Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y = 2 – x if 8 (x, y) = (7)x + (5)y + C .

Q: Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the…

A: Let Q(x,y,z) be the point closest to the point P. Let D be the distance between these two points.…

Q: Construct the function d(x, y) giving the distance from a point (x, y, z) on the paraboloid z = 64 –…

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Q: Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8…

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Q: The cubic y = ax3 + bx? + cx + d tangent to the line y = 12x + 13 at (-1, 1) and have a horizontal…

A: Solution...

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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

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Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

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Q: Find all points (x, y) where f(x, y) has a possible relative maximum or minimum.

A: We have to find the critical points for the function f(x,y)=-x2+2y2+6x-8y+5.

Q: Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

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Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

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

A: Let y = mwhere m = constant

Q: The points P= (x, x, x) and Q (y,3y.y-1) are lines in R' that do not meet. Choose x, y to %3D…

A: Given that P=x,x,x  and Q=y,3y,y-1 Then    P-Q=x,x,x-y,3y,y-1⇒P-Q=x-y,x-3y,x-y+1 then, we solving…

Q: Find the area of one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0<=x<=…

A: To Determine: Find the area of one side of the “wall” standing orthogonally on the curve…

Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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

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Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 50 + 7x2 + 8y2, where x…

A: Differentiate wrt x and y

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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Q: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Let y=2x^2+3x+3. If Δx=0.1 at x=4, use linear approximation to estimate Δy Δy≈

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Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: Suppose that the temperature in degrees Celsius at a point (x, y) on a flat metal plate is T (x, y)…

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Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

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Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Given problem is :

Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

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Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 3x2 + 5y2, where…

A: C(x, y) = 15 + 3x2 + 5y2, x is the cost per pound for material and  y is the cost per hour for…

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: Find the absolute maximum and minimum values of D(x,y)=x²-xy + y² + 1 On the closed triangular plate…

A: Here I am using basic calculus we and also use short method.

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy. Δy≈ ?

A: y=2x2+7x+4, ∆x=0.3 & x=5 Differentiating with respect to x, we get dydx=22x+71+0=4x+7 Now at…

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

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Q: Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the…

A: Here we have to find the point of intersection of the paraboloid x2+y2+2z=4 and the plane x - y + 2z…

Q: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…

Q: Find the length of curve along y = x² from (0,0) into (2,4).

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