53. If oil leaks from a tank at a rate of r(t) gallons per minute at time t, what does 120 r(t) dt represent? A DEC 11 N

Q: -7 13 Let A = 0 6 Find a matrix S, a diagonal matrix D and S-1 such that A = SDS-¹.

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Q: Given the definitions of f(x) and g(x) below, find the value of f(g(0)). ƒ(x) = 2x² − 5x + 12 g(x) =…

A: We will find the required.

Q: Convert the rectangular coordinate point (2,-2) to polar coordinate.

A: To convert into polar coordinates

Q: If the operation is undefined, enter NA. BD = B = sin (a) 4 [362] -9 0 12 8 ar Hint: To create a…

A: To find the product of matrices.

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A: given  4,16,64.................formula for nth term of g.p. is  an=a(r)n-1 where a is first term…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: (ii). (x − 3y + 2)dx + 3(x + 3y - 4)dy = 0 - - Ans. In [(x - 1)² +9(y − 1)²] - 2 arctan x-1 3(y-1) =…

A: Let's solve given differential equation.

Q: Let f(x) = x² g(x³). Suppose g(64) = 7, g(48) = -4, g' (64) = 4, and g' (48) = -3. Find f'(4) =

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Q: The area of a square is increasing at a rate of 70 centimeters squared per second. Find the rate of…

A: Area of square is increasing at a rate of 70 centimetres squared per second. Side is 7 centimetres.

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Q: Page 6 of 7 7. [4] The total accumulated costs C(t) and revenues R(t) (in thousands of dollars),…

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Q: December 10, 2022 at 1:56 PM Starting at age 30, you deposit $2000 a year into an IRA account for…

A: NOTE: Refresh your page if you can't see any equations. . here we have PMT=2000 r=5%=0.05 t=35 years

Q: Consider the following parametric equation. a. Eliminate the parameter to obtain an equation in x…

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Q: The dimensions of a box are x, x + 14, and x + 17. Find how fast is the volume of the box increasing…

A: The dimensions of the box are: x,  x+14  and  x+17Now the shotest edge is: xTherefore: x=12

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A: I have solved step by step in detail...go through the solution.... I have used two perpendicular…

Q: x2 + y2 + z2 - 2x + 6y - 8z = -1 The equation is a sphere what are the first,second third…

A: given that ,  equation of a sphere is      x2+y2+z2-2x+6y-8z=-1then we have to find centre of sphere…

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Q: Write the first five terms of the geometric sequence whose first term is 2, and whose common ratio…

A: Find the first five term

Q: f(1) = 2, f'(1) = 3, f'(2) = 4. Find (f^-1)'(2).

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Q: Suppose an architect is designing a pagoda that will sit on a 8 foot by 8 foot square base centered…

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Q: Consider the following parametric curve. Answer parts a and b. x = 5+2t, y=-3-6t; t = 3 dy a.…

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Q: Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

A: (5) Evaluate the Laplace transform Letsin2t=?

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Q: A point is moving along the circle x²+²=² in the first quadrant such that its x-coordinate changes…

A: The given circle is:x2+y2=r2The radius of the circle is:  6 unitsTherefore:x2+y2=36

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A: Solve the following

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A: Topic:- application of derivatives

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A: Topic:- application of derivatives

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A: To compute the percent error in computing the area of a squarewhose side is measured with an error…

Q: (4-6) Determine the area bounded by: 4. y=x³-4x and y = x² + 2x

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Q: x=5t²+2t _y=2+²+4

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Q: Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x…

A: The answer is given below:

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A: Here we have to find the first 3 terms and last term . Then by using the formula for the sum of…

Q: Use a calculator to evaluate the following expressions. Round your result to three decimal places.…

A: NOTE: Refresh your page if you can't see any equations. . using the calculator, find the value of…

Q: Find the k-component of (curl F) for the following vector field on the plane. F = (xey)i + (2ye*)j

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Q: 11. (The law of cosines) (a) Two straight roads diverge at an angle of 0= 60° . Two cars leave the…

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Q: f(x, y, z) = x² + 3xy − z² + 2y + z + 4, Po(0, 0, 0), v=i+j+ k

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Q: 5- Find 3 geometric means between 7 and 4375.

A: We need to find geometric mean. As per Bartleby guidelines we can solve one question from multiple…

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Q: f(x, y) = 6x² – 3xy+9y² − x+y=7 Local maxima are Local minima are Saddle points are m m … [I]

A: Given function:- fx,y=6x2-3xy+9y2-x+y-7

Q: Find T(): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T5(x) = Using the…

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Q: Find the approximate value of 3 A using differentials if A = 74.2. Round off the final answer to…

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Q: Find the area of the region bounded by the graphs of the given equations. y=2x2-5x+5; y=x2+4x-9

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Q: Find the limit. Use l'Hospital's Rule where appropriate. lim x-0 cos 9x - x² cos 4x

A: Please see the below picture for detailed solution.

Q: Compute the Surface Integral of the function given by f(x, y) = 2x² +2y² over the portion of the…

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Q: The cuberoot of a number can be approximated by the recursive formula А 1 ==2sn-1 3 A₁J²) Sn 25₁-1 +…

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Q: solve for the variation of parameter of: y''+y= tan(x)

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