#set document(title: "11.3 Editing Expressions", author: "OpenStax / XYZ Homework") #set page(width: 8.5in, height: auto, margin: 1in) #import "@preview/cetz:0.5.2" #set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en") #show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math")) #set par(justify: true, leading: 0.62em, spacing: 0.9em) #set enum(spacing: 1.1em) // room between list items so tall inline fractions don't collide #set list(spacing: 1.1em) #set table(stroke: 0.5pt + rgb("#c7ccd3")) #let BLUE = rgb("#183B6F") // brand navy — section bars + example/solution labels (white on navy 11.09:1) #let ORANGE = rgb("#A94509") // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text) #let RED = rgb("#DC2626") // brand error-600 #let GREEN = rgb("#059669") // brand success-600 (decoration only; small green text uses green-text #007942) #show heading.where(level: 1): it => block(width: 100%, above: 0pt, below: 16pt, fill: gradient.linear(BLUE, rgb("#2C5AA0")), inset: (x: 14pt, y: 12pt), radius: 3pt, text(fill: white, weight: "bold", size: 19pt, it.body)) #show heading.where(level: 2): it => block(width: 100%, above: 18pt, below: 10pt, fill: BLUE, inset: (x: 10pt, y: 6pt), radius: 2pt, text(fill: white, weight: "bold", size: 12pt, it.body)) #show heading.where(level: 3): it => text(fill: ORANGE, weight: "bold", size: 12.5pt, it.body) #show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body) #let examplebox(label, title, body) = block(width: 100%, breakable: true, fill: rgb("#EFF1F5"), stroke: 0.5pt + rgb("#CFDDF0"), radius: 4pt, inset: 10pt, above: 12pt, below: 12pt)[ #block(below: 6pt)[#box(fill: BLUE, inset: (x: 6pt, y: 2pt), radius: 2pt, text(fill: white, weight: "bold", size: 8.5pt, label)) #h(0.4em) #strong[#title]] #body] // rail = decorative left rule (raw brand token); labelcolor = AA-safe label text shade #let notebox(label, rail, labelcolor, tint, body) = block(width: 100%, breakable: true, fill: tint, stroke: (left: 3pt + rail), inset: (left: 10pt, rest: 8pt), radius: (right: 4pt), above: 11pt, below: 11pt)[ #text(fill: labelcolor, weight: "bold", size: 7.5pt, tracking: 0.5pt)[#upper(label)] #linebreak() #body] #let solutionbox(body) = block(above: 4pt, below: 8pt)[ #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body] #let figph(msg) = block(width: 100%, height: 60pt, fill: rgb("#f6f7f9"), stroke: (paint: rgb("#c7ccd3"), dash: "dashed"), radius: 4pt, inset: 10pt)[ #align(center + horizon, text(fill: rgb("#889"), style: "italic", size: 9pt, msg))] // Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a // consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the // print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a // degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero. #let _STD_W = 3.5 #let _WIDE_W = 5.6 #let _MAX_H = 3.4 #let _ASPECT_WIDE = 2.2 #let _UPSCALE_MAX = 1.15 #let stdfig(body) = context { let m = measure(body) let w = calc.max(m.width / 1in, 0.01) let h = calc.max(m.height / 1in, 0.01) let tw = if w / h > _ASPECT_WIDE { _WIDE_W } else { _STD_W } let s = calc.min(tw / w, _MAX_H / h, _UPSCALE_MAX) align(center, box(scale(x: s * 100%, y: s * 100%, reflow: true, body))) } #show figure: set block(breakable: false) #set figure(gap: 8pt) #show figure.caption: set text(size: 8.5pt, fill: rgb("#555")) == 11.3#h(0.6em)Editing Expressions === Overwriting We can edit an expression without starting again. If we place the cursor over a symbol and press a new key, the new symbol replaces (overwrites) the old one. #examplebox("Example 1")[][ Correct the error in the following keystrokes for #math.equation(block: false, alt: "120 minus 36")[$120 − 36$]: #math.equation(block: false, alt: "120")[$#h(2em) #h(2em) 120$] (-) #math.equation(block: false, alt: "36")[$36$] ENTER The calculator gives an error message (See Figure.) Select "2:Goto", and a blinking cursor appears over the error. Press - to replace the negative symbol by the subtraction symbol. ] === Recalling an Entry We can recall a previous entry by pressing 2nd ENTER. #examplebox("Example 2")[][ Evaluate #math.equation(block: false, alt: "the square root of 3 plus the square root of 2")[$sqrt(3) + sqrt(2) " " " "$] and #math.equation(block: false, alt: "the square root of 3 minus the square root of 2")[$" " " " sqrt(3) − sqrt(2)$]. First evaluate #math.equation(block: false, alt: "the square root of 3 plus the square root of 2")[$sqrt(3) + sqrt(2)$]: 2nd ) + 2nd #math.equation(block: false, alt: "2")[$2$] ENTER Ans. #math.equation(block: false, alt: "3.14626437")[$3.14626437$] Now press 2nd ENTER to recall the last entry, and use the left arrow key to position the cursor over #math.equation(block: false, alt: "plus")[$+$]. Press to change to #math.equation(block: false, alt: "minus")[$−$], then press ENTER. Your screen should look like Figure. #figure(figph[GC with sum and difference of roots], alt: "GC with sum and difference of roots", caption: none) ] === Inserting a Character To insert a new character #emph[before] a symbol, position the cursor over that symbol and press 2nd DEL to get the #strong[INS] (insert) command. #examplebox("Example 3")[][ Evaluate #math.equation(block: false, alt: "the square root of 3 minus 5 the square root of 2")[$sqrt(3) − 5 sqrt(2)$] by editing the example above. Press 2nd ENTER to recall the last entry, and use the left arrow key to position the cursor over the second #math.equation(block: false, alt: "the square root of")[$sqrt(#h(0.167em))$] from left to right. Press 2nd DEL #math.equation(block: false, alt: "5")[$5$] to insert 5 #emph[before] the #math.equation(block: false, alt: "the square root of")[$sqrt(#h(0.167em))$] symbol, then press ENTER. Your screen should look like Figure. #figure(figph[GC with sum of roots], alt: "GC with sum of roots", caption: none) ] === Recalling an Answer We often want to use the result from a previous calculation in a new calculation, without having to type in the number. We use the #strong[ANS] key, 2nd (-), to recall the answer to the last calculation. #examplebox("Example 4")[][ + Evaluate #math.equation(block: false, alt: "the square root of 5 minus 1")[$sqrt(5) − 1$]2nd #math.equation(block: false, alt: "5")[$5$] ) #math.equation(block: false, alt: "1")[$1$] ENTER Ans. #math.equation(block: false, alt: "1.236067977")[$1.236067977$] + Evaluate #math.equation(block: false, alt: "x squared plus 2 x plus 1")[$x^(2) + 2 x + 1$] for #math.equation(block: false, alt: "x equals the square root of 5 minus 1")[$x = sqrt(5) − 1$]. Because #math.equation(block: false, alt: "x")[$x$] is the last answer the calculator computed, we enter2nd (-) + #math.equation(block: false, alt: "2")[$2 #h(0.167em)$] 2nd (-) + #math.equation(block: false, alt: "1")[$1 #h(0.167em)$] ENTER Ans. #math.equation(block: false, alt: "5")[$5$] #linebreak() Your screen should look like Figure.#figure(figph[GC roots minus 1], alt: "GC roots minus 1", caption: none) ]