equation is also separable:

du/dt = (2t + sec²(t)) / (2u)   ⇒   2u du = (2t + sec²(t)) dt

Integrate both sides:

u² = t² + tan(t) + C

Given u(0) = -6, we have

(-6)² = 0² + tan(0) + C   ⇒   C = 36

and so

u² = t² + tan(t) + 36

u = ± √(t² + tan(t) + 36)

but again we take the negative root here to agree with the initial condition, so

u = - √(t² + tan(t) + 36)


Related Questions

what is c3 - 1 when c = 4

Answers

The answer to your question is 11.
4x3=12-1=11
You just have to substitute
c3-1
4*3-1
12-1
=11

Find the derivative of y=a^x

Answers

If y = aˣ, then y = exp(ln(aˣ)) = exp(x ln(a)). (Here I use exp(x) = eˣ.)

Then using the chain rule, the derivative of y is

dy/dx = exp(x ln(a)) • ln(a)

and undoing the rewriting, we end up with

dy/dx = ln(a) aˣ

The length of a rectangle is times the width. If the perimeter is 32 inches, what is the width of the rectangle

Answers

Let width be “w", length = “l" and perimeter = p

Then l = 3w-4

Perimeter = 2(w+l)

p = 2(w+3w-4) = 2w+6w-8 = 8w-8

Perimeter is 32…

8w-8 = 32

8w = 32+8

8w = 40

w = 5

l = (3×5)-4 = 11

Check… p = 2(5+11) = 2 × 16 = 32

Ans = length is 11

Hope it helps!

Answer:

11

Step-by-step explanation:

Last year, a gardening store ordered 8,910 potted plants. This year, they ordered 9,801 potted plants. What is the percent of increase in the number of potted plants ordered annually?

Answers

Answer:

Step-by-step explanation:

100(9801 - 8910)/8910 = 10%

I need help with this question

Answers

Answer:

check online for more information

if g(x) = |2x-9|, find g(2)+g(3)

Answers

x=5 , x=3 - just plug in 2 and 3 into x and the lines will make it positive instead of negative

Can anyone find all for me please ?​

Answers

Answer:

It's a good question I seen thank you so much for your help and support me in the morning and have a talk

Which Graph is (x—5)^2/25 - (y+3)^2=1

Answers

Answer:

One that looks like this.

Step-by-step explanation:

Create your own example for each cases of multiplying
polynomials

Case 1: Distributive Property
Case 2: FOIL Method
Case 3: Binomial to Polynomial

Pls needed badly
If you have nothing to answer dont answer

Answers

Step-by-step explanation:

CASE 1:2x(3x+7) = 6x^2+14x.CASE 2:(2x + 3)(3x – 1)CASE 3:x2 + 4x

Which table of values represents possible solutions to
the equation y = 0.7x - 4.3?
х
49
у
30
X y
49 40
19 19
-11-12
-31-16
19 19
-11-12
-31 -26
B
Х
у
30
49
19 9
-11-12
-31 -26
Х
у
49 40
19 19
-11 -2.
-31 -16
D

Answers

Step-by-step explanation:

it will be c as shown in the photo

NEED HELP! GIVING OUT BRAINLIEST! (Need long answer)
The diagram below shows a proportional relationship between the number of cans of soup and the price.
Explain what this value means in terms of the soup.

Answers

The constant of proportionality is 1.25 and its meaning is the soup price per can
Step-by-step explanation:
The diagram below shows a proportional relationship between the number of cans of soup and the price.
1st:
$3.75 for 3 cans
per can
2nd:
$6.25 for 5 cans
per can
If x is the number of cans and y is the price of x cans, then

This means the constant of proportionality is 1.25 and its meaning is the soup price per can

if you dont wear a retainer after braces can your teeth still be straight without wearing one cause mine still are and its been 6 months?

Answers

it will eventually go to where they were before braces, please wear your retainers!!
Teeth move so gradually you won't even notice until it's too late and your retainer wont fit anymore. Just wear your retainer. The cost of braces is so much, and to throw that all away because you don't want to wear the retainer is quite foolish.

what is the surface area of a polyhedron with measurements 4cm x 4cm x 7cm?

Answers

Check the picture below.

so let's add all sides and that'd be the area of the rectangular prism.

[tex]\stackrel{\textit{top and bottom}}{2(4\cdot 7)}+\stackrel{\textit{left and right}}{2(4\cdot 4)}+\stackrel{\textit{front and back}}{2(4\cdot 7)}\implies 56+32+56\implies 144[/tex]

Each of the 14 students in the art club needs 4 1/4 ounces of paint for a project. The art store sells paint only in 8 ounce bottles. How many bottles of paint does the art club president need to buy for the project?

A - 3
B - 4
C - 7
D - 8

Answers

Answer:

C-7

Step-by-step explanation:

Answer:  The art club president need to buy 14 bottles of paint for the project.

Step-by-step explanation:  Given that each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles.

We are to find the number of bottles of paint that the art club president need to buy for the project.

We will be using the unitary method to solve the given problem.

Number of bottles filled by 8 ounces of paint = 1.

So, the number of bottles filled by 1 ounce of paint is

So, the number of bottles filled by 4 ounces of paint will be

Now, number of bottles of paint needed by 1 student  

Therefore, the number of bottles of paint needed by 14 students will be

Thus, the art club president need to buy 14 bottles of paint for the project.

The answer is C-7!!!

area of a triangle b-2s^2+3t^2 h-4s^2-3t^2

Answers

Answer:

1 flmpysc - ax + x - y - 2

this could help

A dairy needs 364 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 364 gallons?

Answers

Answer:

Step-by-step explanation:

Let x be gallons of 7%

Let y be gallons of 3%

364 = x + y

y = 364 - x

364(0.06) = x(0.07) + y(0.03)

364(6) = x(7) + y(3)

364(6) = 7x + 3y

364(6) = 7x + 3(364 - x)

364(6 - 3) = 7x - 3x

364(3) = 4x

x = 273

y = 364 - 273 = 91

273 gallons of 7%

91    gallons of 3%

The chart shows the sizes and prices of different sized boxes of Alex's favorite cereal.

Answers

Step-by-step explanation:

Compare the rates

Whichever has the smaller rate is the best deal.

remember, to be able to compare both cereal boxes they must have the same unit of measure (grams with grams, ounces with ounces, etc.)

Answer:

Price of box of cereal #1

---------------------------- = $ per ounce(or other unit)

Size of box #1 (in ounces,

or some other unit)

Help help help help help help help math

Answers

Answer:

Angle 6

Step-by-step explanation:

They are both the same angle size

Answer:

Angle 1

Step-by-step explanation:

Refer to the attached picture

What happens to the median of the data set
{10, 2, 8, 9, 5, 2, 6} if the number 12 is added to the data set?
A. The median increases by 2.
B. The median decreases by 1.
C. The median does not change.
D. The median increases by 1.

Answers

Answer:

D

Step-by-step explanation:

Median- The average

The average can be found by adding the numbers together and dividing by the amount of numbers, in this case that would be 7. 10+2+8+9+5+2+6=42. 42÷7= 6. So the average before 12 is 6. 42+12 is the total adding that 12 and would equal 54. 54÷8=6.75, averaging out to 7. The average increased by about 1. So, the answer is D.

Answer: D. The median increases by 1.

Step-by-step explanation: This is correct.

evaluate the expression when b=3/10 and x= -2/15
3x-b

Answers

Answer:

3x - b

3 (-2/15) - 3/10

-6/15 -3/10

-60/150 - 45/150

- 105/150

what is the slope of -y=-x+6

Answers

Answer:

m = 1b = -6

Step-by-step explanation:

We know that:

-y = -x + 6y = mx + b

First, we need to change the 'y' sign.

=> -y = -x + 6=> y = x - 6

Now, let's compare both of the equations to find slope.

=> (y = x - 6) = (y = mx + b)

We can see that the slope is 1 and the y-intercept is -6.

Conclusion:

Therefore:

m = 1b = -6

Hoped this helped.

Pls help I’ll brainlest help I’m failing do it on a paper and put it in the answer box

Answers

Didn’t have the colors but i labeled what should be what color.

The penalty box on a soccer field extends
54 ft from the goal line. The line where a
player gets to take a penalty kick is 12 yards
from the goal line. What is the ratio of the
distance from the goal line and where a
player takes a penalty kick?

Answers

Answer:

I dont know sorry

next time

A jet can carry up to 200,000 liters of fuel.it used 130,000 liters of fuel during a flight. What percentage of the fuel capacity did it use on this flight

Answers

Percentage=(fuel consumed/ full fuel capacity) *100%
=(130000/200000)*100%
=65%

Please help, I will give good rating and brainliest of possible!!
Thank you!!!!!!!!

Answers

Answer:

[tex]g(x)=x+8[/tex]

Step-by-step explanation:

Translating a function up is very simple, all you need to do here is add 8.

If you want to think of it logically,

[tex]f(x)=x[/tex]

the whole right side of the function here can be our output. If x is 8, then the output, or height, is also 8. if you wanted to translate that up to 10, you'd simply need to add 2 to it, meaning [tex]x+2[/tex]. Then, at any given point on the function, it'd be 2 higher than it would be otherwise.

CAN SOMEONE HELP ME PLEASE <3

Answers

Answer:

It's Micrograms. The rest are from the imperial system, which is the system that is commonly used in the United States. The metric system is an international system for scientists and mathematicians to use so that sharing and giving information is a lot easier when conveying to other people around the world.

A. The graph shows how much money Farrah has in her savings account after weeks of saving on a regular basis. How much money does Farrah have in her savings account after 10 weeks of saving?

Answers

Answer:

Step-by-step explanation:

wheres the graph

Answer:

How much money does priya have after 10 weeks? 320

How long did it take her to save 200? 5

How much did priya have in her savings account when she started to save regularly? 80

Step-by-step explanation:

Graph the solution set to this inequality. -2x+9_> 5x-12

Answers

x ≤  3 (closed dot going to the left)

Solve for x in the triangle. Round your answer to the nearest tenth.

Answers

Answer:

x = 13.9

Step-by-step explanation:

15cos(22) = 13.9

Answer:

x = 13.9

Step-by-step explanation:

For the 22° angle, x is the adjacent leg. The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

cos 22° = adj/hyp

cos 22° = x/15

x = 15 × cos 22°

x = 13.9

Answer: x = 13.9

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $6600 and his stock in Company B was worth $3500. The stock in Company A has increased 7% since last year and the stock in Company B has increased 1%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary). pls asap

Answers

Answer:

4.9%

Step-by-step explanation:

6600 * 107/100 = 66*107 = 7062.

3500 * 101/100 = 35x101 = 3535

7062+3535=10597. Original worth: 10100

10597-10100 = 497

497/10100 = 0.0492079208, or 4.92%, rounds to 4.9%

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