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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2283779

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At t = 2, x = 3 and y = 3/4 dx/dt = 2/3 dy/dt = 13/16 Therefore; Gradient at the tangent and of the curve at t = 2 is; dy/dx = dy/dt÷dx/dt  = (13/16)÷(2/3) dy/dx = 39/32 Notice; Triangle OPQ height coordinate is (3, (3/4)). Triangle OPQ base coordinate is (x1, 0). Calculating x to get X1. ((3/4)-0)/(3-x) = 39/32 x = 31/13 x1 = 3-(31/13) x1 = 18/13. It implies; Triangle OPQ is; Area triangle with height ¾ unit and base (18/13) unit. = ½*(18/13)*¾ = 27/52 square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2283774

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(x/√(3))+x+2x+3x+(3x/√(3)) = 1 (4√(3)x/3)+6x = 1 (4√(3)x)+18x=3 (4√(3)+18)x = 3 x = 3/(4√(3)+18) x = 3(18-4√(3))/(324-48) x = 3(15-4√(3))/276 x = (18-4√(3))/92 x = (9-2√(3))/46 unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2283009

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a = ½(6√(3)) a = 3√(3) units. b = (6-3√(3)) units. cosc = 3√(3)/6 c = acos(½(√(3))) c = 30° d = 90-30 d = 60° sin30 = e/6 e = 3 units. It implies; Area Blue is; Area rectangle with length and width 6√(3) units and 6 units respectively - 2(area sector with angle 60° and radius 6 units + area triangle with height and base 3√(3) units and height 3 units respectively). = 6*6√(3)-2((60π*36/360)+½(3√(3)*3)) = 36√(3)-2(6π+½(9√(3))) = 36√(3)-(12π+9√(3)) = 36√(3)-12π-9√(3) = 27√(3)-12π = 3(9√(3)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2282072

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Let the equal lengths be 1 unit. (1/sin20) = ((1+y)/sin120) 1+y = (sin120/sin20) y = (sin120/sin20)-1 y = 1.5320888862 units. z² = 1+1.5320888862²-2*1.5320888862cos40 z = 1 unit. It implies, the required angle x is; 120-(180-2(40)) = x x = 120-(180-80) x = 120-100 x = 20°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281996

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The equation of the curve is; 0-32=-a(8-4)² -32 = -16a a = 2 Therefore; y-32 = -2(x-4)² y = -2(x²-8x+16) +32 y = -2x²+16x-32+32 y = 16x - 2x² It implies; (Area (2197/24)+ Area triangle with height b unit and base a unit + Area under the curve at x = 8 and x = a) = Area under the curve at x = 8 and x = 0 2197+12ab-192a²+16a³=0 ----------- (1) Notice; b = 16a-2a² --------- (2) Substitute (2) in (1). Therefore; a = ½(13) unit And b = ½(39) unit It implies; Area shaded/Area orange in it...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281987

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a (first term) = 9/7 d (common difference) = 3/7 n (number of terms) = 29 Therefore; Last term of the sequence of values is; L = a + d(n-1) L = (9/7) + (3/7)(29-1) L = (9/7) + 12 L = ((12*7)+9)/7 L = (84+9)/7 L = 93/7

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281977

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Let the side length of the regular heptagon be 1 unit. a = ⅐(180*5) a = ⅐(900)° b = 0.5(360-2(900/7)) b = ⅐(360)° c = 2cos(360/7)+1 c = 2.24697960372 units. d² = 2-2cos(90/7) d = 1.8019377358 units. Where d is the radius of the arc. Area Orange is; 0.5*2.24697960372*1sin(360/7)+0.5*sin(900/7) = 1.26929543856 square units. Let e be alpha. Calculating e. e = 0.5((900/7)-(360/7)) e = ⅐(270)° (1.8019377358/sin(270/7)) = (2.24697960372/sinf) f = 128.96966294132° g = 180-f-e g = 12.4589084...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281959

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a = atan(½)° b² = 2(10)² b = 10√(2) units. c = (45-atan(½))° cos(atan(½)) = d/20 d = 17.88854382 units. Area x is; 0.5*17.88854382*10√(2)sin(45-atan(0.5)) = 40 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281117

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Length AD is; AD = 3√(15) cm. Therefore; Area Orange exactly in cm² is; Area triangle with height √(15) cm and base 3√(15) cm + Area triangle with height 5√(6) cm and base ¼√(615)sin(180-atan(3)-atan(5/4)) cm. = ½*3√(15)*√(15) + ½*5√(6)*¼√(615)sin(180-atan(3)-atan(5/4))) = ½(45) + (15√(410)sin(180-atan(3)-atan(5/4)))/8 = ½(45) + (15√(410)sin(57.094757077))/8 = 22.5 + 31.875 = 54.375 cm² = 435/8 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281111

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Gradient of the curve at x = 3 is; dy/dx = (-19/20) It implies; Area yellow exactly in square unit decimal is; Area triangle with height (5/(4sin(atan(19/20)))) unit and base (5/(4sin(atan(20/19)))) unit = ½*(5/(4sin43.5311992856))*(5/(4sin46.4688007144)) = ½*1.81488345054*1.72413927802 = 1.56455592105 square unit
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