Answer:
-1/8
Step-by-step explanation:
lim x approaches -6 (sqrt( 10-x) -4) / (x+6)
Rationalize
(sqrt( 10-x) -4) (sqrt( 10-x) +4)
------------------- * -------------------
(x+6) (sqrt( 10-x) +4)
We know ( a-b) (a+b) = a^2 -b^2
a= ( sqrt(10-x) b = 4
(10-x) -16
-------------------
(x+6) (sqrt( 10-x) +4)
-6-x
-------------------
(x+6) (sqrt( 10-x) +4)
Factor out -1 from the numerator
-1( x+6)
-------------------
(x+6) (sqrt( 10-x) +4)
Cancel x+6 from the numerator and denominator
-1
-------------------
(sqrt( 10-x) +4)
Now take the limit
lim x approaches -6 -1/ (sqrt( 10-x) +4)
-1/ (sqrt( 10- -6) +4)
-1/ (sqrt(16) +4)
-1 /( 4+4)
-1/8
If <em>x</em>² + <em>y</em>² = 1, then <em>y</em> = ±√(1 - <em>x</em>²).
Let <em>f(x)</em> = |<em>x</em>| + |±√(1 - <em>x</em>²)| = |<em>x</em>| + √(1 - <em>x</em>²).
If <em>x</em> < 0, we have |<em>x</em>| = -<em>x</em> ; otherwise, if <em>x</em> ≥ 0, then |<em>x</em>| = <em>x</em>.
• Case 1: suppose <em>x</em> < 0. Then
<em>f(x)</em> = -<em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = -1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = -1/√2 → <em>y</em> = ±1/√2
• Case 2: suppose <em>x</em> ≥ 0. Then
<em>f(x)</em> = <em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = 1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = 1/√2 → <em>y</em> = ±1/√2
In either case, |<em>x</em>| = |<em>y</em>| = 1/√2, so the maximum value of their sum is 2/√2 = √2.
Yes teachers say to do that all the time it helps you
Simplify both sides of the inequality, then isolate the variable. That should leave you with x> - 4
Answer:
B. Y²⁴
Step-by-step explanation:
For perfect cubes, the exponents are a multiple of three. If yᵃ is a perfect cube, then a/3=k where k is a whole number.
Among the provided choices, the exponent of y²⁴ is divisible by 3.
24/3 = 8.
Thus y²⁴ is a perfect cube.
