<span> Direct-substituting x = -2 gives 0/0, so we know that by the factor theorem, both the numerator and denominator have a factor of x + 2. From there, we can cancel out the conflicting factors and apply the limit.
We can factor the numerator and denominator to get:
x^3 - x^2 - x + 10 = (x + 2)(x^2 - 3x + 5)
x^2 + 3x + 2 = (x + 2)(x + 1).
So we have:
lim (x-->-2) (x^3 - x^2 - x + 10)/(x^2 + 3x + 2)
= lim (x-->-2) [(x + 2)(x^2 - 3x + 5)]/[(x + 2)(x + 1)]
= lim (x-->-2) (x^2 - 3x + 5)/(x + 1), by canceling out x + 2
= [2^2 - 3(-2) + 5]/(-2 + 1)
= (4 + 6 + 5)/(-1)
= -15.
I hope this helps! </span>
This is your perfect answer.
Simplifying
12x = 15y
Solving
12x = 15y
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '12'.
x = 1.25y
Simplifying
x = 1.25y
9514 1404 393
Answer:
309.33π yd³
Step-by-step explanation:
We can subtract the volume of the sphere from the volume of the cone, but we'd like to point out that said difference is irrelevant to the problem. The sphere does not fit into the cone. We cannot tell exactly how the composite figure is constructed.
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Cone volume is ...
V = 1/3πr²h
V = 1/3π(10 yd)²(23 yd) = 2300π/3 yd³
Sphere volume is ...
V = 4/3πr³ = 4/3π(7 yd)³ = 1372π/3 yd³
The difference between the cone volume and the sphere volume is ...
(2300 -1372)π/3 yd³ ≈ 309.33π yd³
Answer:
The terms are - 1, 7 and 15.
Step-by-step explanation:
Let the terms be a-d, a and a+d
ATQ, a-d+a+a+d=21, a=7. a+d-(a+(a-d))=9. d=8. The terms are - 1, 7 and 15.
Answer: 2, 3, 5
Step-by-step explanation:
