Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Terms/Coefficients
- Expand by FOIL (First Outside Inside Last)
- Factoring
<u>Calculus</u>
Differentiation
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
- Integration Property:

- Fundamental Theorem of Calculus:

- Arc Length Formula:
![\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5Ea_b%20%7B%5Csqrt%7B1%2B%20%5Bf%27%28x%29%5D%5E2%7D%7D%20%5C%2C%20dx)
- Surface Area Formula:
![\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20SA%20%3D%202%5Cpi%20%5Cint%5Climits%5Ea_b%20%7Bf%28x%29%20%5Csqrt%7B1%2B%20%5Bf%27%28x%29%5D%5E2%7D%7D%20%5C%2C%20dx)
Step-by-step explanation:
<u>Step 1: Define</u>
![\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Cfrac%7B1%7D%7B3%7Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20-%20x%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5C%5CInterval%3A%20%5B0%2C%20%5Cfrac%7B1%7D%7B3%7D%5D)
<u>Step 2: Differentiate</u>
- Basic Power Rule:

- [Derivative] Simplify:

- [Derivative] Simplify:

<u>Step 3: Integrate Pt. 1</u>
- Substitute [Surface Area]:
![\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20SA%20%3D%202%5Cpi%20%5Cint%5Climits%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D_0%20%7B%28%5Cfrac%7B1%7D%7B3%7Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20-%20x%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%20%5Csqrt%7B1%2B%20%5B%5Cfrac%7B1%7D%7B6%5Csqrt%7Bx%7D%7D%20-%20%5Cfrac%7B3%5Csqrt%7Bx%7D%7D%7B2%7D%7D%5D%5E2%7D%7D%20%5C%2C%20dx)
- [Integral - √Radical] Expand/Add:

- [Integral - √Radical] Factor:

- [Integral - Simplify]:

- [Integral] Integration Property:

<u>Step 4: Integrate Pt. 2</u>
- [Integral] Define:

- [Integral] Assumption of Positive/Correction Factors:

- [Integral] Expand - FOIL:

- [Integral] Integrate - Basic Power Rule:

- [Expression] Multiply:

<u>Step 5: Integrate Pt. 3</u>
- [Integral] Substitute/Integral - FTC:

- [Integrate] Evaluate FTC:

- [Expression] Multiply:

<em>It is in ft² because it is given that our axis are in ft.</em>
<u>Step 6: Find Amount of Glass</u>
<em>Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.</em>
- Convert ft² to in²:

- Multiply:

And we have our final answer! Hope this helped on your Calc BC journey!
Answer:
The Discriminant is 25
Step-by-step explanation:
For this case, the discriminant will be given by
b ^ 2 - 4 * a * c
Where
b = 7
a = 3
c = 2
substituting
b ^ 2 - 4 * a * c = (7) ^ 2 - 4 * (3) * (2) = 25
Therefore the value of the discriminant is 25.
How many x-intercepts does this function have?
It has two intercepts with the x axis and can be found by equaling the function to zero. That is to say,
3x2 + 7x + 2 = 0
The results will be the interceptions with x.
What are the number of zeros for this function?
The number of zeros for this function is
two real number solutions
Because it is a quadratic function.
Answer:
2
Step-by-step explanation:
7x - 2x = 13 - 3
5x = 10
x = 2
Given:
The expression is
.
To find:
The shows the correct way to use the rule ""multiply by the reciprocal"" for the given expression.
Solution:
According to the rule "multiply by the reciprocal", if a,b,c,d are four number, then

We have,

It can be written as

Using the rule "multiply by the reciprocal", we get



Therefore, the correct option is D.
Answer:
5 + 2 x 9
Step 1 = 7 x 9
Step 2 = 63
Step-by-step explanation:
= 5 + 2 x 9
= 5 + ( 2 x 9 )
= 5 + 18
= 23
Step 2 = 7 x 9
= 63
Step 3 = 63
C. jin did not make a mistake
<em>Sorry </em><em>i'm </em><em>wrong </em><em>:</em><em>)</em>