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3 years ago

What is the center of the circle with the equation: X2 + y2 +18x + 14y + 105 = 0

Mathematics

1 answer:

professor190 [17]3 years ago

8 0

Answer:

(9, -7)

Step-by-step explanation:

$x^2+y^2+18x+14y+105=0\\$

Rearrange like x and y terms next to each other, then complete the square on both.

$(x-9)^2-361 + (y+7)^2 - 49 + 105 = 0$

The negative of the # numbers instead the brackets give you the centre of the circle.

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2 years ago

Find a particular solution to the differential equation y′′+2y′+y=2t2−t+3e−2t. y′′+2y′+y=2t2−t+3e−2t.

Jlenok [28]

$y''+2y'+y=2t^2-t+3e^{-2t}$

The characteristic equation is

$r^2+2r+1=(r+1)^2=0\implies r=-1$

so the characteristic solution is

$y_c=C_1e^{-t}+C_2te^{-t}$

For the particular solution, we can try looking for a solution of the form

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Substituting into the ODE, we have

$(2a+4de^{-2t})+2(2at+b-2de^{-2t})+(at^2+bt+c+de^{-2t})=2t^2-t+3e^{-2t}$
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3 years ago

Izzy recently took a math test were each answer a on the main part of the test was worth 8.7 points she also correctly so the bo

anygoal [31]

Answer:

Step-by-step explanation:

8.7A+10=105.7

8.7A=95.7

A=11

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3 years ago