![\"Figure1\"/](\"resources/question-resources/figure1.png\")
In NUMBAS, to insert the equation $A = BC + \\frac{\\sqrt{D}}{E^2}$, the correct format is as follows: A = B*C + sqrt(D)/E^2. Please make a note of this.
\n\nA cellular system that comprises of hexagonal cells with radius is shown in Figure 1.
", "advice": "Part A:
\nThe adjacent side of the right-angled triangle has a length of $i_hd\\sqrt{3}+j_hd\\sqrt{3}\\cos{(60^\\circ)}$ and the opposite side has a length of $j_hd\\sqrt{3}\\sin{(60^\\circ)}$.
\nTherefore:
\n$U=\\sqrt{(i_hd\\sqrt{3}+j_hd\\sqrt{3}\\cos{(60^\\circ)})^2+(j_hd\\sqrt{3}\\sin{(60^\\circ)})^2}$
\n$U=\\sqrt{3i_h^2d^2+3i_hj_hd^2+3j_h^2d^2(\\cos^2{(60^\\circ)}+\\sin^2{(60^\\circ)})}$
\n$U=\\sqrt{3}\\sqrt{i_h^2+i_hj_h+j_h^2}$
\n\nPart B:
\nIf $K=i_h^2+i_hj_h+j_h^2$ and $U=3\\sqrt{d}\\sqrt{i_h^2+i_hj_h+j_h^2}$
\n$U=d\\sqrt{3K}$
\n$U/d=\\sqrt{3K}$
\n", "rulesets": {}, "extensions": [], "variables": {"U": {"name": "U", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "i_h": {"name": "i_h", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}, "j_h": {"name": "j_h", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["U", "d", "i_h", "j_h"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Starting from the original cell, the destination cell is reached by moving $i_h$ cells vertically, rotating $60^\\circ$, and then moving $j_h$ cells in this direction
\nIf the distance between neighbouring cell centres is $d\\sqrt{3}$, derive the distance $U$ between the source and destination cell in terms of $i_h$ and $j_h$.
\nAnswer here: [[0]]
\n\n
Given that the number of cells in a cluster, $K$, is defined as $K=i_h^2+i_hj_h+j_h^2$, derive an expression for the co-channel reuse distance $U/d$ in terms of $K$.
\nAnswer here: [[0]]
\n", "gaps": [{"type": "jme", "useCustomName": true, "customName": "GAP1", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "U/d=sqrt(3*K)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "d", "value": ""}, {"name": "k", "value": ""}, {"name": "u", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Paul Anthony Haigh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9407/"}]}]}], "contributors": [{"name": "Paul Anthony Haigh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9407/"}]}