Integrating with shells is the easier method.
<em>V</em> = 2<em>π</em> ∫₁³ <em>x</em> (√<em>x</em> + 3<em>x</em>) d<em>x</em>
That is, at various values of <em>x</em> in the interval [1, 3], we take <em>n</em> shells of radius <em>x</em>, height <em>y</em> = √<em>x</em> + 3<em>x</em>, and thickness ∆<em>x</em> so that each shell contributes a volume of 2<em>π</em> <em>x</em> (√<em>x</em> + 3<em>x</em>) ∆<em>x</em>. We then let <em>n</em> → ∞ so that ∆<em>x</em> → d<em>x</em> and sum all of the volumes by integrating.
To compute the integral, just expand the integrand:
<em>V</em> = 2<em>π</em> ∫₁³ (<em>x </em>³ʹ² + 3<em>x</em> ²) d<em>x</em>
<em>V</em> = 2<em>π</em> (2/5 <em>x </em>⁵ʹ² + <em>x</em> ³) |₁³
<em>V</em> = 2<em>π</em> ((2/5 ×<em> </em>3⁵ʹ² + 3³) - (2/5 × 1⁵ʹ² + 1³))
<em>V</em> = 4<em>π</em>/5 (9√3 + 64)
38.
38/40=.95 so 2answers incorrect is the answer
Just so you know, it has to be written as a lowercase i to represent an imaginary number.
a) 2i
The square root of 4 is 2, the negative under the square root is what makes it imaginary
b) 2i times the square root of 3
c) 5 + (5i times the square root of 2)
d) 3 - (i times the square root of 2)
Answer:
4000
Step-by-step explanation:
V=4/3(3)(10)^3
V= 4/3 (3)(1000)
V=4/3 (3000)
V=4000
Answer:
All circles are similar. Since they are all the same shape; they are all alike. It is a property.
Step-by-step explanation: