Question 1: Find an explicit formula for the geometric sequence with a₁ = 10 and a4 = 80. a_n= Question 2: If {a} is a geometric sequence with a2 = 96 and a7 = 98304, what is the common ratio r? Question 3: If (an) is a geometric sequence with a3 = -375 and ag = 1171875, what is de? Answer 8 M

Q: Use mathematical induction to prove that the statement is true for every positive integer n. n(n +…

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Q: Use Variation of Parameter to find a particular solution for y"-4y'-12y=x

A: The given differential equation:y''-4y'-12y=xWe need to find the particular solution using variation…

Q: can you answer the last question?

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Q: a building so that its foot moves away from the building at the note of 3 feet per second. When the…

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Q: Determine the open intervals on which the graph of the function f(x)= x²+64 is concave upward or…

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Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

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Q: -1 Find f-¹(x) if f(x) Of-¹(x) Of-¹(x) Of-¹(x) f-¹(x) = = = 2x + 1 3 2+x 3x 2x - 1 3 2 - x 2 2 3x +…

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Q: Solve the following initial valuc problem using the method of Laplace transforms y" - 4y + 5y = 8c³;…

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Q: 5) Find the divergence of (√x² + y² + z² 5) kî + yî yj + zk)

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Q: 2- Say whether each given sequence is an arithmetic sequence. Find the common difference and the…

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Q: ) The derivative of y=e¹4x, x>0 is: a) b) x√16x¹-1 243-1 c) RV168--1 d) None of the above

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: _f(x) = 2 X 1 - 2x

A: To solve the following problem

Q: Given the non-homogeneous differential equation y "+ 3y + 2y = 4e* The roots of its auxiliary…

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Q: 40. Solve forx: -3+ tan² x=0

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Q: 10. If f(x)=√√x²-1 and g(x) = x + 1 a. 1+ b. √√x²+2x , which expression is equal to c. (x+1)²-1 d.…

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Q: 4. Using a right triangle, find the exact value of cos cos (tan-¹²).

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Q: 4 Suppose that f(x, y) = 2x² + 2y¹ − 1xy Then the minimum is

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Q: Find dy/dx. x=tsin(t), y = t² + 5t

A: SOLUTION-

Q: This answer is incorrect. Can you try again?

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Q: bounded by the following curves: y = x³/2, y = 8, x = 0, y = 0. Find the volume of the solid…

A: Given ,       y = x32 ,  y=8  ,  x= 0 , y=0.  From Shell method-     Since the revolution is around…

Q: (c) At what points is the height 40 m? (Round your answers to two decimal places.) (x, y) = -52.825…

A: The given equation of the arch:y=211.49-20.96 cosh0.03291765x

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

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Q: The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but…

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Q: Find the area enclosed by  x=2cos(t) + cos(2t), y=2sin(t) - sin(2t) 0<t<2

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Q: 6. Change the order of integration and evaluate 1 3 3y e-² dxdy.

A: To change the order of integration and to evaluate ∫01∫3y3e-x2 dx dy.

Q: Determine the x-coordinate(s) of any relative extrema and inflection points of the function y=x³ In…

A: Solution: y=x3lnx4 This can be written as y=x3(ln(x)-ln(4)) Then: for having any relative extrema…

Q: The region bounded by f(x) 4x² + 20x + 56, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: Sketch the curve. r = 9 cos(8) O -4 ac -2 O y 2 -8…

A: Given query is to sketch the curve and find the area.

Q: d²y y = cos xtanx 18.Determine dx2 for

A: The function is given as y = cos(x)tan(x) Simplifying the given expression, Substitute tan(x) =…

Q: 38. Simplify: cos 40° cos 110° - sin 40° sin 110⁰ 39. Simplify: cos 50° cos 20° + sin 50° sin 20⁰

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Q: 2k, {}) 4k

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Q: 22. g(x) has an inflection point(s) at:

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Q: y = ln x, xy = 4, x = 1, x = 3

A: NOTE: Refresh your page if you can't see any equations. . here we have and the given interval is…

Q: What is the Remainder R, when ƒ(x) = is divided by (x + 1)? 20 16 22 30 30 4x³ + x² - 3x + 2 3 =…

A: To find the remainder

Q: Evaluate the integrals: COS cos √x √√x -dx

A: I=∫cosxxdxwe know that  ∫cosxdx=sinx+cdxndx=nxn-1

Q: Evaluate each of the following expressions using the given table of values. 3 4 5 7 6 5 3 4 7 6 5 5…

A: we need to find out the values of the composite functions.

Q: es for the point (4, IN

A: given (r,θ)=(4,2π3)formula for other coordinates is  (r,θ+2nπ) or  (-r,θ+(2n+1)π)

Q: 9. Use the comparison theorem to show that So L'√T- 10. Find √1 + x² dx ≤ Also show that ²√1 + x dx…

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Q: A force of 6 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. How…

A: Given that, Force required = 6 pounds to hold spring streched 0.6 feet beyond its natural length. To…

Q: The graph of one complete period of a sine curve is given. n 3A 54°F Partly cloudy (a) Find the…

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Q: Find f such that f'(x) = 8x² + 7x-7 and f(0) = 2. f(x) =

A: Given query is to find indicated function m

Q: A ladder 15 feet long is leaning against the wall of a house (see the figure below). The base of the…

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Q: 11. a =(3, 1); b =(− 6, − 2). Evaluate 2 12. a =(3, 1); b =(-6, -2). 3(a - b) Evaluate 3 a-b

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Q: Find the sum of the series 65+ 513 5/9 + LO 5 27 - 5 81 +

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Q: 16) Sinx-cosy-2=0; dy = ? A) -cot X c) CosX siny B) -cot y d) -cscy cos X E) 2-COS X siny

A: given 16) sinx - cosy - 2 = 0

Q: Does the series converge conditionally ot absolutely

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Q: X √4- 4+3x² -dx

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Q: 9. What is the slope of the normal to a. -3 y = x²-1 x+5 at (1, 0)? Show your work. C.

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Q: Let f(x,y) = 5xy4 + 5x²y. Find 224 ах = a²fa²fa²f 1 2' ахду' ax2' ay²' and 224 дудх

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Q: The Cartesian coordinates of a point are given. (a) (6, -6) (i) Find polar coordinates (r, e) of the…

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