Consider the ellipse 25x² + 64y² = 1600. Consider the point P(16,5). Find an equation for both lines tangent to the ellipse that pass by the point P(16,5). (a) The tangent line with the steepest slope is

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A: Use the derivative of log function.

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A: Solution below

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A: I have appended the formula used in the solution part of the question

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Q: Find fo go h. f(x) X g(x) = x³, h(x) = x + 6

A: Given :

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A: NOTE: Refresh your page if you can't see any equations. . the given function is find the partial…

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Q: Solve the following differential equation by finding h and k so that the substitutions x=u+h, y=v+ k…

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Q: Determine algebraically the solution to the system:  x^2 + 2y^2 = 11 3x^2 - 2y^2 = 25

A: Solutions are : (3,1),(3,-1),(-3,1) &(-3,-1) For detail...go through the solution...I have…

Q: Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y =…

A: Given differential equation:- 6dydx-12xy-x=0

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Q: The cost of manufacturing x electric woks in one day is given by C (x) = 2x³ – 16x² + 4x and the…

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Q: Determine the volume of the region bounded by y=x^(2)-2x and y=x that is rotated about y=4

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Q: 7. Find dy fo dx for x³ -y + y² = 4.

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Q: 2. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x, y, z) :…

A: We have to use cylindrical coordinates in order to find the volume of thegiven region.

Q: A volume is described as follows: 1. the base is the region bounded by x = -y² +12y +7 and x = y² −…

A: Given that x=-y2+12y+7 and x=y2-24y+151we have to find volume of object

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Q: Evaluate the given integral by changing to polar coordinates. 160-x²-1² dA, where D is the region…

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Q: The passcode for this gate is found by determining the domain of the derivative of f(x) and 45 then…

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Q: so what is the answer for xi and f(xi)?

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Q: A rectangular field adjacent to a river is to be enclosed. Fencing along the river costs $5 per…

A: A rectangular field adjacent to a river is to be enclosed. Fencing along the  river costs $5 per…

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Q: Show that the lines L₁ : x = 3-t, y = 2t, z = 2+t and L₂: x = 1 + 4t, y = 3-8t, z = 5 - 4t are…

A: Solution is given below:

Q: The price-demand equation for hamburgers at a fast food restaurant is given by the equation below.…

A: The solution is shown below-