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tangare [24]
3 years ago
12

Solve e^x = e^2x + 5.

Mathematics
1 answer:
Aliun [14]3 years ago
5 0

Answer:

x= -0.782588

Alternative form= 5/1-e2

Step-by-step explanation:

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Step-by-step explanation:

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a new car is purchased for 207000 dollars. the value of the car depreciates at 11% per year. what will the value of the car be,
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What is the radius of a circle with the equation x^2+y^2+6x-2y+3?
atroni [7]

Answer:

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Step-by-step explanation:

Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms:  x^2 + 6x            + y^2 -2y             = 3.  Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."  

We need to "complete the square" of x^2 + 6x.  I'll just jump in and do it:  Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x:     x^2 + 6x  + 3^2 - 3^2.  Then do the same for y^2 - 2y:  y^2 - 2y + 1^2 - 1^2.

Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2.  Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1.  Making these replacements:

(x + 3)^2 - 9 + (y - 1)^2 -1 = 3.  Move the constants -9 and -1 to the other side of the equation:  (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13

Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r:  r^2 = 13, so that the radius is r = √13.


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