Answer:
4) c = 10
5) b = 10
6) b = 12
7) a = 4
Step-by-step explanation:
<h3>Pythagorean Theorem = a^2 + b^2 = c^2</h3>
to solve these, just substitute a, b, and c for the values given.
4) a = 8, b = 6
a^2 + b^2 = c^2
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
c = ![\sqrt{100}](https://tex.z-dn.net/?f=%5Csqrt%7B100%7D)
c = 10
5) a = 24, c = 26
a^2 + b^2 = c^2
24^2 + b^2 = 26^2
576 + b^2 = 676
subtract 576 from both sides
b^2 = 676 - 576
b^2 = 100
b = 10
6) a = 5, c = 13
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
subtract 25 from both sides
b^2 = 169 - 25
b^2 = 144
b = 12
7) b = 11, c = ![\sqrt{137}](https://tex.z-dn.net/?f=%5Csqrt%7B137%7D)
a^2 + b^2 = c^2
a^2 + 11^2 = 137
a^2 + 121 = 137
a^2 = 137 - 121
a^2 = 16
a = 4
Answer: 90
Step-by-step explanation:
Answer:
![\displaystyle 51](https://tex.z-dn.net/?f=%5Cdisplaystyle%2051)
General Formulas and Concepts:
<u>Algebra I</u>
- Terms/Coefficients
- Factoring
- Functions
- Function Notation
<u>Algebra II</u>
<u>Calculus</u>
Limits
- Right-Side Limit:
![\displaystyle \lim_{x \to c^+} f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%20c%5E%2B%7D%20f%28x%29)
Limit Rule [Variable Direct Substitution]: ![\displaystyle \lim_{x \to c} x = c](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20x%20%3D%20c)
Limit Property [Addition/Subtraction]: ![\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%20%3D%20%20%5Clim_%7Bx%20%5Cto%20c%7D%20f%28x%29%20%5Cpm%20%5Clim_%7Bx%20%5Cto%20c%7D%20g%28x%29)
Limit Property [Multiplied Constant]: ![\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20bf%28x%29%20%3D%20b%20%5Clim_%7Bx%20%5Cto%20c%7D%20f%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cleft%20%5C%7B%20%7B%7B3%5Csqrt%7B2x%20-%201%7D%2C%20%5C%20x%20%5Cleq%202%7D%20%5Catop%20%7B6%282x%20-%201%29%5E2%20-%203%2C%20%5C%20x%20%3E%202%7D%7D%20%5Cright.)
<u>Step 2: Solve</u>
- Substitute in function [Limit]:
![\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%202%5E%2B%7D%206%282x%20-%201%29%5E2%20-%203)
- Factor:
![\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%202%5E%2B%7D%203%5B2%282x%20-%201%29%5E2%20-%201%5D)
- Rewrite [Limit Property - Multiplied Constant]:
![\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%203%5Clim_%7Bx%20%5Cto%202%5E%2B%7D%202%282x%20-%201%29%5E2%20-%201)
- Evaluate [Limit Property - Variable Direct Substitution]:
![\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%203%5B2%282%20%5Ccdot%202%20-%201%29%5E2%20-%201%5D)
- Simplify:
![\displaystyle 51](https://tex.z-dn.net/?f=%5Cdisplaystyle%2051)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Answer:
Step-by-step explanation: