Suppose that the elevation on a hill is given by flx, y) = 200 – 4,² – 5. From the site at (4, 2), in which direction will the rain run off? The rain will run off in the direction

Q: The trajectory of a ball can be computed with; * +Yo 2v, cos² 8, y= (tan 6, )x - where y= the height…

A: Given,      y=(tanθ0)x+g2vo2cos2θ0x2+y0              (i)

Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

A:

Q: 16. If m/STU = (13x – 6)', mSƯ = (21x + 8)', and mUT = 143', find mST. %3D %3D U T

A:

Q: Find the equation of the line tangent to Y 3x2 + x + 1 at x = -3. у 3 —17г — 26 O y = 6x – 3 O y =…

A:

Q: If airplanes A and B are moving southwest with peed VA=550 mph, and northwest with speed VB= 459…

A: Given that the plane A and B are moving southwest and northwest with speed 550 mph and 549 mph…

Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: Find (au/ay), at the point (u,v) =(√2,3), if x = u² + v² and y= uv. ди (2) = (Simplify your answer.)…

A: Given query is to find indicated partial derivative.

Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

A:

Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

Q: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

A:

Q: Find the tangent plane to the equation z = - 32² – y² + 3y at the point ( – 5, 3, – 75)

A: z=-3x2-y2+3y  and the point (-5,3,-75)

Q: In ARST, mZR = 47°, m 2S = 3y - 7, and mT = 2(y + 10). Find the value of y. %3D %3D %3!

A:

Q: The antiderivative of a constant is the family of lines.

A: Let y = mwhere m = constant

Q: Suppose that these two lines are the paths of two particles. If t and s measure ime in seconds, and…

A: We have given the equations of two lines : l1 : x,y,z=2+2t,8+t,10+3t l2 : x,y,z=5+s,12-2s,17-s…

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

A:

Q: Find (au/ay), at the point (u,v)=(√2,-2), if x=u² + v² and y= uv. du (Simplify your answer.) ay…

A: Given x=u2+v2,y=uv   u,v=2,-2

Q: T(z, y) = e-2z?–3y²

A:

Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

A:

Q: I. Determine la ecuación del plano tangente a la superficie dada en el punto especificado 1. z = 4x2…

A:

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

A:

Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x>0,     t>0ux, 0=fxu0, t=0

Q: dz dz and at the point (3, 6, 1) where z is defined implicitly by the equation z4 + z?x2 - y - 4 =…

A:

Q: Find Duf at P. 2, -k 3' 2 f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u = i+ 3 -

A:

Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: The temperature at the point (x, y) on a metal plate is x² + y? " Find the direction of greatest…

A:

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

A:

Q: on of the tangent to y = 3e" + 3ex that is parallel to

A:

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

A:

Q: If the equation of the tangent plane to x2+y²-83z2=0 at (1,1,/2/83) is x+ay+Bz+y=0, then a+ß+y=

A:

Q: An airplane is traveling at a speed of 130 km/hr with a bearing of 10° at a fixed altitude with…

A:

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

A:

Q: y = mx + b is called the v ---Select--- rm of the equation of a line. standard Additional Materials

A:

Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

A:

Q: An automobile, traveling at a constant rate, starts at home at ime t = 0 and ends up 10 hours later…

A:

Q: Find the gereral Solution of the fille d dffferential equation. 3,n1 %3D | -

A:

Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: If x represents the average velocity of a plane in still air and y represents the average velocity…

A: If x represents the average velocity of a plane in still air and y represents the average velocity…

Q: O whion of the line: y--2x+8 Poliowing line5 ave perpendicular to this. B. ut

A:

Q: Suppose A = xy" where x, y e R". Show that ||A||2 = ||x||2||y||2-.

A:

Q: P to the line L is equal P that is orthogonal to t

A: Given as, The distance is given as, d=AP→sinθ

Q: where c is a constant, then prove that the foot of perpendicular from the origin upon the straight…

A: