# Week 3 – Precalc 11

This week in Precalculus 11, we started the Absolute Value and Radicals unit. We first learned about the absolute value of a real number. The absolute value of a real number is its distance from zero on a number line, or the principal square root of its square. The principal square root is the positive (+) square root.

Example: $\sqrt{1}$ = ±1     +1 = principal square root     -1 = negative square root

The symbols “||” represent absolute value.

Example: <-0-1-2-3-4-5->     |0| = 0

|0|

= $\sqrt{0^2}$

= 0

This is a new concept I had not yet learned about and can add to my knowledge of Pre-Calculus.

# Week 2 – Precalc 11

This week in Precalculus 11, we learned about geometric sequences. A geometric sequence is a list of terms in which a common ratio exists between the terms.

Example: 1, 2, 4, 8, 16     common ratio = 2

The common ratio is “r”.

Example: r = 2

To find the value of a term in a geometric sequence, we use the formula $t_n$ = $t_1$ · $r^{n - 1}$.

Example: Find $t_{10}$: 1, 2, 4, 8, 16

$t_n$ = $t_1$ · $r^{n - 1}$

($t_{10}$) = (1)$(2)^{(10) - 1}$

$t_{10}$ = 1 · $2^9$

$t_{10}$ = 1 · 512

$t_{10}$ = 512

This method of finding the value of terms in an geometric sequence is faster than extending the list.

# 6 Kingdoms

Eubacteria

Bacillus anthracis

https://en.m.wikipedia.org/wiki/Bacillus_anthracis

Escherichia coli

https://en.m.wikipedia.org/wiki/Escherichia_coli

Bacillus anthracis and Escherichia coli are members of the Eubacteria Kingdom because they have prokaryotic cells, are unicellular, and their cells have a cell wall of peptidoglycan.

Archaebacteria

Halobacterium salinarum

http://rachelyscientist2.blogspot.com/2008/02/archaebacteria-halobacterium-salinarum.html

Sulfolobus acidocaldarius

https://microbewiki.kenyon.edu/index.php/Sulfolobus_acidocaldarius

Halobacterium salinarium and Sulfolobus acidocaldarius are members of the Archaebacteria Kingdom because they have prokaryotic cells, are unicellular, and their cells have a cell wall containing uncommon lipids.

Protista

Aegagropila linneai

https://en.m.wikipedia.org/wiki/Marimo

Undaria pinnatifida

https://en.m.wikipedia.org/wiki/Wakame

The Aegagropila linnaei and the Undaria pinnatifida are members of the Protista Kingdom because they have eukaryotic cells, and their cell wall is cellulose.

Fungi

Hericium erinaceus

https://en.m.wikipedia.org/wiki/Hericium_erinaceus

Hydnellum peckii

https://en.m.wikipedia.org/wiki/Hydnellum_peckii

The Hericium erinaceus and the Hydnellum peckii are members of the Fungi Kingdom because they have eukaryotic cells, are multicellular, are heterotrophs, and their cell walls are chitin.

Plantae

Hydnora africana

https://en.m.wikipedia.org/wiki/Hydnora_africana

Rafflesia arnoldii

https://en.m.wikipedia.org/wiki/Rafflesia

The Hydnora africana and the Rafflesia arnoldii are members of the Plantae Kingdom because they have eukaryotic cells, are multicellular, are autotrophs, and their cell walls are cellulose.

Animalia

Hydropotes inermis

https://en.m.wikipedia.org/wiki/Water_deer

https://en.m.wikipedia.org/wiki/Purple_frog

The Hydropotes inermis and the Nasikabatrachus sahyadrensis are members of the Animalia Kingdom because they have eukaryotic cells, are multicellular, are heterotrophs, and have no cell wall.

# Week 1 – My Arithmetic Sequence

13, 26, 39, 52, 65…

$t_n$ = $t_1$ + d(n – 1)

($t_{50}$) = (13) + (13)[(50) – 1]

$t_{50}$ = 13 + 13 · 49

$t_{50}$ = 13 + 637

$t_{50}$ = 650

$S_n$ = $\frac{n}{2}$($t_1$ + $t_n$)

($S_{50}$) = $\frac{(50)}{2}$[(13) + (650)]

$S_{50}$ = 25 · 663

$S_{50}$ = 16575

# Week 1 – Precalc 11

This week in Pre-Calculus 11, we started the Sequences and Series unit. We first learned about arithmetic sequences. An arithmetic sequence is a list of terms in which a common difference exists between the terms.

Example: 0, 1, 2, 3, 4     common difference = +1

The first term of a sequence is “t₁”, the second term is “t₂”, etc. The common difference is “d”.

Example: 0, 1, 2, 3, 4     d = +1

t₁  t₂  t₃  t₄  t₅

To find the value of a term ($t_n$) in an arithmetic sequence, we use the formula $t_n$ = t₁ + d(n – 1).

Example: Find t₁₀: 0, 1, 2, 3, 4     $t_n$ = t₁ + d(n – 1)

(t₁₀) = (0) + (1)[(10) – 1]

(t₁₀) = 0 + 1 · 9

(t₁₀) = 0 + 9

(t₁₀) = 9

This method of finding the value of terms in an arithmetic sequence is faster than extending the list.