Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1999278

Considering similar triangles ADC and CDB ratios. Let CD be a. 16 = a a = 4 Cross Multiply. a² = 64 a = 8 units c² = 16²+8² c = 8√(5) units. c = AC. Calculating r1. 16r1+8r1+8√(5)r1 = (16*8) r1(24+8√(5)) = 128 r1 = 128/(24+8√(5)) r1 = 16/(3+√(5)) r1 = (12-4√(5)) units. d² = 8²+4² d = 4√(5) units. d is BC. Calculating r2. 4r2+8r2+4√(5)r2 = (8*4) r2(12+4√(5)) = 32 r2(3+√(5)) = 8 r2 = 8/(3+√(5)) r2 = (6-2√(5)) units. Calculating EF. (EF)² = (r1+r2)²+(r1-r2)² (EF)² = ((12-4√(5))+(6-2√...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1997920

Calculating a. (1/sin120) = (a/sin20) a = 0.39493084363 units. Calculating b. (1/sin120) = (b/sin40) b = 0.74222719897 units. Therefore, observing the proof; (1/a)+(1/b) = 3ab+3 (1/a)+(1/b) is; 1/0.39493084363+1/0.74222719897 = 3.8793852416 3ab+3 is; 3*0.39493084363*0.74222719897+3 = 3.87938524156 Proved.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1997583

Notice; a² = 5² - (⅕(√(481)))² a = ⅕(12) units. b = 5-a b = ⅕(13) units. c² = 4²-(⅕(12))² c = ⅕(16) units. d = atan(4/3)° (a) Area A exactly is; ½*⅕(16)*(5+⅕(13)) - atan(4/3)π*16/360 = ((8*38)/25) - (2atan(4/3)π/45) = (304/25) - ((2atan(4/3)π)/45) = (2736-10πatan(4/3))/225 square units. = 4.74163825599 square units. (b) Calculating Area B to 2 decimal places. ½*10(10+5) - ½*⅕(16)(5+⅕(13)) - ((atan½+ata¾)π*16/360) - (⅕(13)*⅕(34-√(481))) - ½*⅕(√(481))(5+⅕(13)) - ((atan(12/√(481))+(2t...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1997564

Let AB be 1 unit. BC = 3 units. It implies; AC = 1+3 AC = 4 units. AC is a side length of the square. Radius of the inscribed half circle a is; ½(BC) a = ½(3) units. a = 1.5 units. b = 1.5+AB b = 1.5+1 b = 2.5 units. b = ½(5) units. c²+(1.5)² = (2.5)² c² = 2.5²-1.5² c = 2 units. Considering similar triangle ratios. 2 = 4 1.5 = d Cross Multiply. d = 3 units. tane = (3/4) e = atan(3/4)° f = atan(4/3)° Calculating g, side length of the regular triangle. (4/sin120) = (g/sin(atan(4/3)))...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1996975

Let a be 1 unit. (1/sin48) = (b/sin24) b = 0.54731813925 units. (1/sin48) = (c/sin108) c = 1.27977277603 units. DC = 1.27977277603+0.54731813925+1 DC = 2.82709091528 units. Therefore, the required angle x is; (2.82709091528/sin36) = (1/sinx) x = 12°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1996244

Let the radius R, of the half circle be 1 unit. sin30 = c/1 c = ½ units. c = 0.5 units. cos30 = d/1 d = ½√(3) units. d = 0.86602540378 units. e = 1-0.86602540378 e = 0.13397459622 units. f² = (0.13397459622)²+(0.5)² f = 0.51763809021 units. Calculating r, radius of the small inscribed yellow circle. Considering similar triangle ratios. 0.51763809021 = (1-r) 0.5 = (0.5+r) Cross Multiply. 0.5-0.5r = 0.51763809021r+0.2588190451 0.5-0.2588190451 = 0.5r+0.51763809...

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Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service. We make teaching and learning Mathematics fun for learners, we expose the simplicity and beauty of Mathematics to our learners, and mentor them to appreciate and love Mathematics. Communicate us to mentor/educate you Mathematics better online at affordable tuition. We are smart and clever.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1995689

Let the small inscribed circle's radius be x. x = 6 cm. Let the big inscribed circle's radius be y. y = 8 cm. Let the ascribed semi circle's radius be z. = 18 cm. a² = 10²-8² a = 6 cm. b² = 12²-6² b = 6√(3) cm c = atan(z/b)° c = atan(18/6√(3))° c = atan√(3)° c = 60° d = atan(z/a)° d = atan(18/6) d = atan(3)° (a) Angle theta exactly is; Let it be e. e = 180-c-d e = 180-60-atan3 e = (120-atan3)° e = (atan(⅓)+30)° (b) Calculating Area Shaded to 1 decimal place cm². f = atan(1/√(3)) = 3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1994045

Let r be the radius of the circle. 3x+3 = 2r --- (1). r² = (r-1)²+(r-2x)² r² = r²-2r+1+r²-4xr+4x² 4xr+2r = r²+4x²+1 --- (2). From (1). 3x+3 = 2r x = ⅓(2r-3) --- (3). Calculating r. Therefore, Substituting (3) in (2). 4( ⅓(2r-3))r+2r = r²+4(⅓(2r-3))²+1 ⅓(8r²-6r) = r²+4(⅑(4r²-12r+9))+1 ⅓(8r²-6r) = ⅑(9r²+16r²-48r+36+9) ⅓(8r²-6r) = ⅑(25r²-48r+45) 24r²-18r = 25r²-48r+45 r²-30r+45 = 0 Solving the quadratic equation. r ≠ (15+6√(5)) units. r = (15-6√(5)) units. r = 1.583592135 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1993663

Notice; Hexagon Area = 24√(3) square units. Calculating hexagon side length. Let it be a. (6a²)/(4tan30) = 24√(3) ½(3√(3))a² = 24√(3) 3a² = 48 a = 4 units. Equation of the curve is; y = ½(x²) ------ (1). sin60 = b/4 b = 2√(3) units. cos60 = c/4 c = 2 units. Gradient = ((4√(3)+2)-(2√(3)+2))/(2-4) Gradient = -√(3) (y-(4√(3)+2))/(x-2) = -√(3) y = -√(3)x+6√(3)+2 ---- (2). Equation (1) and (2). ½(x)² = -√(3)x+6√(3)+2 x = 3.53906 y = ½(3.53906)² y = 6.2624728418 d = 2(3.53906) d = 7....

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