Simplify. Rationalize the denominator. -3/5 + √3
1 answer:
Answer: -3-5 / 5
Step-by-step explanation
To write as a fraction with a common denominator, multiply by 5/5.
-3/5 + * 5/5
Then combine fractions, so that the numeratiors over the common denominator.
-3 + 5 /5
Simplify with factoring out.
Rewrite -3 as -1 (3). Next factor -1 out of 5 . Then facotr -1 out of -1(3) - (-5
). After that move teh negative in front of the fraction.
Exact Form: - 3-5 / 5
Decimal Form: 1.13
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Answer:
maximum: y = 1
minimum: y = 0.
Step-by-step explanation:
Here we have the function:
y = f(x) = √(1 + x^2 - 2x)
we want to find the minimum and maximum in the segment [0, 1]
First, we evaluate in the endpoints, which are 0 and 1.
f(0) =√(1 + 0^2 - 2*0) = 1
f(1) = √(1 + 1^2 - 2*1) = 0
Now let's look at the critical points (the zeros of the first derivate)
To derivate our function, we can use the chain rule:
f(x) = h(g(x))
then
f'(x) = h'(g(x))*g(x)
Here we can define:
h(x) = √x
g(x) = 1 + x^2 - 2x
Then:
f(x) = h(g(x))
f'(x) = 1/2*( 1 + x^2 - 2x)*(2x - 2)
f'(x) = (1 + x^2 - 2x)*(x - 1)
f'(x) = x^3 - 3x^2 + x - 1
this function does not have any zero in the segment [0, 1] (you can look it in the image below)
Thus, the function does not have critical points in the segment.
Then the maximum and minimum are given by the endpoints.
The maximum is 1 (when x = 0)
the minimum is 0 (when x = 1)
