FInd the equation of a linw whose gradient is 3/2 and which passes through the point P,where P drives the join of A(-2,6) and B(3,-4) in ration 2:3

Q: The line with equation 7x + 5y – 4 = 0 (a) Cuts the x-axis at the value x = (a) Cuts the y-axis at…

A: The equation of the line is: 7x+5y-4=0 The problem can be solved as follows:

Q: Find the gradient of the function at the given point. g(x, y) = 6xeYlx, (14,0) Vg(14, 0) :

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Q: The line 3x + 2y +14 0 has a gradient of and y-intercept of Where appropriate, give your answer as a…

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Q: 5. Find the gradient of the curve i) y = 3e-2x – 1 at the point where x =. ii) y = xv2x - 3 at the…

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Q: Suppose that the amount of energy E(x,y, z) emanating from a source at (0,0,0) is inversely…

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Q: If f(x, y, z) = x² +y² – 4.xz, find the rate of change of f at P(3, 1, –2) in the direction from P…

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Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

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Q: Find the gradient of the function at the given point. In(x2 - Y) - 9, (3, 8) Vz(3, 8) =

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Q: Find the gradient of the function f(x.y) = /2x+ 3y at the point (- 1,2). Then sketch the gradient…

A: Solve the following

Q: 18,8grt(10)) 10 f(x) = V2x – 2 compute the instantaneous slope at: (6, v10) Start with two points A:…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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Q: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Sub Yに3yこ1 passes through the point (3, 1), where its gradient is ax +b 3 Ify = 1-2x find the value…

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Q: Q3. Find the coordinates of the point(s) of the function y 3x'-5x+2, where the tangent has a…

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Q: Q3: Find gradient of the following function at given point f(x, y. =) = (x² + y° + :')"? + In(xyz).…

A: The detailed solution is as follows below:

Q: Q3: Find gradient of the following function at given point 3) f(x, y, 2) = x² +y² – 2=² + = In(x).…

A: The gradient at the point (1,1,1) is, (3, 2, - 4)  The detailed solution is as follows below:

Q: Q3: Find gradient of the following function at given point 2) g(x, y) = y – x². (-1,0)

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 8, –3) Vw(9, 8, -3) =

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Q: Q3. Find the coordinates of the point(s) of the function y=3x – 5x +2, where the tangent has a…

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Q: Find the gradient of the function at the given point. In(x² – y) - 9, (3, 8) z = Vz(3, 8) =

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Q: Find the gradient of the function at the given point. In(x? - y) - 3, (2, 3) Vz(2, 3) -

A: We have to find the gradient of the function z = lnx2-yx-3 at the point 2, 3.

Q: Find the gradient of the following function. 3 f(x, у) %3 5x° - ху Vf(x, y) =

A: Gradient of f(x,y) is given by∇f(x , y) = i⇀ ( fx ) + j⇀( fy )

Q: (a) Find the derivative of ƒ(x, y, z) = x3 - xy2 - z at P0(1, 1, 0) in the direction of v = 2i - 3j…

A: We have given function fx,y,z=x3-xy2-z, point P01,1,0 and vector v=2i^-3j^+6k^

Q: F(x.y)=e-2x2-y P(-3,-2)

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Q: Find in what directions does flx, y, z) = 4x 2– 9z + 2z In(y) increase and decrease most rapidly at…

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Q: Find the gradient of the function at the given point. In(x² – y) – 6, (3, 8) z = Vz(3, 8) =

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Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Find the gradient of the function: y = (5x ln (x)/ 6) + x/3 at the point with x-coordinate 1. Give…

A: We can solve this problem as follows:

Q: 1. Find the Gradient of the following F = x*e" - y': b. F, = 4x - 3y + 5=? а.

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Q: Calculate the gradient. h(x, у, 2) %3 хуz7 Vf =

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Q: A line I has a gradient of m₁ = Which one of the following lines will intersect I at right angles? 4…

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Q: Find the gradient of ?:V x²+y²1Z²

A: Gradient of a function f(x,y,z) is given by ∂f∂xi  ∂f∂yj + ∂f∂zk

Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (17, 6, -3)

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Q: Find the gradient of the function at the given point. g(x, y) = 5xev/x, (8, 0)

A: Follow the procedure given below.

Q: 1. Find the Gradient of the following a. F, = x'e" - y': b. F, = 4x' - 3y +5=?

A: Solution is given as below:

Q: Find the gradient of the function at the given point. g(x, y) 6xey/x, (1, 0)

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Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: w = 3x² – 5y² + 2z², (1,1, –2)

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Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = z =

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: Suppose that the amount of energy (x, y, z) emanating from a source at (0, 0, 0) is inversely…

A: a)  The energy function is proportional to z And, it is inversely proportional to 11+x2+y2    So,…

Q: First, compute the gradient of the function p(x.y) /29-4x -y. Then evaluate it at the point (-2,2).…

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Q: Q3: Find gradient of the following function at given point 1) f(x,y)=y-x, (2,1)

A: We find the gradient of the given function by using the definition of gradient. The gradient of a…

Q: Find the gradient of the function at the given point. 2 = In(x2 – y) - 9, (2,3) Vz(2, 3) = Need…

A: This is a problem related to derivation. Please follow the procedure given below for solution.

Q: First, compute the gradient of the function f(x.y) = 3+ 3x - 7y. Then evaluate it at the point (-3,-…

A: Given:      f( x , y ) = 3 + 3x2 - 7y2      Point : ( -3 , -4)

Q: If ø = 3r²y – y³,2. Find gradient Vø at the point (1, –2, –1).

A: The solution is given as

Q: Find the gradient of the function at the given point. w = x tan(y + z), (12, 7, -2) Vw(12, 7, -2) =

A: Gradient of function wx, y, z=xtany+z at point 12, 7, -2