Відео

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Very good, thank you sir

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Nice! 2y - x = 4 → y = x/2 + 2 = f(x); y - 3x = -5 → y = 3x - 5 = g(x) → m1 = df(x)/dx = 1/2; m2 = dg(x)/dx = 3 → tan⁡(θ) = (m1 - m2)/(1 + m1m2) = 1 → θ = 45° or: φ = 30°; m2 = tan⁡(α) = 3 → sin⁡(α) = 3√10/10 → cos⁡(α) = √10/10 m2 = tan⁡(β) = 1/2 → sin⁡(β) = √5/5 → cos⁡(β) = 2√5)/5 → sin⁡(α - β) = sin⁡(α)cos⁡(β) - sin⁡(β)cos⁡(α) = (3√10/10)( (2√5)/5) - (2√5/5)(√10/10) = √2/2 → α - β = 3φ/2 or: φ = 30°; tan⁡(α) = 3 → cot⁡(α) = tan⁡(γ) = 1/3 tan⁡(β) = 1/2 → arctan⁡(γ) + arctan⁡(β) = arctan⁡( 3φ/2) → α - β = 3φ/2

Nice! 56 = -x^2 - 16xy = 4y^2 - 12xy → y + x/2 = 0 → y = -x/2 → -4y^2 -16(-2y)y = 56 → y = √2 → x = -2√2 → xy = -4

Nice, many thanks, Sir! ∎GFED → GF = FE = DE = GD = a; ∆ ABC → AB = 5; BC = 4; AC = 3; sin⁡(BCA) = 1; ABC = DEC = GDA = δ → sin⁡(δ) = 3/5 → BE = 5a/3 → CE = 4a/5 → 4 = 5a/3 + 4a/5 = 37a/15 → a = 60/37

Very good sir 👍👍👍 Thank you

Very good sir 👍👍👍 Thank you

Very good sir 👍👍👍 Thank you

Very good sir 👍👍👍 Thank you

Very good sir 👍👍👍 Thank you

Very good sir 👍👍👍 Thank you

Very good sir 👍👍👍

Very good sir

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Thank you sir, very good 👍👍👍

Thank you sir, very good 👍👍👍

Thank you sir, very good 👍👍👍

Thank you sir, very good 👍👍👍

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Very good problem, thank you

Very good problem, thank you

Very good problem, thank you

Very good problem, thank you

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A question that is a combination of physics and math, great. Thank you

It's much easier, I did it in my mind in less than 1 min. D+12+D+12+D=22+D+16+D+22 3D+24=2D+60 3D-2D=60-24 D=36

I just labeled the unknown lengths x1 and x2. Doing so gave me three equations envolving d, x1 and x2. Solving the system I got an unique solution S = (x1 = 14, x2 = 10, d = 36)!!!

This was from a 2019 paper from Singapore

Great video!! Thank u. A hug from brazil

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Emeğinize sağlık hocam...

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Nice! One teaching point might be that only the slopes matter. Convert equations into y=mx+b form. One line has m=0.5 and the other m=3 Answer is tan-1(3)-tan-1(.5)=0.785 or 45 degrees. The difference in slopes gives the between angle Your way is a bit longer but it is very clear. Non-calculator approach for tests….use angle difference identities. Tan (a-b)= (tan(a)-tan(b))/(1 +tan(a)tan(b))= (3-.5)/(1+(3)(.5)) =1 therefore angle =45 degrees using unit circle chart.

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