The measure of angle ABC is 100 because all you do is add the 60 to the 40 and get 100.
The answer is 3 pounds
48=3
Answer:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4x%5E%5Cbigg%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Exponential Properties
- Exponential Property [Rewrite]:

- Exponential Property [Root Rewrite]:
![\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D)
<u>Step 2: Differentiate</u>
- Simplify:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D%20%5Cbigg%29%27)
- Rewrite [Derivative Property - Multiplied Constant]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%7D%20%5Cbigg%29%27)
- Rewrite [Exponential Rule - Root Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7Bx%5E%5CBig%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%20%5Cbigg%29%27)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20x%5E%5Cbigg%7B%5Cfrac%7B-1%7D%7B2%7D%7D%20%5Cbigg%29%27)
- Derivative Rule [Basic Power Rule]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B-1%7D%7B2%7D%20x%5E%5Cbigg%7B%5Cfrac%7B-3%7D%7B2%7D%7D%20%5Cbigg%29)
- Simplify:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4%7D%20x%5E%5Cbigg%7B%5Cfrac%7B-3%7D%7B2%7D%7D)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4x%5E%5Cbigg%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation

in simplest form:
First, find the greatest common factor (GCF) of 12, 15.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 15: 1, 3, 5, 15
The GCF is 3.
Second, divide the numerator (12) by the GCF. / Your problem should look like: 12 ÷ 3 = 4
Third, divide the denominator (15) by the GCF. / Your problem should look like: 15 ÷ 3 = 5
Fourth, rewrite the fraction in the simplified form. / Your problem should look like:

Answer:
Answer:
0.204 KN
Step-by-step explanation:
Height above cube h= (100-15)/100 = 0.85 m
a) force on the top of the cube = ρgh×area
= 1000×9.81×0.85 = 8330 N/m^2
= 833 KN/m^2*0.15^2= 0.187 KN
b) Force on one side of the cube
on top = 8.33 KN/m^2
at bottom ρgh
= 1000×9.8×100/100
=9800 N/m^2
Net Force = area of the diagram
= 8.33×(15/100)^2 + 1/2(9.8-8.33)×(15/100)^2
= 0.204 KN