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GeometryQuestion and Answers: Page 110

Question Number 15782 Answers: 1 Comments: 1

Question Number 15700 Answers: 1 Comments: 1

Question Number 15699 Answers: 1 Comments: 0

3+5x=58

$$\mathrm{3}+\mathrm{5x}=\mathrm{58} \\ $$

Question Number 15672 Answers: 1 Comments: 0

solve the equation: {5^x } +5x=140 please show workings.....

$$\:{solve}\:{the}\:{equation}: \\ $$$$\:\:\left\{\mathrm{5}^{{x}} \right\}\:+\mathrm{5}{x}=\mathrm{140} \\ $$$${please}\:{show}\:{workings}..... \\ $$

Question Number 15642 Answers: 1 Comments: 0

Question Number 15572 Answers: 2 Comments: 1

Question Number 15567 Answers: 2 Comments: 3

Question Number 16613 Answers: 1 Comments: 2

Question Number 15440 Answers: 3 Comments: 9

Question Number 15434 Answers: 1 Comments: 8

Question Number 15318 Answers: 2 Comments: 6

Question Number 15175 Answers: 2 Comments: 1

Question Number 15170 Answers: 2 Comments: 2

Question Number 15017 Answers: 0 Comments: 0

Calculate the heat neccessary to raise the temperature of 5.00 mol of butane from 290K to 593K at a constant pressure. where Cp(19.41 + 0.233T)J/mol/K

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{heat}\:\mathrm{neccessary}\:\mathrm{to}\:\mathrm{raise}\:\mathrm{the}\:\mathrm{temperature}\:\mathrm{of}\:\mathrm{5}.\mathrm{00}\:\mathrm{mol}\:\mathrm{of}\:\mathrm{butane} \\ $$$$\mathrm{from}\:\mathrm{290K}\:\mathrm{to}\:\mathrm{593K}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{pressure}.\:\mathrm{where}\:\mathrm{Cp}\left(\mathrm{19}.\mathrm{41}\:+\:\mathrm{0}.\mathrm{233T}\right)\mathrm{J}/\mathrm{mol}/\mathrm{K} \\ $$

Question Number 14965 Answers: 2 Comments: 2

Question Number 14964 Answers: 0 Comments: 0

proof that ∀ x,y ∈N ∃ a,b,c ∈N ∍ (4/(x^2 +y^2 ))=(1/a) + (1/b) + (1/c)

$$\mathrm{proof}\:\mathrm{that}\: \\ $$$$\forall\:{x},{y}\:\in\mathbb{N}\:\:\exists\:{a},{b},{c}\:\in\mathbb{N}\:\backepsilon\:\frac{\mathrm{4}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }=\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}} \\ $$

Question Number 15212 Answers: 1 Comments: 1

Question Number 14940 Answers: 2 Comments: 12

For those who are interested in Geometry: A triangle has an area of 1 unit. Each of its sides is divided into 4 equal parts through 3 points. The first and the last point of each side will be connected with each other to form 2 inscribed triangles and these 2 triangles form a hexagon. Find the area of the hexagon. What is the result, if each side is equally divided into 5 parts, or generally into n parts?

$${For}\:{those}\:{who}\:{are}\:{interested}\:{in}\: \\ $$$${Geometry}:\: \\ $$$${A}\:{triangle}\:{has}\:{an}\:{area}\:{of}\:\mathrm{1}\:{unit}.\:{Each} \\ $$$${of}\:{its}\:{sides}\:{is}\:{divided}\:{into}\:\mathrm{4}\:{equal}\:{parts} \\ $$$${through}\:\mathrm{3}\:{points}.\:{The}\:{first}\:{and}\:{the}\:{last} \\ $$$${point}\:{of}\:{each}\:{side}\:{will}\:{be}\:{connected} \\ $$$${with}\:{each}\:{other}\:{to}\:{form}\:\mathrm{2}\:{inscribed} \\ $$$${triangles}\:{and}\:{these}\:\mathrm{2}\:{triangles}\:{form} \\ $$$${a}\:{hexagon}.\:{Find}\:{the}\:{area}\:{of}\:{the}\:{hexagon}. \\ $$$$ \\ $$$${What}\:{is}\:{the}\:{result},\:{if}\:{each}\:{side}\:{is} \\ $$$${equally}\:{divided}\:{into}\:\mathrm{5}\:{parts},\:{or} \\ $$$${generally}\:{into}\:{n}\:{parts}? \\ $$

Question Number 14905 Answers: 0 Comments: 5

Question Number 14863 Answers: 1 Comments: 8

Question Number 14810 Answers: 0 Comments: 0

7 real numbers are given in the interval (1, 13). Prove that atleast 3 of them are the lengths of a triangle′s sides.

$$\mathrm{7}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{given}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{1},\:\mathrm{13}\right).\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{atleast}\:\mathrm{3}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}'\mathrm{s}\:\mathrm{sides}. \\ $$

Question Number 14809 Answers: 1 Comments: 2

Let ABC be an acute triangle. Find the positions of the points M, N, P on the sides BC, CA, AB, respectively, such that the perimeter of the triangle MNP is minimal.

$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{an}\:\mathrm{acute}\:\mathrm{triangle}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{positions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{points}\:{M},\:{N},\:{P}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA},\:{AB},\:\mathrm{respectively}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle} \\ $$$${MNP}\:\mathrm{is}\:\mathrm{minimal}. \\ $$

Question Number 14807 Answers: 0 Comments: 0

Prove that the medians of a given triangle can form a triangle.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{medians}\:\mathrm{of}\:\mathrm{a}\:\mathrm{given} \\ $$$$\mathrm{triangle}\:\mathrm{can}\:\mathrm{form}\:\mathrm{a}\:\mathrm{triangle}. \\ $$

Question Number 14797 Answers: 1 Comments: 12

Question Number 14724 Answers: 2 Comments: 1

Question Number 14661 Answers: 1 Comments: 1

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