Answer:
150 Newton Meters (Nm) = 110.634 Foot-Pound Force (ft lbf) 1 Nm = 0.737562 ft lbf. 1 ft lbf = 1.355818 Nm.
Step-by-step explanation:
It's best to move a dresser with the drawers inside so you can wrap and protect it before carrying it through doorways. But, if it's solid wood and too heavy to move, you can take the drawers out to lighten the load.
Is it a game?
I think I’ve played this before
Answer:
n = 8
Step-by-step explanation:
The angles are vertical angles and so they are equal
9n = 8n+8
Subtract 8n from each side
9n - 8n = 8n+8-8n
n = 8
Answer:
Diverges
General Formulas and Concepts:
<u>Algebra I</u>
- Exponential Rule [Dividing]:
![\displaystyle \frac{b^m}{b^n} = b^{m - n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bb%5Em%7D%7Bb%5En%7D%20%3D%20b%5E%7Bm%20-%20n%7D)
<u>Calculus</u>
Limits
- 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)
Series Convergence Tests
- P-Series:
![\displaystyle \sum^{\infty}_{n = 1} \frac{1}{n^p}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum%5E%7B%5Cinfty%7D_%7Bn%20%3D%201%7D%20%5Cfrac%7B1%7D%7Bn%5Ep%7D)
- Direct Comparison Test (DCT)
- Limit Comparison Test (LCT):
![\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Ba_n%7D%7Bb_n%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum%5E%7B%5Cinfty%7D_%7Bn%20%3D%2019%7D%20%5Cfrac%7B8n%5E3%20-%202n%5E2%20%2B%2019%7D%7B6%20%2B%203n%5E4%7D)
<u>Step 2: Apply DCT</u>
- Define Comparison:
![\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{n^3}{n^4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cdisplaystyle%20%5Csum%5E%7B%5Cinfty%7D_%7Bn%20%3D%2019%7D%20%5Cfrac%7Bn%5E3%7D%7Bn%5E4%7D)
- [Comparison Sum] Simplify:
![\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cdisplaystyle%20%5Csum%5E%7B%5Cinfty%7D_%7Bn%20%3D%2019%7D%20%5Cfrac%7B1%7D%7Bn%7D)
- [Comparison Sum] Determine convergence:
![\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n} = \infty , \ \text{div by P-Series}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cdisplaystyle%20%5Csum%5E%7B%5Cinfty%7D_%7Bn%20%3D%2019%7D%20%5Cfrac%7B1%7D%7Bn%7D%20%3D%20%5Cinfty%20%2C%20%5C%20%5Ctext%7Bdiv%20by%20P-Series%7D)
- Set up inequality comparison:
![\displaystyle\frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \geq \frac{1}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B8n%5E3%20-%202n%5E2%20%2B%2019%7D%7B6%20%2B%203n%5E4%7D%20%5Cgeq%20%5Cfrac%7B1%7D%7Bn%7D)
- [Inequality Comparison] Rewrite:
![\displaystyle n(8n^3 - 2n^2 + 19) \geq 6 + 3n^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n%288n%5E3%20-%202n%5E2%20%2B%2019%29%20%5Cgeq%206%20%2B%203n%5E4)
- [Inequality Comparison] Simplify:
![\displaystyle 8n^4 - 2n^3 + 19n \geq 6 + 3n^4 \ \checkmark \text{true}](https://tex.z-dn.net/?f=%5Cdisplaystyle%208n%5E4%20-%202n%5E3%20%2B%2019n%20%5Cgeq%206%20%2B%203n%5E4%20%5C%20%5Ccheckmark%20%5Ctext%7Btrue%7D)
∴ the sum
is divergent by DCT.
<u>Step 3: Apply LCT</u>
- Define:
![\displaystyle a_n = \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}, \ b_n = \frac{1}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a_n%20%3D%20%5Cfrac%7B8n%5E3%20-%202n%5E2%20%2B%2019%7D%7B6%20%2B%203n%5E4%7D%2C%20%5C%20b_n%20%3D%20%5Cfrac%7B1%7D%7Bn%7D)
- Substitute in variables [LCT]:
![\displaystyle \lim_{n \to \infty} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \cdot n](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B8n%5E3%20-%202n%5E2%20%2B%2019%7D%7B6%20%2B%203n%5E4%7D%20%5Ccdot%20n)
- Simplify:
![\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B8n%5E4%20-%202n%5E3%20%2B%2019n%7D%7B6%20%2B%203n%5E4%7D)
- [Limit] Evaluate [Coefficient Power Rule]:
![\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4} = \frac{8}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B8n%5E4%20-%202n%5E3%20%2B%2019n%7D%7B6%20%2B%203n%5E4%7D%20%3D%20%5Cfrac%7B8%7D%7B3%7D)
∴ Because
and the sum
diverges by DCT,
also diverges by LCT.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
Answer:
<h3>1. x = 15° | y = 120°</h3><h3>2. x = 4.5 | y = 60°</h3>
Step-by-step explanation:
1. 4x° + 4x° + 4x° = 180° ( The sum of all interior angles of any triangle is equal to 180° )
![4x + 4x + 4x = 180 \\ 12x = 180 \\ x = \frac{180}{12} \\ x = {15}^{o} \\](https://tex.z-dn.net/?f=4x%20%2B%204x%20%2B%204x%20%3D%20180%20%5C%5C%2012x%20%3D%20180%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B180%7D%7B12%7D%20%20%5C%5C%20x%20%3D%20%20%7B15%7D%5E%7Bo%7D%20%20%5C%5C%20)
4x° + 4x° = y° ( An exterior angle of a triangle is equal to the sum of its two interior opposite angles. )
![4x + 4x = y \\ 4(15) + 4(15) = y \\ 60 + 60 = y \\ {120}^{o} = y](https://tex.z-dn.net/?f=4x%20%2B%204x%20%3D%20y%20%5C%5C%204%2815%29%20%2B%204%2815%29%20%3D%20y%20%5C%5C%2060%20%2B%2060%20%3D%20y%20%5C%5C%20%20%7B120%7D%5E%7Bo%7D%20%20%3D%20y)
2. y° + 60° + 60° = 180° ( The sum of all interior angles of any triangle is equal to 180° )
![y + 60 + 60 = 180 \\ y + 120 = 180 \\ y = 180 - 120 \\ y = {60}^{o} \\](https://tex.z-dn.net/?f=y%20%20%2B%2060%20%2B%2060%20%3D%20180%20%5C%5C%20y%20%20%2B%20%20120%20%3D%20180%20%5C%5C%20y%20%3D%20180%20-%20120%20%5C%5C%20y%20%3D%20%20%7B60%7D%5E%7Bo%7D%20%20%5C%5C%20)
All three internal angles are also congruent to each other and are each 60°. Therefore this is a equilateral triangle.
Perimeter = 4x + 4x + 4x ( An equilateral triangle is a triangle with all three sides of equal length. )
![54 = 4x + 4x + 4x \\ 54 = 12x \\ \frac{54}{12} = x \\ x = 4.5](https://tex.z-dn.net/?f=54%20%3D%204x%20%2B%204x%20%2B%204x%20%5C%5C%2054%20%3D%2012x%20%5C%5C%20%20%5Cfrac%7B54%7D%7B12%7D%20%20%3D%20x%20%5C%5C%20x%20%3D%204.5)