To visit his grandmother, Michael takes a motorcycle 3.853.853, point, 85 kilometers and a horse 3.323.323, point, 32 kilometers. In total, the journey takes 50.5450.5450, point, 54 minutes. How many kilometers is Michael's journey in total?

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Ответ:

JorgeW5St

24.03.2021

Mathematics

0.286 ft per minute ( approx )

Step-by-step explanation:

Let r represents the radius and h represents the height of the cone,

If the conical tank is 10 feet across and 12 ft deep,

Diameter = 10 ft, h = 10 ft

⇒ 2r = 10 ⇒ r = 5 feet,

Now, radius of a cone and its height is always in same proportion,

$\frac{r}{h}=\frac{5}{12}$

$\implies r =\frac{5}{12}h-----(1)$

Now, volume of a cone,

$V=\frac{1}{3}\pi r^2 h$

From equation (1),

$V = \frac{1}{3}\pi (\frac{5}{12} h)^2 h$

$V = \frac{1}{3}\pi (\frac{25}{144} h^2)h$

$V=\frac{25}{432}\pi h^3$

Differentiating with respect to t ( time ),

$\frac{dV}{dt}=\frac{25}{432}\pi (3h^2)\frac{dh}{dt}$

$\frac{dV}{dt} = \frac{25}{144}\pi h^2\frac{dh}{dt}$

Here, $\frac{dV}{dt}=10\text{ cubic ft per min}, h = 8\text{ ft }$

$10 =\frac{25}{144}\pi (8)^2 \frac{dh}{dt}$

$10 = \frac{25\times 64\pi }{144} \frac{dh}{dt}$

$10 =\frac{25\times 4\pi }{9}\frac{dh}{dt}$

$\implies \frac{dh}{dt}=\frac{10\times 9}{100\pi }=0.286\text{ ft per minute}$

Hence, the rate of change of the depth of the water would be 0.286 ft per minute

Aconical tank is 10 feet across and 12 feet deep if water is flowing into the tank at a rate of 10 c

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