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)
Step-by-step explanation:
to divide by a fraction is the same as to multiply by the upside-down fraction.
in your example
4 / 2/5 = 4 × 5/2 = 20/2 = 10
by the way, also a whole number is a fraction.
4 = 4/1
so, fully formal, the whole operation above looks like
(4/1) / (2/5) = (4/1) × (5/2) = (4×5) / (1×2) = 20/2 = 10/1 = 10
Answer:
she and her friends will each get 2.5 cookies
Step-by-step explanation:
it simple
you divide 10 / 4 and you get 2.5 cookies
each person will get 2.5 cookies
Answer:
(a) The daily total revenue realized from the sale of 210 units of the toaster oven is $6,195.
(b) The additional revenue realized when the production (and sales) level is increased from 210 to 310 units is $1,400.
Step-by-step explanation:
The marginal revenue gives the actual revenue realized from the sale of an additional unit of the commodity given that sales are already at a certain level. The derivative <em>R'</em> of the function <em>R</em> measures the rate of change of the revenue function.
We know that the daily marginal revenue function is given by
(a) To find the the daily total revenue you must:
- Integrate the daily marginal revenue function,
,
where C is a constant.
- Find the value of C, using the fact that if you sell 0 units your daily revenue is $0.
The daily total revenue realized from the sale of 210 units of the toaster oven is
x = 210 units
(b) To find the additional revenue realized when the production (and sales) level is increased from 210 to 310 units you must:
- Find the daily total revenue realized from the sale of 310 units
The additional revenue realized when the production (and sales) level is increased from 210 to 310 units is
