Mathematics College

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

Write the equation of the line in slope intercept form that goes through points (-2, 5) and (3, 3)

Answers

Answer:

y=-2/5x+21/5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3-5)/(3-(-2))

m=-2/(3+2)

m=-2/5

y-y1=m(x-x1)

y-5=-2/5(x-(-2))

y-5=-2/5(x+2)

y=-2/5x-4/5+5

y=-2/5x-4/5+25/5

y=-2/5x+21/5

The Smith family goes out for lunch, and the price of the meal is $45.The sales tax on the meal is 6%, and the family also leaves a 20%tip on the pre-tax amount. What is the total cost of the meal?

Answers

Answer:

$56.70

Step-by-step explanation:

45 x 6% = 2.7 Multiply price of meal with the percentage of sales tax

45 x 20% = 9 Multiply price of mean with the percentage of tip

$9 is the tip amount

$2.70 is the sales tax

$45 + $2.70 + $9 = $56.70. Add the price of the meal with the sales tax and tip amount to get the total cost of the meal.

Help: Whats 8-2x=10?

Answers

Answer:

x=-1

Step-by-step explanation:

8-2x=10

(8-2x)-8=10-8

-2x=2

-2x/-2=2/-2

x=-1

You are delt 1 card from a 52 card deck. Find the probability that you are not dealt a 10

Answers

Answer:

Step-by-step explanation:

There are 4 tens.

There are 48 cards that are not a 10. The probability of drawing 1 of the 48 is

P(~10) = 48/52 which is quite high as you might imagine.


If you borrow $2,000 at 5 percent simple interest, how much will you owe
after one year?
O A. You will owe the principal of $2,000 only.
O B. You will owe the principal of $2,000 minus 5 percent of the
principal
O c. You will owe the principal of $2,000 plus 5 percent of the principal.

Answers

Answer:

it is c I think that it is c good luck

find the slope of (5,-6) and (-1,8)

Answers

the slope is -14/6 or the simplified version is -7/3

2+2 THIS IS A LIFE OR DEATH QUESTION PLZZ

Answers

The ANSWER for this question is 2+2=4

UMMM I THINK IT'S UH A CARROT, I'M SMART the real answer is 4 though lol

The position of a scuba diver relative to the water surface was −22 1/3 feet. He saw something interesting beneath him and increased his depth by 12 1/2 feet.

What is the position of the scuba diver now relative to the water surface?

Enter your answer as a mixed number, in simplified form, in the box.

Answers

Answer=-34 5/6

Explanation= just do this: -22 1/3 - 12 1/2
You subtract since the diver is diving deeper DOWN

Answer:

-34 5/6

Step-by-step explanation:

Hope this helps

Have a blessed day

Help hep help help math math math

Answers

Answer:

<4 corresponds with <8

Step-by-step explanation:

They correspond because they are in the same position relative to the lines.

As you can see, it is in the exterior area and it matches up exactly with the other angle. I attached an example picture of a corresponding angle


Round 4.789443 to the nearest whole number

Answers

Answer:

5

Step-by-step explanation:

I don't think I should have to explain this but if it's in between 4.5 and 5 it will be 5 and if it's 4.5-4 it would be 4

5. 7 is above 5 so you round the number higher

11/2-2/3 help me plz

Answers

4.83

answer above answer above answer above

Hope this helped, bye:)

If 2 people can paint 2 fences in 5 hours, how many hours in all will it take for 8 people to paint 8 fences.

Answers

Answer:

I believe that it would take 5 hours for 8 people to paint 8 fences.

Step-by-step explanation:

If 2 people are painting 2 fences in 5 hours, then 8 people can also paint 8 fences in the same time because each person is painting one fence. It take 5 hours to paint 1 fence if 1 person is painting it. The same goes for 2 or 8 people painting the same amount of fences as there are people. Im not 100% sure if this is accurate but I hope it helps.

Simplify. (5b2−3b+2)+(2b−4)
A.5b2+5b+6
B.5b2−5b−6
C.5b2−b−2
D.6b4−2

Answers

Answer:

5b2 - b -2

Step-by-step explanation:

The answer is (c)

The answer is: C

5b^2-b-2

What type of angle of this?

Answers

Answer:

angle x is equal to 60º so its an acute angle

Step-by-step explanation:

Answer:

x = 60

Step-by-step explanation:

obtuse angle is 180 degres so you subtract the amount that you see and you will get x. This only works for questions like this contact me if you need more help with questions like these

180-120=60

10. Saul works two part-time jobs. Last week, he worked 14 hours at a shoe store, and 19
hours as a telemarketer. His total pay was $240.30. The week before, he made
$300.00 for 19 hours at the shoe store and 22 hours telemarketing. Find his hourly
wage for each job

Answers

Answer:

shoe store $7.80/hour

telemarketer: $6.90/hour

Step-by-step explanation:

Let s = hourly salary at the shoe store.

Let t = hourly salary as a telemarketer.

14s + 19t = 240.3

19s + 22t = 300

Multiply both sides of the first equation by 19. Multiply both sides of the second equation by -14. Then add them.

         266s + 361t = 4565.7

(+)     -266s - 308t = -4200

----------------------------------------

                       53t = 365.7

t = 6.9

Substitute 6.9 for t in the first equation and solve for s.

14s + 19(6.9) = 240.3

14s + 131.1 = 240.3

14s = 109.2

s = 7.8

Answer:

shoe store $7.80/hour

telemarketer: $6.90/hour

Number 8 Please!!!!!
Thank You!!!

Answers

Answer:

x = 2 + 5i√2 / 6 and x = 2 - 5i√2 / 6

Step-by-step explanation:

If this isn't right, I'm sorry. Also, you can put x = 2 ± 5i√2 /6 to make it shorter and not have two answers. Hope this helps :)

Six points are plotted on the number line.



Which points on the number line are opposites?

Answers

Answer: P and U

Step-by-step explanation:

please help! ASAP I need help fast!!

Answers

Answer: 4.8

Explanation: divide total needed of blue paint (3) by 1/2 to find the ratio, which is 6. then multiply that by 4/5 to get the total of yellow paint, which is 4.8

The triangle and rectangle belowhave the same area what is the value of w?

(I[m Assuming W =10cm)

Answers

the formula for area of a triangle is 1/2 times the base (4 cm) times the height (5 cm) so the area of the triangle would be 10 cm. to find the area of the rectangle you would divide 10 by 4, which means that w=2.5 cm

Can someone help me please

Answers

Answer:

31.25

Step-by-step explanation:

Divide 250 by 8=31.25

Need help please and thank you.​

Answers

Answer:

[tex]log_4(\frac{1}{64})=-3[/tex]

Step-by-step explanation:

[tex]log_b(b^x)=x[/tex]

Let b = base and x = the exponent

    Looking at the equation given, we know the base (the number with the exponent) is 4, the exponent itself is -3, and the value is 1/64. Based on this information, fill in the formula and simplify any values.

[tex]log_4(4^{-3})=-3\\log_4(\frac{1}{64})=-3[/tex]

Therefore, the logarithmic form is [tex]log_4(\frac{1}{64})=-3[/tex].

PLEASE HELP ME WITH THIS!!

Answers

Answer:

A 3x10^-6

Step-by-step explanation:

The candy store is selling Twizzlers. They have a sale of four Twizzlers for $6.00. Which equation below represents this proportional relationship?
A. y=1.5x C. y= x 2/3 B. x= 4y D. x= 6y

Answers

Answer:A. y=1.5x

Step-by-step explanation:

x represents the number of twizzlers

1.5 represents the the price that you have to pay for each Twizzlers

And y represents the total cost

100 drops of water weigh 9 grams so how many tons do 100 million drops of water weigh

Answers

Answer:

100 drops of water weigh about 9 grams. So how many tons do 100 million drops of water weigh?

Step-by-step explanation:

please mark my answer in brainlist plz

100 drops = 9 grams
100 million is 100 x million
so 9 x million is 9 million

A
B
(7y+9)
If
2yº
04
с
What’s m

Answers

Answer:

acute angles A and C are 38°obtuse angles B and D are 142°

Step-by-step explanation:

We assume the figure is a parallelogram, so the sum of the marked angles is 180°.

  2y +(7y +9) = 180

  9y +9 = 180 . . . . . . . simplify

  y +1 = 20 . . . . . . . . . divide by 9

  y = 19

m∠BCD = 2y° = 38°

m∠ABC = (7y+9)° = (7·19 +9)° = 142°

0.5 + (-1.5) - (-5.5) =

Answers

Answer:

4.5

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

0.5 + ( -1.5 ) = -1

-1 - (-5.5) = 4.5

Hopefully this helped you. :)

What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work.
y = -2x - 7
y = 2x + 17
y = 1/2x + 8
y = -1/2x + 2

Answers

Answer:

y = m x + b    equation for a straight line

m m' = -1    for perpendicular lines

Thus m' = -1/2    is required

Check:

-1/2 * -6 + 2 = = 3 + 2 = 5 = y    for the last equation give

a sphere has a volume of 2,304 pi mm3. find the diameter of the sphere

Answers

Answer:

24

the formula of sphere is

[tex]v = \frac{4}{3} {r}^{3} [/tex]

Since we know the volume, and have to find the diameter (twice the radius), we need to determine the radius first.

Hence, using the given data:

[tex]2304\pi = \frac{4}{3} \pi {r}^{3} [/tex]

We can cancel

We can cancel π from each side.

[tex]2304 = \frac{4}{3} {r}^{3} [/tex]

Multiply both sides by

[tex] \frac{3}{4} [/tex]

hope I help you ☺️❤️

Apply the distributive property to create an equivalent expression.
(6m -7)x4 =

Answers

Answer:

6mx^4-7x^4

Step-by-step explanation:

0.03249 in standard form to 3 significant figures is

(A) 3.24 × 10−1

(B) 3.24 × 10−2

(C) 3.25 × 10−2

(D) 3.25 × 10−3

​

Answers

I think the answer is d
Other Questions
What does the simile mean between a roller coaster can feel like flying 1) How many moles of hydrogen gas can be produced if 0.57 moles of hydrochloricacid, HCl, reacts with excess solid zinc according to the following chemicalequation?2 HCl + Zn Hz + ZnCl2 PLS ANSWER WILL GIVE BRAINLYEST Create a timeline of ancient egypt history please someone help me quickkkkk Why was the transfer of power after the election 1800 significant?A. It set the precedent that intense campaign elections hurt the peaceful transfer of power and should be avoided.B. It set the precedent that elections should never be decided by the House of Representatives because that threatened a peaceful transfer of power.C. It set the precedent that political parties would always challenge the results of the election to make sure the transfer of power was legitimate.D. It set the precedent that the losing faction would accept the election results and help with a peaceful power transfer.........................................................................................What was significant about Jefferson's 1801 inaugural address?A. It was used to suggest that political parties were bad for the nation.B. It was used to call for a more fair election process.C. It was used to explain why the Federalists were bad leaders.D. It was used to unify the nation.................................................................................How did the ruling of McCulloch v. Maryland affect the federal government?A, It established that the Supreme Court would judge all cases involving the U.S. Constitution.B. It allowed state courts to judge cases in which state and national laws conflicted, weakening the U.S. Supreme Court's authority.C. It increased the power of Congress to carry out its lawmaking duties.D. It limited the ability of the president to enforce laws, giving more power to state governors.................................How did Marbury v. Madison help balance the federal government in the United States?A. It declared that states could decide whether or not to follow federal laws.B. It empowered Congress to review cases made by the courts through the "necessary and proper" ruling.C. It allowed the president to decide which law to follow if Congress and the Supreme Court had differing opinions.D. It allowed the Supreme Court to check the actions of the other two branches through judicial review.....(please answer all of them if your gonna answer) Where is the Christian population concentrated?in the United Statesin North Americain Europeall over the world Help me please With one worker, total production is 100. When a second worker is added, total product increases to 300. The marginal product of the second worker is .???100.200.400.300. (Plz can anyone help me with this.) Not sure how this works as a fraction to place the dot in the right place Laying fiber-optic cable is expensive. Cable companies want to make sure that if they extend their lines to less dense suburban or rural areas, there will be sufficient demand so the work will be cost-effective. They decide to conduct a survey to determine the proportion of households in a rural subdivision that would buy the service. They select a simple random sample of 5 blocks in the subdivision and survey each family that lives on one of those blocks.a. What is the name for this kind of sampling method?b. Give a possible reason why the cable company chose this method. Maybe Audrey waited 6 pounds 14 in ounces at birth convert her weight to ounces What is the molarity of a 75.0 mL solution that contains 0.225 g of potassium nitrate? If p is the smallest of four consecutive even integers, what is their sum interms of P?plz be fast I need full step by step the explanation Here is 100 points!!!!!! Hope these will help you!!!! 12/14 , 15/, 19/24 which one is greater? What is x, the distance between points A and A'? 2. 4 units 4. 8 units 13. 6 units 14. 4 units. Can Someone plz help me? :(( what type of pandemic hit during the war in (1918- 1919).a,AIDSb,FLUc, PLAGUEd,none of these whats 3y/2 if y = -2 which president signed the bill that created of the u.s. air force?