Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

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

976_graph.jpg

(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

In order to help pay for college fatima invested part of

In order to help pay for college, Fatima invested part of $8000 she earned in an account paying 10% interest and the rest at 12% interest (simple interest). if her annual income from these investments was $900, how much ...

Production is modeled by the cobb douglas production

Production is modeled by the Cobb Douglas production function where x represents the number of units of labor, and y the number of units of capital. If each unit of labor costs $500 and each unit of capital $200, and the ...

Assignment applications of graph theoryin 1736 a famous

Assignment: Applications of Graph Theory In 1736, a famous Swiss mathematician Leonhard Euler (1707 - 1783) started the work in the area of Graph Theory through his successful attempt in solving the problem of "Seven Bri ...

Three sides of a triangle are consecutive odd integers and

Three sides of a triangle are consecutive odd integers and the perimeter of the triangle is 81 inches. Find the length of each of the three sides. (Show all of the algebra and include the units in your answer).

How to find out the cube root of perfect cubes within

How to find out the cube root of perfect cubes within seconds To find out the cube roots of a perfect cube, you need to know some of the basic cubes 1 3 = 1, 2 3 = 8, 3 3 = 27, 4 3 = 64, 5 3 = 125 6 3 = 216, 7 3 =343, 8 ...

The perimeter of a rectangular garden is 126 meters the

The perimeter of a rectangular garden is 126 meters. The length is 6 meters longer than twice the width. Find the dimensions of the garden.

How can the multiplication principle permutations and

How can the multiplication principle, permutations, and combinations be used in problems concerned with probability?

A jury pool consists of 27 people 14 men and 13 women

A jury pool consists of 27 people, 14 men and 13 women. Compute the probability that a randomly selected jury of 12 people is all male.

Frogs have been breeding like flies at the enormous state

Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago ...

1 show that x2 is a strictly convex function on r without

1. Show that x 2 is a strictly convex function on R without using any knowledge of the differentiability of the function (that is, using the convex-combination condition of a convex function). 2. Prove that a concave fun ...

  • 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

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate