2 years ago

PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A similarity transformation maps

Mathematics

1 answer:

erica [24]2 years ago

3 0

The scale factor would be 3.5

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mihalych1998 [28]

Answer:

(1/4) ⁴

= 1⁴/4⁴

= 1 / 256

Step-by-step explanation:

hope it helps you

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Find the interest on a Principal Balance of $10,000 over the course of eight years with an interest rate of 5.5%. Do this for: S

o-na [289]

10,000$(1+0.055*8)
This is the formula of simple interest

10,000+10,000(0.055*t)
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A tile factory earns money by charging a flat fee for delivery and a sales price of $0.25 per tile. One customer paid a total of

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3 years ago

Algebra!!!! Answer QUICK PLZ<br> 5 questions!!! 50 POINTS!!!!

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Step-by-step explanation:

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2 years ago

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Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu

Alisiya [41]

Let $y=C_1x+C_2x^3=C_1y_1+C_2y_2$ . Then $y_1$ and $y_2$ are two fundamental, linearly independent solution that satisfy

$f(x,y_1,{y_1}',{y_1}'')=0$
$f(x,y_2,{y_2}',{y_2}'')=0$

Note that ${y_1}'=1$ , so that $x{y_1}'-y_1=0$ . Adding $y''$ doesn't change this, since ${y_1}''=0$ .

So if we suppose

$f(x,y,y',y'')=y''+xy'-y=0$

then substituting $y=y_2$ would give

$6x+x(3x^2)-x^3=6x+2x^3\neq0$

To make sure everything cancels out, multiply the second degree term by $-\dfrac{x^2}3$ , so that

$f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y$

Then if $y=y_1+y_2$ , we get

$-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0$

as desired. So one possible ODE would be

$-\dfrac{x^2}3y''+xy'-y=0\iff x^2y''-3xy'+3y=0$

(See "Euler-Cauchy equation" for more info)

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3 years ago