Find the values of a and b that make f continuous everywhere. f(x) = x^2 − 4 / x − 2 if x < 2 ax^2 − bx + 3 if 2 ≤ x < 3 4
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Hello again! So we will be using the pythagorean theorem (
) to solve for the bottom leg of the triangles. After we do that, we'll subtract the value of the legs from 31, and that'll be x.
Plug in 17 and z (or any variable that isn't x) into the leg variable and 19 into the hypotenuse variable, and from there we can solve.
Solve the exponents to get
Subtract 289 on each side to get
Lastly, square root each side of the equation and your answer should be
(To get more accurate answers, you shouldn't round until the end of the problem)
Nextly, we will need to subtract
from 31. And since there are 2 triangles, you'll need to multiply by 2.
In short, x = 14.0
Plug in 17 and z (or any variable that isn't x) into the leg variable and 19 into the hypotenuse variable, and from there we can solve.
Solve the exponents to get
Subtract 289 on each side to get
Lastly, square root each side of the equation and your answer should be
Nextly, we will need to subtract
In short, x = 14.0