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

(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

answer: dead jah

step-by-step explanation:

bullet + jah= dead jah

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.