Mathematics College

y/x dy/dx=(1+x^2)^-1/2(1+y^2)^1/2

Answers

Answer 1

Answer:

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+c

Step-by-step explanation:

This is separable.

Multiply x dx on both sides and divide both sides by (1+y)^(1/2) to obtain:

y/(1+y)^(1/2)=(1+x)^(-1/2) x dx

Using law of exponents to get rid of negative exponent by finding reciprocal:

y/(1+y)^(1/2)=x/(1+x)^(1/2) dx

Let u=(1+y)^(1/2).

Then u^2=1+y.

Differentiate: 2 u du=dy

[Let v=(1+x)^(1/2).]

Plug in our substitution:

(u^2-1) 2u du/u=(v^2-1) 2v dv/v

Simplify:

(u^2-1) 2 du=(v^2-1) 2 dv

Integrate both sides:

(u^3/3-u) 2+L=(v^3/3-v) 2+K

Divide both sides by 2:

u^3/3-u +L/2=v^3/3-v+K/2

K/2-L/2 is just a constant value C:

u^3/3-u=v^3/3-v+C

Use substitution again to put back in terms of x and y:

((1+y)^(1/2))^3/3-(1+y)^(1/2)=((1+x)^(1/2))^3/3-(1+x)^(1/2)+C

Simplify the exponent part a bit:

(1+y)^(3/2)/3-(1+y)^(1/2)=(1+x)^(3/2)/3-(1+x)^(1/2)+C

I don't like the division by 3 so multiply both sides by 3:

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+3C

3C is still just an unknown constant, c.

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+c

Related Questions

51 is 10% of what number

Answers

Answer:

10 percent of 51 is 5.1

Answer:

51=10

510=100

Step-by-step explanation:

51=10/100

x10

510

Problem 3: If a single six-sided die is rolled five times, what is the probability that a six is thrown exactly three times

Answers

Answer:

So the probability that a die thrown 5 times will result in a 6 exactly 3 times is 0.03215.

Step-by-step explanation:

HOPE IT HELPS I'M FILIPINO STUDENTS

please help i am stuck

Answers

Explanation:

All of these are done the same way.

1. Set your compass to a distance slightly longer than the distance from the point to the line you want the perpendicular to.

2. Using the point as a center, draw an arc that intersects the line in 2 places. Consider those points to be "P" and "Q".

3. You can leave the compass as is, or set it to any other distance longer than half the distance between P and Q. Using this radius, and using P and Q as centers, draw intersecting arcs on the other side of the line from the original point. Consider the intersection of those arcs to be point "R".

4. A line through the original point and point R will be perpendicular to the line, as you want.

_____

In problem 1, the point and line are obvious.

In problem 2, the point is the vertex opposite the line of interest. (There will be 3 similar constructions.)

18)Angel A and angle b are vertical angles so they are congruent angles. If angle A is (4x+5)° and angle B (-2(x-17.5))° Find the measure of angle B

Answers

Answer:

Measure of Angle B = 25°

Step-by-step explanation:

Something to keep in mind: Angle A and B are Vertical Angles so they will always be equal

so;

Angle A = Angle B

(4x + 5) = (-2(x - 17.5))

4x + 5 = -2x + 35 (<= Solved by distributive property)

6x + 5 = 35

6x = 30

x = 5

Now we can find the measure of Angle B, by substituting x by 5 in the B equation;

-2 (x - 17.5) = Angle B

-2 (5 - 17.5) = Angle

-2 (-12.5) = Angel B

25 = Angle B

so measure of angle B = 25

Hope this helps!

Hi, I got 8 points off on this problem, can you help me figure out what I did wrong?

Answers

Answer:

Possible errors: Triangle classification and definition.

Step-by-step explanation:

An isoceles triangle has at least two congruent sides of the same length.

Given the triangle that has two equal angles, and that you'll have to prove that the triangle also has two equal sides.

Using the Converse of Isoceles Triangle Theorem, where it states that if a triangle has two congruent angles < PQR ≅ < PRQ, for which opposite sides of those angles are congruent:

The opposite side of <PQR is line PR.The opposite side of <PRQ is line PQ.

Additionally, connecting point P to point X along the line QR such that PX ⊥ QR, divides △PQR into two symmetrical sections, where points Q and R are equidistant from point X.

Answer:

Possible errors: Triangle classification and definition.

plz help me find this answer

Answers

Answer:

You have to check which of numbers is the lowest.

Cheers :D

a line with slope -2 passes through the point (-2,3). What is the equation of the line?

Answers

y=-2x+4 i believe is the answer

Which of the following is the greatest common factor of 48 and 32?

Answers

Answer:

Step-by-step explanation:

cus...

Hi. can you help me?

Answers

Answer:

Sure

Step-by-step explanation:

First you need to ____

Next you need to ____

Last, put nothing

That's what you did, so I helped you out.

Is dis good

i- I think you forgot to put the picture.

Two integers are relatively prime if, and only if, their greatest common divisor is 1. For example, 2 and 3 are relatively prime, 1 and 1 are relatively prime, but 2 and 2 are not. You toss two dice, one blue and one gray. What is the probability that when the dice stop rolling that the pip count on the blue die is relatively prime to the pip count on the gray die and the gray die is showing six pips

Answers

Answer:

Step-by-step explanation:

A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)

How to find answer to: 8% of ? = 20

Answers

Answer:

You have to do 8/100 * 20

Step-by-step explanation:

Steps to solve "what percent is 8 of 20?" If you are using a calculator, simply enter 8÷20×100 which will give you 40 as the answer.

help me does anyone know the answer to this? what is 4y+13=?

Answers

Answer:

I think Colorfulmusic is correct

Step-by-step explanation:

3.25 I'm pretty sure

How many pounds are in 1 1/2 pounds and 8 ounces?

Answers

Answer:

2 pounds

Step-by-step explanation:

Because 8 ounces = 0.5 pounds

1.5+0.5=2

A farmer had 21 goats all but 9 died how many survive ?

Answers

Answer:

Step-by-step explanation:

All but 9

Answer:

Step-by-step explanation:

I used a calculator I hhhhhhj

Which value of x is a solution of the inequality?
3x−3≥9

Answers

Answer:

It's probably X since X doesn't have a written number for it it equals 1.

Step-by-step explanation:

Help pls

A hot-air balloon is 1550 feet off the ground and its altitude is slowly changing at a constant rate of −7 1/2 feet per second.

How many seconds, s, will it take for the balloon to drop to below 465 feet?

Drag and drop a symbol and value to correctly complete the solution to this inequality.

Answers

Answer:

s> 144 2/3

Step-by-step explanation:

I took the test in k12 and i got it right so yea !

Answer: the other person was right

Step-by-step explanation:

The graph shows the distribution of the amount of time (in minutes) people spend watching TV shows on a popular streaming service. The distribution is approximately Normal, with a mean of 71 minutes and a standard deviation of 15 minutes.
A graph titled Streaming T V has time (minutes) on the x-axis, going from 11 to 131 in increments of 15. The highest point of the curve is at 71.
What percentage of people spend between 41 and 56 minutes watching TV shows on this streaming service?
a- 13.5%
b- 34%
c- 47.5%
d- 95%
answer:a 13.5

Answers

Using the normal distribution, it is found that the percentage of people spend between 41 and 56 minutes watching TV shows on this streaming service is:

a) 13.5%

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The mean is of 71, hence [tex]\mu = 71[/tex]The standard deviation is of 15, hence [tex]\sigma = 15[/tex]

The proportion between 41 and 56 minutes is the p-value of Z when X = 56 subtracted by the p-value of Z when X = 41, hence:

X = 56:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{56 - 71}{15}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.16

X = 41:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{41 - 71}{15}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.025

0.16 - 0.025 = 0.135

0.135 x 100% = 13.5%

Hence option a is correct.

A similar problem is given at https://brainly.com/question/25769446

Pls answer will give brainiest

Answers

Answer:

D. is your answer

A jogger ran 13.5 miles in 3 hours.

What is the unit rate?

Answers

Answer:

Unit rate = 4.5 mph.

Step-by-step explanation:

Unit rate: 13.5/3

=> Unit rate: 4.5 mph.

Hoped this helped.

-
What are the odds of winning a game, if the probability of winning the game is 4/10

Answers

Answer:

40%

Step-by-step explanation:

4/10 = 40/100

40/100 as a percentage is 40%

Solve the inequality -3/4(12x+16)<9-5x.

Answers

Answer:

x > -21/4

Step-by-step explanation:

Answer:

x > -24/4

Step-by-step explanation:

-3/4 (12x + 16) < 9 - 5x

-3/4 * 12x - 3/4 * 16 < 9-5x

-9x - 3/4 * 16 < 9 - 5x

-9x - 12 < 9 - 5x

-4x - 12 < 9

-4x < 21

Second Graph problem! Can anybody please help me out with this? (Almost done for today) (Algebra graph problem)

Answers

Answer:

x = -2

Step-by-step explanation:

The expression f(x) = 1 corresponds to the point on the graph that is 1 unit above the x-axis. You can locate that horizontal line and see where it intersects the graph. That point of intersection is 2 grid squares to the left of the y-axis, where x = -2.

f(-2) = 1

x = -2

solve pls brainliest

Answers

Answer:

for the first one it 2

An elevator travels 310 feet in 10 seconds.

1. At that speed, how far can this elevator travel in 12 seconds?

Answers

Answer:

372

Step-by-step explanation:

1 sec=31 feet

10 sec=310 feet

12 sec=372 feet

Pls answer, will award brainliest

Answers

1.00065528... Is the correct answer.

The graph of f(x) = x2 has been shifted into the form f(x) = (x - h)2 + k:
5
365
What is the value of k? (1 point)
0 1
0-1
O-2
O 2

Answers

The value of k would be 1. This is because the points (h, k) is the vertex and since k is the y-value of the vertex, we can see from the graph that it’s 1.

QUICK! I NEED HELP ASAP
---------------------
w−(−1/3)=2.05

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

w =

Answers

Answer:

w=6

Step-by-step explanation: you should just look it up on line

Answer:

The correct answer is 1 43/60

Step-by-step explanation:

you convert 2.05 to a fraction and get 2 23/60 - (-1/3) = 1 43/60

i also took the test

-2-(3(x+6)-9-(7-x)-3x

Answers

Answer:

- 24 - 5x

Step-by-step explanation:

1) Remove Parentheses

-2 - 3x - 6 - 9 - 7 + x - 3x

2) Collect like terms

( -2 - 6 - 9 - 7) + (-3x+x-3x)

3) Simplify

Please take a look at the picture

Answers

Answer:

Step-by-step explanation:

-6-(-5)=-6+5

=-1

Answer:

D) The number that is 5 to the right of -6 on the number line

Hope this helps :)

Which graph represents the function y = 2x - 4?
ТУ
2
2
.
4
X +
x
-4 -3 -2 -1
X
TO
O
-3 -2 -1
2.34

Answers

Answer:

the third graph.

the one where x intercept with 2

Step-by-step explanation:

2x-4=0

2x=4

x=2

therefore the graph should have a line that have a x-intercept of 2

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