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ANTONII [103]
4 years ago
11

Point Q is located at (-4, 6) Point R is located at (8, 6) What is the distance from point Q to point R?

Mathematics
2 answers:
mafiozo [28]4 years ago
8 0
\text {Distance = } \sqrt{(Y2-Y1)^2+ (X2-X1)^2}

\text {Distance = } \sqrt{(6-6)^2+ (8+4)^2}

\text {Distance = } \sqrt{12^2}

\text {Distance = } 12 \text { units}
 
Answer: Distance between QR = 12 units.
Eddi Din [679]4 years ago
7 0
\sqrt{ (8+4)^{2}+ (6-6)^{2}  }
                             ↓
\sqrt{ 12^{2}+ 0^{2}  }
                      ↓
\sqrt{144+0}
           ↓
\sqrt{144}
         ↓
12
The distance between Points Q and R is <em>12 units</em>.
Have a nice day!
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Answer:

c

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How do you do (a) and (b)?
bulgar [2K]

Answer:

See solution below

Step-by-step explanation:

(a) If n=0 or 1, the equation

(1)  y' = a(t)y + f(t)y^n

would be a simple linear differential equation. So, we can assume that n is different  to 0 or 1.

Let's use the following substitution:

(2) z=y^{n-1}

Taking the derivative implicitly and using the chain rule:

(3) z'=(1-n)y^{-n}y'

Multiplying equation (1) on both sides by

(1-n)y^{-n}

we obtain the equation

(1-n)y^{-n}y' = (1-n)y^{-n}a(t)y+(1-n)y^{-n}f(t)y^n

reordering:

(1-n)y^{-n}y' = (1-n)y^{-n}ya(t)+(1-n)y^{-n}y^nf(t)

(1-n)y^{-n}y' = (1-n)y^{1-n}a(t)+(1-n)y^{0}f(t)

(1-n)y^{-n}y' = (1-n)y^{1-n}a(t)+(1-n)f(t)

Now, using (2) and (3) we get:

z'= (1-n)za(t)+(1-n)f(t)

which is an ordinary linear differential equation with unknown function z(t).

(b)

The equation we want to solve is

(4)   xy'+ y = x^4 y^3  

Here, our independent variable is x (instead of t)

Assuming x different to 0, we divide both sides by x to obtain:

y'+\frac{1}{x}y = x^3 y^3

y' = -\frac{1}{x}y+x^3 y^3

Which is an equation of the form (1) with

a(x)=-\frac{1}{x}

f(x)=x^3

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So, if we substitute

z=y^{-2}

we transform equation (4) in the lineal equation

(5) z'=\frac{2}{x}z-2x^3

and this is an ordinary lineal differential equation of first order whose

integrating factor is

e^{\int (-\frac{2}{x})dx}

but

e^{\int (-\frac{2}{x})dx}=e^{-2\int \frac{dx}{x}}=e^{-2ln(x)}=e^{ln(x^{-2})}=x^{-2}=\frac{1}{x^2}

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e^{\int (\frac{2}{x})dx}=x^2

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z(x)=x^2\int (\frac{-2x^3}{x^2})dx+Cx^2=-2x^2\int xdx+Cx^2=\\\ -2x^2\frac{x^2}{2}+Cx^2=-x^4+Cx^2

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Reversing the substitution  

z=y^{-2}

we obtain the general solution of (4)

y=\sqrt{\frac{1}{z}}=\sqrt{\frac{1}{-x^4+Cx^2}}

Attached there is a sketch of several particular solutions corresponding to C=1,4,6

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<u>Y-intercept:</u>

The same goes for the opposite coordinate: if we picture a point at where the line intercepts the y-axis, there will be a point at -10 on the y-axis. Since the point is directly at 0 on the x-axis (meaning that it doesn't go left nor right) we know that the x-coordinate will be 0.

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Answer:

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6 0
4 years ago
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