Answer:
660 m squared
Step-by-step explanation:
5 x 12 = 60
60 / 2 = 30
22 x 30 = 660
the volume is 660 m squared
Answer:
![\frac{dh}{dt} = \frac{216}{1875\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cfrac%7B216%7D%7B1875%5Cpi%7D)
Step-by-step explanation:
Given
Represent radius with r and height with h
![h = 12ft](https://tex.z-dn.net/?f=h%20%3D%2012ft)
![r = 10ft](https://tex.z-dn.net/?f=r%20%3D%2010ft)
when ![h = 10ft](https://tex.z-dn.net/?f=h%20%3D%2010ft)
Express radius in terms of height
![\frac{r}{h} = \frac{10}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%7D%20%3D%20%5Cfrac%7B10%7D%7B12%7D)
![\frac{r}{h} = \frac{5}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%7D%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
![r = \frac{5}{6}h](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B5%7D%7B6%7Dh)
First, we need to determine the volume of the cone in terms of height.
![Volume = \frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Substitute ![r = \frac{5}{6}h](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B5%7D%7B6%7Dh)
![V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%20%5Cpi%20%2A%20%28%5Cfrac%7B5%7D%7B6%7Dh%29%5E2%20%2A%20h)
![V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%20%5Cpi%20%2A%20%5Cfrac%7B25%7D%7B36%7Dh%5E2%20%2A%20h)
![V = \frac{1}{3} * \pi * \frac{25}{36}h^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%20%5Cpi%20%2A%20%5Cfrac%7B25%7D%7B36%7Dh%5E3)
![V = \frac{25}{108} \pi h^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B25%7D%7B108%7D%20%5Cpi%20h%5E3)
Differentiate both sides w.r.t time (t)
![\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%203%20%2A%20%20%5Cfrac%7B25%7D%7B108%7D%20%5Cpi%20h%5E%7B3-1%7D%20%2A%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B75%7D%7B108%7D%20%5Cpi%20h%5E%7B2%7D%20%5Cfrac%7Bdh%7D%7Bdt%7D)
Solve for ![\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bdv%7D%7Bdt%7D%20%2A%20%5Cfrac%7B108%7D%7B75%5Cpi%20h%5E2%7D)
At this point,
and ![\frac{dv}{dt} = \frac{8ft^3}{min}](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%20%5Cfrac%7B8ft%5E3%7D%7Bmin%7D)
So, we have:
![\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%208%20%2A%20%5Cfrac%7B108%7D%7B75%5Cpi%2010%5E2%7D)
![\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cfrac%7B8%20%2A%20108%7D%7B75%5Cpi%2010%5E2%7D)
![\frac{dh}{dt} = \frac{864}{7500\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cfrac%7B864%7D%7B7500%5Cpi%7D)
![\frac{dh}{dt} = \frac{216}{1875\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cfrac%7B216%7D%7B1875%5Cpi%7D)
Hence:
The rate is ![\frac{216}{1875\pi} ft/min](https://tex.z-dn.net/?f=%5Cfrac%7B216%7D%7B1875%5Cpi%7D%20ft%2Fmin)
Answer:
it is (8;1)
Step-by-step explanation:
Answer:
c = 7.6
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
<em>a</em> = 7
<em>b</em> = 3
<u>Step 2: Solve for </u><em><u>c</u></em>
- Substitute in variables [Pythagorean Theorem]: 7² + 3² = c²
- Evaluate exponents: 49 + 9 = c²
- Add: 58 = c²
- [Equality Property] Square root both sides: √58 = c
- Rewrite: c = √58
- Evaluate: c = 7.61577
- Round: c = 7.6
I think answer should be 20 please give me brainlest let me know if it’s correct thanks bye have a great day