Ask Question, Ask an Expert


Ask Math Expert

Home >> Math

1. Solve the subsequent functions for x (where x is a real number). Leave your answers in precise form,

(a) 3x3x23x3 = 331x

(b) 4e2x = 21 − e4x

(c) log2(x − 10) + log2(x) = log2(119)

2. A manager has determined the cost C, in dollars, for manufacturing is

C(q) = 85 log10 (10 + q/2)

for manufacturing, where q is the number of units produced in a given day.

(a) What is cost of manufacturing before any units are produced?

(b) What is cost of manufacturing if 1980 units are produced in a given day?

(c) How many units would be produced if the cost of manufacturing is $150 in a given day?

3. Find out all solutions of the following equations in the interval [0, 2 π)

(a) sin(2x) =√2 cos(x).

(b) 2 cos2(x) + 3 sin(x) = 3.

4. (a) Sketch the graph of the circular function

f(θ) = 1 − 2 cos(3θ + π)

i. State clearly the amplitude, phase shift, period and the equation of the midline.

ii. Show working for all θ- and y-intercepts for the function y = f(θ).

iii. Show at least two periods for the graph of y = f(θ), and label the axes clearly.

(b) Prove the following identity

2 sin(1/2(x + y)) cos (1/2(x − y)) = sin(x) + sin(y) .

Make sure you demonstrate all working and give clear explanations.

5. Consider the function

f(x) = ½ (2x + 2−x)

which has the graph


(a) Elucidate why f has no inverse function. You must include an ex to support your explanation.

(b) Determine the largest possible domain, which includes x = 1, for f(x) such that the inverse function f-1(x) does exist.

(c) Given your answers in (b) find the inverse function f-1(x). Clearly elucidate key steps and show all working.

(d) Sketch the graph of y = f(x) for the restricted domain in (b) and y = f-1(x) on the same set of axes. All points of intersection and axes-intercepts should be easily determined from your sketch or clearly labeled. Furthermore axes must be clearly labeled with appropriate scaling.

Math, Academics

  • Category:- Math
  • Reference No.:- M91655

Have any Question? 

Related Questions in Math

Distribution strategiesone very important decision that

Distribution Strategies One very important decision that marketers need to make is which  channel of distribution  to use for its products or services. Four primary considerations need to be analyzed before making the di ...

Let s d isin f be a bargaining game denote by x2nbsp gx1

Let (S, d) ∈ F be a bargaining game. Denote by x 2  = g(x 1 ) the equation defining the north-east boundary of S. Prove that if g is strictly concave and twice differentiable, then the point x∗ = N (S, d) is the only eff ...

A car was purchased for 3495 and will depreciate 20 each

A car was purchased for $3,495 and will depreciate 20% each year. Find a linear function for the value of the car at time t in years. Define variables clearly. Graph the function you found in part A. A claim is made that ...

In 450 words with referenceshow would you describe apples

In 450 words with references: How would you describe Apple's (or United Way) brand strategy? Discuss other brand strategies marketers use to develop brand loyalty. Give a detailed description of what in involved with the ...

The graph shows the functions fx px and gxgraph of function

The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1.8 to the power of x. The straight line f of x joins ordered pairs 6, 2 and 2, minus 2 and is extended on both sides. The str ...

Suppose we have a cyclic data-dependence graph with nodes a

Suppose we have a cyclic data-dependence graph with nodes a, b, c, and d. There are edges from a to b and from c to d with label h0; 1i and there are edges from b to c and from d to a with label h1; 1i. There are no othe ...

The demand function for a certain brand of cd is given by p

The demand function for a certain brand of CD is given by p = -0.01x2- 0.3x + 49 where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the con ...

Create a chart to compare and contrast the major

Create a chart to compare and contrast the major legislative influences on the labor relations process. Your chart must contain at least five major legislative acts and how they affect management and unions. Columns shou ...

Business ethicsprepare a code of ethics for a fictional

Business Ethics Prepare a code of ethics for a fictional company, which should include a minimum of 10 elements. Once you have compiled the code of ethics, respond to the following questions: 1. Why did you include each ...

Predict two 2 trends that are likely to impact public

Predict two (2) trends that are likely to impact public service in the future. Next, choose two (2) skills that public personnel managers may seek in response to these trends. Provide a rationale and support your positio ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro