average cost per gigabyte of RAM can be approximated by the function C(t)= 8,500,000(0.65)^ t, where t is measured in years since 1980, and C is cost in US$. Find the average cost per gigabyte of RAM for 1980 to 2010.

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A: Intersection points:y=x3, x=2, y=00=x3(0, 0)y=23 =8(2, 8)

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A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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A: To find the length of the parametric curve  r(t)=4t2+1,8t2-5,t3 over the interval 0≤t≤2. Here, let…

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A: Solve the following

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A: Given query is to find the position of the partical at t = 4.

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Q: (x³ +2x)" Find dy/dx, given the following: y = V2x-4 (2³ +2x)“ V(2r–4) 17 -36a²+10x-24 %3D (2x–4)²…

A: Quotient Rule of differentiation :  ddx (uv) = v.dudx-u.dvdxv2. dxndx=n.xn-1

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A: Given function fx,y=1ex2+1Region R is bounded by -5≤x≤5 and 0≤y≤1.Surface area of over region R is…

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A: Given query is to find the average velocity.

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A: We have to find the formula for function S(x, y, z).

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Q: State as TRUE or FALSE. d) 143 = -40 (mod 5) e) –4 = 788 (mod 3)

A: a≡b(mod n) means a-b is divisible by n

Q: TEST 1. DETERMINE WHETHER EACH OF THE FOLLOWING FUNCTI a. CONTINUOUS b. DIFFERENTIABLE 1. f(x) = 5x-…

A: To determine whether the given functions are continuous and differentiable or not.

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A: We want to check true or false.

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Q: y 71. f(x, y) y %3D

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Q: The dimensions of avectargubr region are varying with the bimeltsaccoding 1-2728 cmfsee and wa3t+6…

A: L= 2t2-8w= 3t+6Let A be the area of rectanglegiven : dAdt= 360 cm2/sec   A= L×wA=(…

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A: Given data÷

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Q: x2 8. 36 y2 3D1 4 ニ 「て

A: This question can be solved using the concepts of standard equation of hyperbola.

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A: Given query is to find the volume.

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Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) 12 dt 3t +4

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Q: In Problems 17-20, find the indicated values of f(x, y, z) = 2x - 3y2 + 5z - 1 19. f(6, -5, 0)

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Q: Find the gradient of the function at the given point. g(x, y) = 20xeY/x, (9, 0) %3D Vg(9, 0) =

A: We can find the gradient as below.

Q: 1. Apply Maclaurin's series to establish the power series of tanx.

A: Answer is in below step.

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A: A)C(x)=0.425 x1954-xwhere, x is the miles of the wall.cost to build 1000 miles of…

Q: ewrite int _0^1 int _0^{2-2x} int _0^{{1/2} (6-6x-3y)} dzdydx as dzdxdy and dydxdz

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A: First find the magnitude of the vector and the find unit vector

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A: Given

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A: The solution is given below.

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A: