After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked, its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released. s(t)=-16t² + 30t+3 a. How high will it go? b. How long is it in the air?

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A: Step 1:  Given Limit ExpressionWe must assess the following boundaries:…

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A: Let's solve the problem step by step.Given the equation of motion: s=t3−6t2+9 Step 1: Find velocity…

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A: Step 1:Step 2: Step 3: Step 4:

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Q: 2. Find each derivative. Write answers with positive exponents. a) Dx 9x -3 [97] b) f'(3) if f(x) =…

A: Step 1:Step 2: Step 3: Step 4:

Q: Use series to evaluate the limit. lim X-0 12 2 - + x − In(1 + x) X

A: If you have any problem let me know in the comment section thankyou.

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Q: #19

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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Q: 2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below. a. Evaluate f(-3). If you…

A: If you have any help please let me know in comment box thankyou.

Q: Find this expression in frequency domain in a expression y(t), in time, that is.

A: Step 1:

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Q: the correct answer is A could you show me how to solve this using gauss theorem of divergence

A: Step 1: Compute the Divergence of F: div F=∂x∂​(5x−3y)+∂y∂​(2x−5y)+∂z∂​(x2+y2+3z)=5−5+3=3. Apply the…

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A: Let us analyze the transformation of the graph of f(x) = x2 as follows:Step 1: Identify the key…

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A: Step 1: Understand the Basic The general form of an absolute value function is: y=a∣x−h∣+k• h:…

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A: I have solved the problem and given the answer with proper steps and explanation. Kindly check it…

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A: Here is the sample matrix:  Rank = 7 , Nullity = 2

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Q: If f(x)=x2+4, g(x)=x-6, h(x)=sq root of x, then (f o g o h)(x)=

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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A: Step 1: Step 2: Step 3: Step 4:

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A: Identified points from the graph: 1. First segment: Points: (−6, −3), (-4, 0), (-2, 3) 2. Second…

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A: Question 3. We find the equation of the tangent line to the graph of the function f(x) = x-4 - x-3…

Q: y"-9y+20y= 80t-156 y(0) = −6, y'(0) = 5 y(t) =

A: Step 1:Step 2:Step 3:Step 4:

Q: #25

A: 25. Graphically, a function is not differentiable at:Sharp Corners/Cusps (abrupt changes in…

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 2. (5 points) Let f(x) = = - - - x² − 3x+7. Find the local minimum and maximum point(s) of f(x), and…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: (1) (16 points) Let f(x, y) = 2x + 3y + In(xy) (a) (6 points) Calculate the gradient field Vf(x, y)…

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