A particle is moving along the curve y = 4√4x + 4. As the particle passes through the point (3, 16), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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A: Given: A wire of length x is bent into the shape of a square. (a) To express the perimeter p of the…

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A: Given: n = 15 r = 3 Formula Used: Prn = n!(n-r)!

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Q: Find the following limit. lim x-x 2+ x - 4x³-4 5 x³x²+1 Number

A: ans=  -4/5

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A: Given diagram:- Here,  θ=Angle

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A: To solve this question we would use the following supporting formulas   ddxcosx=-sinx ddxsinx=cosx…

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Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

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A: First of all we will solve the denominator then we will solve the integration.

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Q: graph each equation.   3x - 2y = 12

A: Given data:- The given equation is, 3x-2y=12

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Q: For the function f(x) = 5x² 2x, evaluate and simplif f(x+h)-f(x) h 11

A: f(x)=5x2-2x hence f(x+h)=5x+h2-2x+hf(x+h)=5x2+5h2+10xh-2x-2h

Q: Sorry forgot to specify, find the zeros

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Q: Differentiate: e6x² A) 6e6x²-1 D) 12xe*-1 B) e 6x² E) 12xe6x² C) 2ex-1 F) 12xe*

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Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D.4 O E. None of the Choices alt + dx…

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Q: Evaluate the following integral. 4x Jetz 4* sin(2x) dx =

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Q: 55. Differentiate each trigonometric identity to obtain a new (or familiar) identity. sin x cos x…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) B.…

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Q: For a particular function h, we know h 0 (2) = 6 and h(2) = −3. Write an equation for the line…

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Q: Evaluate (2x + 4)(3x + 2) d dx A) 6 C) 12x + 16 B) 6x² + 16x + 8 D) 30x² + 43x + 8

A: Given query is to find the Indicated derivative.

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A: Note:- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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A: The given function y=ln x2x We have to find the derivative of y using logarithm differentiation.

Q: Determine the solution of the differential equation: (3tanx-2cosy)sec²x dx + tan x siny dy = 0

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Q: write law of cosines.

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Q: 11 Find the derivative of f(x) = -15sinx + +3√√x-5. X

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Q: p(x)=3x^3−x^2−8x−25 k=3 Use synthetic division to determine if the given value for k is a zero of…

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Q: The equation y = 1x - c2 2 defines a family of parabolas,one parabola for each value of c. On one…

A: Given, y=x-c2                     ... 1

Q: Find the directional derivative of f at the point P in the direction of a. P(4,0); f(x, y) = 4x³y³;…

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Q: lim 1 - cos(sin(³-1)) 73 - 1

A: As per the instruction, we will be answering the first question. The graph of y=1-cossinx3-1x3-1.

Q: Problems: 1.(x³ + xy² − y)dx + (y³ + x²y + x)dy = 0 2. (ex siny + ey)dx - (xe-y-e* cosy)dy = 0

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Q: (Question-Solution-Final Answer-Conclusion format) B. Generate differential equation by elimination…

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Q: Evaluate the sum 50 Σ(2 · k + 5) = k=1 50 Σ5₁(2. k+5). k=1

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Q: 3 x² + y² the direction of (-3, −3). Then, Suppose f(x, y) (a) ▼ f(x, y) (b) ▼ ƒ(1,4) = = = (c) fu…

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