Question 7 of 10
1 answer:
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Answer:
the volume of the solid is
Step-by-step explanation:
Given the data in the question;
y = x and y = x²
so
x = x²
x - x² = 0
Radius will be; r = ( x - x² )/2
Area of the circular disk πr² = π[ ( x - x² )/2 ]²
A = ( x - x² )²
So, our volume will be;
V = ₀∫¹ A(x) dx
we substitute
= ₀∫¹ ( x - x² )² dx
{ lets expand; ( x - x² )² = x(x-x²) -x²(x-x²) = x² - x³ - x³ + x⁴ = x² + x⁴ - 2x³ }
so we have;
= ₀∫¹ ( x² + x⁴ - 2x³ ) dx
=
+
-
= [
+
-
]
= [
]
V =
Therefore, the volume of the solid is
Answer:
t = 15.42 s
Step-by-step explanation:
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.
We ned to find the time when the rocket will the ground. For this, y = 0
It is a quadratic equation whose solution is given by :
Here, a = -16, b = 242 and c = 73
Neglecting negative value.
So, it will hit the ground in 15.42 s.