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  1. the gradient is < 2 x / 9 , y / 2 , 2 z >... at (3 , 0 , 0 ) the tangent plane is : ( 2 / 3 ) ( x - 3 ) = 0 ; at ( 0 , 2 , 0 ) the tangent plane is : ( y - 2 ) = 0 ; at ( 0 , 0 , -1 ) the tangent plane is - 2 ( z + 1 ) = 0 ; at ( 1 , 1 , - √23 / 6 ) the tangent plane is ( 2/9) ( x - 1) + ( 1...

    2 Answers · Science & Mathematics · 19/05/2019

  2. See Graph https://www.desmos.com/calculator/pgs41pcird

    2 Answers · Science & Mathematics · 07/06/2019

  3. When z = sqrt(3), you have x^2 + y^2 = 5. The level curve is a circle whose radius is around 2.24. I see no need for partial derivatives, a line perpendicular to a circle is a radius. At (-2,1) the equation of the radius is x + 2y = 0.

    1 Answers · Science & Mathematics · 20/05/2019

  4. The region of integration is the region between z = |x| and the xy-plane (which is z = 0) where x is in [-1, 1] and y is in [0, 1]. [I'd sketch the region under z = |x| with x in [-1, 1] in the xy-plane first; this gives a triangular region. Then, I'd extend...

    1 Answers · Science & Mathematics · 02/06/2019

  5. Yes. (Given Jesus, all is possible.)

    1 Answers · Science & Mathematics · 08/06/2019

  6. r = < t , t² , 0 > ; r ' = < 1 , 2t , 0 > ; r ' ' = < 0 , 2 , 0 > = a_T T + a_N N = 2 T + a_N N===> N = < 0 , - 1 , 0 > all at (0,0,0)...B = T x...

    1 Answers · Science & Mathematics · 20/05/2019

  7. m = ∫∫D ρ(x,y) dA ....= ∫(x = -1 to 1) ∫(y = 0 to 2) x²y dy dx ....= ∫(x = -1 to 1) x²y²/2 {for y = 0 to 2} dx ....= ∫(x = -1 to 1) 2x² dx ....= 2x³/3 {for x = -1 to 1} ....= 4/3. Mx = ∫∫D xρ(x,y) dA ....= ∫(y = 0 to 2) ∫(x = -1 to 1) x...

    1 Answers · Science & Mathematics · 02/06/2019

  8. ...4, so: 360 / 4 = 90 unique 4-digit PINs using the 6 digits shown.

    3 Answers · Science & Mathematics · 01/10/2019

  9. Are you sure that's the question? If so, hints: Rewrite as 2( sin(x) + cos(x) ) = 1. And recall sin(π/4 + x) = (sin(x) + cos(x) )*√2/2. And thus... π/4 + x = ? ... I would detail further if u were not anonymous though.

    2 Answers · Science & Mathematics · 03/04/2019

  10. It's showing up for me. Y!A has tons of issues with questions and answers just not showing up. It happens. I'm glad it worked out for you.

    1 Answers · Science & Mathematics · 19/01/2019

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