Which number has the the greatest absolute value? -20 -10 0 10

Solve the Differential equation 2(y-4x^2) dx + x dy = 0

padilas [110]

Assume a solution of the form $\Psi(x,y)=C$ . Taking the differential of both sides would give the ODE

$\Psi_x\,\mathrm dx+\Psi_y\,\mathrm dy=0$

where $\Psi_x=2y-8x^2$ and $\Psi_y=x$ . The ODE is exact if $\Psi_{xy}=\Psi_{yx}$ . We have

$\Psi_{xy}=(2y-8x^2)_y=2$

$\Psi_{yx}=(x)_x=1$

so the ODE is not exact. However, multiplying both sides by $x$ gives

$(2xy-8x^3)\,\mathrm dx+x^2\,\mathrm dy=0$

and now

$(x\Psi_x)_y=(2xy-8x^3)_y=2x$

$(x\Psi_y)_x=(x^2)_x=2x$

so the ODE is now exact.

Now,

$\Psi_x=2xy-8x^3\implies \Psi(x,y)=x^2y-2x^4+f(y)$

$\Psi_y=x^2=x^2+f_y\implies f_y=0\implies f(y)=C$

So the ODE has solution

$\Psi(x,y)=x^2y-2x^4+C=C$

or simply

$\boxed{x^2y-2x^4=C}$

3 0

4 years ago

George wants to rent a car for a road trip with his friends. He checked the rentals with two companies. Company A charges a non-

andre [41]

Answer:

Company A has a greater daily rate

Step-by-step explanation:

Given

Company A

$Base\ Charges=\$50$

$Daily\ Rate = \$150$

Company B

$f(x) = 50(2x +1)$

Required

Determine the company with greater rate

Simplify the expression of company B

$f(x) = 50(2x +1)$

$f(x) = 50 * 2x + 50 * 1$

$f(x) = 100x + 50$

In a linear function:

$f(x) = mx + b$

m represents the rates.

This implies that the rate of company B is:

$Rate =100$

and the rate of company A is

$Daily\ Rate = \$150$

By comparison:

Company A has a greater daily rate

7 0

3 years ago

Given: AP=AQ, BP=BQ, CP=CQ Prove: A, B and C are collinear.

meriva

Solution:

Given: In the given figure, where there are pair of Quadrilateral, in which AP=A Q, BP=B Q, C P=C Q .

To Prove : A, B and C are collinear.

Construction: Join AC , the point where it intersects P Q is M.

Proof:

AP=A Q, C P=C Q,

So, the quadrilateral A P C Q is a kite.→→If in a quadrilateral One pair of adjacent sides are equal, then the quadrilateral is a kite.

As we know in a kite Diagonals bisect each other at right angles.

∠AMP=∠A M Q=∠CM P=∠C M Q=90°

Also, BP=B Q, C P=C Q.

So, the quadrilateral B P C Q is a kite.

∠B MP=∠B M Q=∠CM P=∠C M Q=90°

As you can see that , 1. ∠AMP +∠CM P=90°+90°=180°→→Shows Point A and C are in line.------------(1)

2. ∠B MP +∠CM P=90°+90°=180°→→→Shows Point B and C are in line.------------------(2)

Combining (1) and (2),

Shows that point A, B,C lie in a line.

It means Points A, B,C are Collinear.

3 0

3 years ago

Which of the following functions is graphed below?

telo118 [61]

Answer:

i think it is Answer D i am not sure

Step-by-step explanation:

8 0

3 years ago

How do I work this problem out..23÷560

attashe74 [19]

Divide 560 by 23, 23 goes into 560 24.347 times.

5 0

4 years ago

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