Find the tangent plane and normal line from x2 + y2 + z2 = 30 in (1, -2, 5)

Q: Find the tangent and normal to the equation 5x? +6y³ = 930 at ( -6, 5)

A: 5x2 + 6y3 = 930⇒ 6y3 = 930 - 5x2⇒y3 = 930 - 5x26⇒y = 930 - 5x263 dydx = d(930 - 5x26)1/3dx ⇒dydx…

Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: What is the point on the curve at which the normal line is parallel to the line Y = - 3X + 6? (The…

A: The function is given by y = 2x+1 The equation of the line is y = -3x+6 To evaluate: The point on…

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Solve the given O.D.E. by the method of "Variation of Parameters"; 1 Y" - 4 Y' + 4 Y = [12 x2 -…

A: The solution is given as