therronvictorjr

04.05.2020 •

Mathematics

Item 5
Question 1
Find and interpret the mean absolute deviation of the data.

Prices of Remote-Controlled Drones (dollars)
300 550 500 650 750
500 850 350 450 600

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Ответ:

brackendillman

18.04.2021

Mathematics

The volume of the cone is shrinking at the rate $100\pi$ cubic inches / min.

Step-by-step explanation:

Formula:

$\frac{d}{dx}(uv)=v\frac{du}{dt}+u\frac{dv}{dt}$ $\frac{d}{dx}(u^n)=nu^{n-1}\frac{du}{dx}$

Given that,

The base of a cone is expanding at the rate of 1 in / min while it height is shrinking at the rate 3 in/ min.

i.e

$\frac{dr}{dt}=1 \ in/min$

and

$\frac{dh}{dt}= -3 \ in/min$ [ since height is shirking]

The volume of a cone is

$V=\frac13 \pi r^2h$

Differentiating with respect to t

$\frac{dV}{dt} =\frac13\pi \{h \frac{d}{dt}(r^2)+r^2\frac{d}{dt}(h)\}$

$\Rightarrow\frac{dV}{dt}=\frac13\pi (h.2r \frac{dr}{dt}+r^2\frac{dh}{dt})$

Now putting $\frac{dr}{dt}=1 \ in/min$ and $\frac{dh}{dt}= -3 \ in/min$

$\frac{dV}{dt}=\frac13\pi \{h.2r (1)+r^2(-3)\}$

$\Rightarrow \frac{dV}{dt}=\frac13\pi (2hr -3r^2)$

To find the rate of changing volume at the moment when base radius is 30 in and the height is 40 in, we need to put r= 30 in and h=40 in.

$\frac{dV}{dt}|_{r=30,h=40}=\frac13\pi \{2.40.30 -3(30)^2\}$

$=-100\pi$ cubic inches / min

The volume of the cone is shrinking at the rate $100\pi$ cubic inches / min.

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Item 5 Question 1 Find and interpret the mean absolute deviation of the data. Prices of Remote-Controlled Drones (dollars) 300 550 500 650 750 500 850 350 450 600