# EMBRY RIDDLE MATH112 all discussion (module 1-9)

Question

Module 1 – Discussion: Application CIN Problems

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Upon completion of this assignment, you will have an overview of calculus and discover the tools that are available for you to use in this course.

In each module, you will work two custom problems based on your unique Calculus Identification Number (CIN) provided by your instructor. Your instructor will assign this five digit CIN once you have sent an confirmation email as instructed in the Start Here module (you may already have received it). The letters that are in bold in brackets below correspond to you CIN. The first digit is [a], the second digit is [b], etc.

You are encouraged to view and comment on your classmates’ posts. Sometimes it is helpful if you are having difficulty to ask how they arrive at their solutions. To do this, use the Reply button associated with their orignal post.

Problems

Find the slope of the line passing through the points ([c], [d]) and (1, [b]). The write-up for this problem should be one line in MathType. Round your answer to two decimal places.

If f\left(x\right)=\left[a\right]-\left[b\right]x+x^2\:.instructure.com/equation_images/f%255Cleft%2528x%255Cright%2529%253D%255Cleft%255Ba%255Cright%255D-%255Cleft%255Bb%255Cright%255Dx%2Bx%255E2%255C%253A” alt=”f\left(x\right)=\left[a\right]-\left[b\right]x+x^2\:”> and g\left(x\right)=\frac{x}{x-\left[c\right]+1g(x)=xx?[c]+1.5 , find

a) f\left(g\left(\left[d\right]\right)\right).instructure.com/equation_images/f%255Cleft%2528g%255Cleft%2528%255Cleft%255Bd%255Cright%255D%255Cright%2529%255Cright%2529″>f(g([d]))

b) g\left(f\left(\left[d\right]\right)\right).instructure.com/equation_images/g%255Cleft%2528f%255Cleft%2528%255Cleft%255Bd%255Cright%255D%255Cright%2529%255Cright%2529″>g(f([d]))

Round your answers to two decimal places.

mdoule 2

When you read the textbook introduction pages to the four chapters that we cover in this course (Chapters 23-27), you are introduced to a number of famous mathematicians. Sir Isaac Newton and Gottfried Leibnitz are the two mathematicians who are credited with the creation of calculus. They are our persons of interest for this discussion activity.

Your discussion activity for this module is to research these two men and write a couple of sentences about each of them. Your goal is to add a new fact to the Discussion Board about each of these men.

module 3

In the discussion area, solve your two custom application problems using the concepts you have learned. Apply your CINs in the bracketed spaces (the first digit is [a], the second digit is [b], and so forth.)

Problems

Find the first derivative of the following functions and evaluate at the given point. Show supporting work and underline your answer. Please use MathType for your supporting work.

1. Quotient Rule- Round your answer to two decimal places.g\left(x\right)\:=\:\frac{\left[a\right]x\:-\left[b\right]}{\left[c\right]x\:+\left[d\right]}\:and\:evaluate\:at\:x\:=\:\left[d\right].instructure.com/equation_images/g%255Cleft%2528x%255Cright%2529%255C%253A%253D%255C%253A%255Cfrac%257B%255Cleft%255Ba%255Cright%255Dx%255C%253A-%255Cleft%255Bb%255Cright%255D%257D%257B%255Cleft%255Bc%255Cright%255Dx%255C%253A%2B%255Cleft%255Bd%255Cright%255D%257D%255C%253Aand%255C%253Aevaluate%255C%253Aat%255C%253Ax%255C%253A%253D%255C%253A%255Cleft%255Bd%255Cright%255D” alt=”g\left(x\right)\:=\:\frac{\left[a\right]x\:-\left[b\right]}{\left[c\right]x\:+\left[d\right]}\:and\:evaluate\:at\:x\:=\:\left[d\right]”>2. Product and Power Rules- Your answer will be a large number.h\left(x\right)\:=\:\left[c\right]x^2\left(\left[e\right]x\:+\left[d\right]\right)^4\:and\:evaluate\:at\:x\:=\:\left[a\right].instructure.com/equation_images/h%255Cleft%2528x%255Cright%2529%255C%253A%253D%255C%253A%255Cleft%255Bc%255Cright%255Dx%255E2%255Cleft%2528%255Cleft%255Be%255Cright%255Dx%255C%253A%2B%255Cleft%255Bd%255Cright%255D%255Cright%2529%255E4%255C%253Aand%255C%253Aevaluate%255C%253Aat%255C%253Ax%255C%253A%253D%255C%253A%255Cleft%255Ba%255Cright%255D” alt=”h\left(x\right)\:=\:\left[c\right]x^2\left(\left[e\right]x\:+\left[d\right]\right)^4\:and\:evaluate\:at\:x\:=\:\left[a\right]”>

module 4

In the discussion area, solve your two custom application problems using the concepts you have learned. Apply your CINs in the bracketed spaces (the first digit is [a], the second digit is [b], and so forth.)

Problems

For both problems, show supporting work and underline your answer. Please use MathType.

Find the second derivative of f\left(x\right)=\left(\left[d\right]x+\left[b\right]\right)^4.instructure.com/equation_images/f%255Cleft%2528x%255Cright%2529%253D%255Cleft%2528%255Cleft%255Bd%255Cright%255Dx%2B%255Cleft%255Bb%255Cright%255D%255Cright%2529%255E4″>f(x)=([d]x+[b])4 and evaluate it at x=3.instructure.com/equation_images/x%253D3″>x=3.

Find the equation of the line tangent to the following curve at x = 1. Write your answer in y = mx + b format.

y=\left[a\right]x^2+\left[c\right]x-\left[d\right].instructure.com/equation_images/y%253D%255Cleft%255Ba%255Cright%255Dx%255E2%2B%255Cleft%255Bc%255Cright%255Dx-%255Cleft%255Bd%255Cright%255D”>y=[a]x2+[c]x?[d]

module 5

In the discussion area, solve your two custom application problems using the concepts you have learned. Apply your CINs in the bracketed spaces (the first digit is [a], the second digit is [b], and so forth.)

Problems

The x- and y-coordinates of a moving particle are given by two parametric equations..

x=\left[a\right]t^2+t.instructure.com/equation_images/x%253D%255Cleft%255Ba%255Cright%255Dt%255E2%2Bt”>x=[a]t2+t

y=2-\left[c\right]t.instructure.com/equation_images/y%253D2-%255Cleft%255Bc%255Cright%255Dt”>y=2?[c]t

Find the magnitude and direction of velocity at t = 3 sec. Distance is measured in meters. Round your answers to one decimal place and don’t forget to use the degree symbol.

A 6-ft tall man walks away from a [a]*[c]-ft tall streetlight at [b] ft/sec. How fast is his shadow increasing when he is [e] feet from the streetlight?

module 6

Problems

A rock is thrown upward from the edge of a cliff. The rock follows the equation below.

s=\left[b\right]\times\left[d\right]+64t-16t^2.instructure.com/equation_images/s%253D%255Cleft%255Bb%255Cright%255D%255Ctimes%255Cleft%255Bd%255Cright%255D%2B64t-16t%255E2″>s=[b]×[d]+64t?16t2

What is the greatest height above the ground that this rock will go?

You are designing a rectangular enclosure with [a] rectangular interior sections separated by parallel walls. If you have 300*[c] feet of fencing, what is the maximum area that can be enclosed?

module 7

In the discussion area, solve your two custom application problems using the concepts you have learned. Apply your CINs in the bracketed spaces (the first digit is [a], the second digit is [b], and so forth.)

Problems

The constant of integration can be found if you know one point on the curve. For the following problem, find the constant of integration. These problems may be easier if you have worked problem #13 from the MML HW Mod 7.

Find the constant of integration, C if:

y=\int\left(9x^2+2x-\left[b\right]\right).instructure.com/equation_images/y%253D%255Cint%255Cleft%25289x%255E2%2B2x-%255Cleft%255Bb%255Cright%255D%255Cright%2529″>y=∫(9×2+2x?[b]) dx and the curve passes through the point ([a], [e]).

Find the constant of integration, C if:

y=\int12x\left(x^2+3\right)^5.instructure.com/equation_images/y%253D%255Cint12x%255Cleft%2528x%255E2%2B3%255Cright%2529%255E5″ alt=”y=\int12x\left(x^2+3\right)^5″> dxand the curve passes through the point ([c], [d]).

module 8

[e]

Problems

Evaluate \int_1^{\left[c\right]}x\sqrt{\left[b\right]x^2+\left[d\right]}.instructure.com/equation_images/%255Cint_1%255E%257B%255Cleft%255Bc%255Cright%255D%257Dx%255Csqrt%257B%255Cleft%255Bb%255Cright%255Dx%255E2%2B%255Cleft%255Bd%255Cright%255D%257D”>∫1[c]x[b]x2+[d] dx and round your answer to two decimal places.

Approximate the area under the curve defined by the following data points.

x 1 4 7 10 13 16 19 22 25

y [a] 4.6 [b] 6.2 [c] 5.5 [d] 7.8 [e]

mdoule 9

In the discussion area, solve your two custom application problems using the concepts you have learned. Apply your CINs in the bracketed spaces (the first digit is [a], the second digit is [b], and so forth.)

Problems

The acceleration of a particle is given by the equation:

A=\left[a\right]\times t

Find S at t=2 sec.

Find the area between the curves for the equations below and round your answer to one decimal place.

y=x^2+\left[b\right]x-4\:and\:y=x+\left[a\right].instructure.com/equation_images/y%253Dx%255E2%2B%255Cleft%255Bb%255Cright%255Dx-4%255C%253Aand%255C%253Ay%253Dx%2B%255Cleft%255Ba%255Cright%255D” alt=”y=x^2+\left[b\right]x-4\:and\:y=x+\left[a\right]”>

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