1: Mahitaji
- Page ID
- 178135
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Katika sura hii, tutaangalia seti ya idadi na mali ya shughuli zinazotumiwa kuendesha namba. Uelewa huu utatumika kama ujuzi wa lazima katika utafiti wetu wa algebra na trigonometry.
- 1.0: Utangulizi wa Mahitaji
- Kupima na kurekodi sifa za hali ya hewa inahitaji matumizi ya idadi tofauti. Kuhesabu nao na kuitumia kufanya utabiri inahitaji uelewa wa mahusiano kati ya idadi. Katika sura hii, tutaangalia seti ya idadi na mali ya shughuli zinazotumiwa kuendesha namba. Uelewa huu utatumika kama ujuzi wa lazima katika utafiti wetu wa algebra na trigonometry.
- 1.1: Hesabu halisi - Muhimu wa Algebra
- Katika sehemu hii, sisi kuchunguza seti ya idadi, mahesabu na aina tofauti ya idadi, na matumizi ya idadi katika maneno.
- 1.2: Watazamaji na Nukuu ya kisayansi
- Wanahisabati, wanasayansi, na wanauchumi kwa kawaida hukutana na idadi kubwa sana na ndogo sana. Lakini inaweza kuwa dhahiri jinsi takwimu hizo zilivyo kawaida katika maisha ya kila siku.
- 1.3: Radicals na Maneno ya busara
- Mizizi kuu ya mraba ya a imeandikwa kama √a. ishara inaitwa radical, neno chini ya ishara inaitwa radicand, na kujieleza nzima inaitwa kujieleza radical.
- 1.4: Polynomials
- Katika sehemu hii, sisi kuchunguza polynomials, ambayo ni kiasi cha au tofauti ya maneno, kila yenye variable alimfufua kwa nguvu nonnegative integer.
- 1.5: Factoring Polynomials
- Sababu kubwa ya kawaida, au GCF, inaweza kuhesabiwa nje ya polynomial. Kuangalia kwa GCF lazima hatua ya kwanza katika tatizo lolote factoring. Trinomials na mgawo wa kuongoza 1 inaweza kuhesabiwa kwa kutafuta namba zilizo na bidhaa ya muda wa tatu na jumla ya muda wa pili. Trinomials inaweza kuhesabiwa kwa kutumia mchakato unaoitwa factoring kwa kikundi. Vipande vya mraba kamili na tofauti za mraba ni bidhaa maalum na zinaweza kuzingatiwa kwa kutumia equations.
- 1.6: Maneno ya busara
- Quotient ya maneno mawili ya polynomial inaitwa kujieleza kwa busara. Tunaweza kutumia mali ya vipande kwa maneno ya busara, kama vile kurahisisha maneno kwa kufuta mambo ya kawaida kutoka kwa nambari na denominator. Ili kufanya hivyo, sisi kwanza tunahitaji kuzingatia namba zote na denominator.
Thumbnail: Njia ya mkato inayoitwa FOIL wakati mwingine hutumiwa kupata bidhaa ya binomials mbili. Inaitwa FOIL kwa sababu tunazidisha maneno ya kwanza, maneno ya nje, maneno ya ndani, na kisha maneno ya mwisho ya kila binomial.