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
Free_Kalibri [48]
2 years ago
13

If the graph of y=f(x) passes through the point (0,1), and dy/dx=xsin(x^2)/y, then f(x)= ?

Mathematics
1 answer:
Zigmanuir [339]2 years ago
4 0

The differential equation

d<em>y</em>/d<em>x</em> = <em>x</em> sin(<em>x</em> ²) / <em>y</em>

is separable as

<em>y</em> d<em>y</em> = <em>x</em> sin(<em>x</em> ²) d<em>x</em>

Integrate both sides:

∫ <em>y</em> d<em>y</em> = ∫ <em>x</em> sin(<em>x</em> ²) d<em>x</em>

∫ <em>y</em> d<em>y</em> = 1/2 ∫ 2<em>x</em> sin(<em>x</em> ²) d<em>x</em>

∫ <em>y</em> d<em>y</em> = 1/2 ∫ sin(<em>x</em> ²) d(<em>x</em> ²)

1/2 <em>y</em> ² = -1/2 cos(<em>x</em> ²) + <em>C</em>

Solve for <em>y</em> implicitly:

<em>y</em> ² = -cos(<em>x</em> ²) + <em>C</em>

Given that <em>y</em> = 1 when <em>x</em> = 0, we get

1² = -cos(0²) + <em>C</em>

1 = -cos(0) + <em>C</em>

1 = -1 + <em>C</em>

<em>C</em> = 2

Then the particular solution to the DE is

<em>y</em> ² = 2 - cos(<em>x</em> ²)

Solving explicitly for <em>y</em> would give two solutions,

<em>y</em> = ± √(2 - cos(<em>x</em> ²))

but only the one with the positive square root satisfies the initial condition:

√(2 - cos(0²)) = √1 = 1

-√(2 - cos(0²)) = -√1 = -1 ≠ 1

So the unique solution to this DE is

<em>y</em> = √(2 - cos(<em>x</em> ²))

You might be interested in
To which place value is the number rounded? 8.293 to 8.29?
lana66690 [7]
Rounded to 1 decimal place
8 0
3 years ago
Read 2 more answers
The change in altitude of a bird after 2 __ 1 2 seconds was –41 __ 1 4 feet. What was the average change in altitude of the bird
svlad2 [7]

Answer:

Average\ Change = -1\frac{7}{10} ft/s

Step-by-step explanation:

Given

Altitude\ Change = -4\frac{1}{4} \ ft

Time = 2\frac{1}{2}\ s

Required

Determine the average change

This is calculated as follows:

Average\ Change = \frac{Altitude\ Change}{Time}

This gives:

Average\ Change = \frac{-4\frac{1}{4}}{2\frac{1}{2}}

Average\ Change = -4\frac{1}{4}/2\frac{1}{2}

Convert to improper fractions

Average\ Change = -\frac{17}{4}/\frac{5}{2}

Convert to multiplication

Average\ Change = -\frac{17}{4}*\frac{2}{5}

Average\ Change = -\frac{17}{2}*\frac{1}{5}

Average\ Change = -\frac{17}{10}

Average\ Change = -1\frac{7}{10} ft/s

8 0
2 years ago
Antoine Purchase 1.8 kg of apples and 315 dekagrams of oranges This was 1350 g more than the weight of bananas bridges what was
victus00 [196]

Answer: 3600 grams

Step-by-step explanation:

A dekagram means 10 grams.

1 kilogram = 1000 grams

Therefore the total number of grams when Antoine Purchase 1.8 kg of apples and 315 dekagrams of oranges will be:

= (1.8 × 1000) + (315 × 10)

= 1800 + 3150

= 4950 grams

Since this was 1350g more than the weight of bananas, the weight of the bananas Antonio purchased in grams will be:

= 4950 - 1350

= 3600 grams

6 0
3 years ago
Select all the values that cannot be probabilities a. 3/5b. 1c. -0.45d. 0.06e. 1.16f. 0g. 5/3h. √2
nikitadnepr [17]

Answer:

c,-0.45 ,

e. 1.16

g. 5/3

h. √2

Cannot be probability.

Step-by-step explanation:

Probability of any occurrence is always in the interval of 0 to 1. 0 and 1 inclusive.

0≤P(A)≤1

Any value outside this boundaries cannot be probability.

Therefore, -0.45,1.16,5/3 and √2 cannot be probability.

4 0
3 years ago
17. Find m2 USW if m_ USW = 7x - 34 and m2 TSR = 4x + 29.​
SVEN [57.7K]

Answer:

Step-by-step explanation:

Find the diagram attached. From the diagram, we can see that;

<USW = <TSR (vertically opposite angles)

Given

<USW = 7x-34

<TSR = 4x+29

Equate

7x-34 = 4x+29

7x-4x = 29+34

3x = 63

x = 63/3

x = 21°

Find <USW

<USW =7x-34

<USW =7(21)-34

<USW = 147-34

<USW = 113°

Hence the measure of <USW is 113°

5 0
3 years ago
Other questions:
  • 2. A rock is thrown from the top of a tall building. The distance, in feet,
    10·1 answer
  • If I equals PRT which equation is equivalent to T
    12·1 answer
  • Which of the following is the correct factorization of this trinomial?
    9·1 answer
  • Alisa bought 3 shirts for $29 each and then spent $15 on lunch. She has $31 left. How much money did she have before?
    9·2 answers
  • Use the general solution to solve 5 - 6x = 8x + 17
    11·2 answers
  • At the zoo, there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys are there
    14·2 answers
  • An elevator descends at a<br> constant speed. What is the change in elevation<br> after 19 seconds?
    7·2 answers
  • What is 4 1/2 plus 6 2/5
    8·2 answers
  • Evaluate without using a calculator sin(90-x)cos(180-x)+tanx.cos(-x)sin(180+x)​
    13·1 answer
  • 5х2 +х — 4<br> Factor completely
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!