1. Solve a. e^.05t = 1600 0.05t = ln(1600) 0.05t = 7.378 t = 7.378/.05 t = 147.56 b. ln(4x)=3 4x = e^3 x = e^3/4 x = 5.02 c. log2(8 – 6x) = 5 8-6x = 2^5 8-6x = 32 6x = 8-32 x = -24/6 x = -4 d. 4 + 5e-x = 0 5e^(-x) = -4 e^(-x) = -4/5 no solution‚ e cannot have a negative answer 2. Describe the transformations on the following graph of f (x) log( x) . State the placement of the vertical asymptote and x-intercept after the transformation. For example‚ vertical shift
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Introduction to C# .NET and the .NET Platform In this chapter‚ you will • Learn about the .NET Framework • Become familiar with the .NET languages • Discover the environment surrounding C# .NET • Compile your first C# program • Learn the basics of the C# language • Be introduced to object-oriented programming • Learn to use abstraction and encapsulation • Learn to differentiate between instance data and class data If you have been around the programming world for a while‚ you may have
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Choices: 1. What is the average of A‚ B‚ C? a. ABC/3 c. 3(A+B+C)/.3 b. (A+B+C)/3 d. ABC/A+B+C 2. Which of the following has the LEAST Numerical value? a. 11/12 b. 6/8 c. 5/7 d. ¾ 3. If 2 apples cost P25.00‚ how many apples can be purchased for P100.00? a. 8 aplles c. 2 dozens b. ½ dozen d. 1 ½ dozens 4. If 2 tablespoons= 1 liquid oz.‚ and 5 tablespoons = ¼ cup‚ then‚ how many liquid ounces are there in one cup? a. 4 ounces c. 16 ounces b. 10 ounces d. 24 ounces
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save a lot of digging. What is x? So‚ if you walk x paces north‚ then 2x+4 paces east‚ you have moved roughly east northeast to a distance of 2x+6 paces. This is a right angle‚ with 2x+6 on the hypotenuse or line c‚ so we must solve using the Pythagorean Theorem: a² + b² = c² add in the values (x)² + (2x+4)² = (2x+6)² multiply inside the parenthesis x² + 4x² + 16x + 16 = 4x² + 24x + 36 subtract 4x² + 24x + 36 from both sides x² - 8x - 20 = 0 factor the quadratic equation (x -10)(x
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|AC | | | | | | |533 |1.1 |There are many causes of dementia. Dementia is caused by changes to the brain; there are different | | | |types of Dementia. Vascular dementia is caused when the brains blood supply is disrupted‚ the brain|
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Aluminum GuttersOf all the types of gutters to choose from‚ there is a very good reason why aluminum dominates the gutter market. The metal is corrosion-resistant‚ lightweight‚ easy to work with‚ available in wide range of colors‚ and less expensive than the other alternatives. Copper GuttersCopper gutters will not hold up that much better or last longer than aluminum gutters for the added cost. There are certain long term and short term advantages to copper gutters‚ as long as they are installed
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is an isosceles triangle. By that logic‚ ∠O=∠P’. Now‚ I looked at the triangle that is already drawn in the above figure‚ ΔAOP. We know that this triangle is also isosceles because OP=AP. By that logic‚ ∠A=∠O. Using the law of cosines c^2=a^2+b^2-2abcos(C)‚ which works for any triangle‚ I assigned θ to ∠O and determined that cos(θ)=1/(2*OP). Then‚ using the law of sines (insert law of sines here)‚ sin(θ)/1=sin(180-2θ)/OP’ OP’=sin(180-2θ)/sin(θ) OP’=sin(2θ)/sin(θ) OP’=2cos(θ) But because
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2 OBJECTIVES We students taking Additional Mathematics are required to carry out a project work whilewe are in Form 5. This year the Curriculum Development Division‚ Ministry of Education hasprepared four tasks for us. We are to choose and complete only ONE task based on our area of interest. This project can be done in groups or individually‚ but each of us are expected tosubmit an individually written report. Upon completion of the Additional Mathematics ProjectWork‚ we are to gain valuable experiences
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Homework Assignment 1 1. For each of the following equations determine whether it is linear in its variables or not. Explain your decision. a) b) c) 2. Solve each of the following systems and comment on geometric interpretation of its solutions. a) b) c) 3. Solve the following linear systems by Gauss-Jordan method: 4. Each of the following matrices is an augmented matrix of some linear system. In each case‚ determine : the ranks
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UNIVERSITI SAINS MALAYSIA School of Management Semester II‚ Academic Session 2007/2008 MID-TERM EXAMINATION ACW 110/3 ¨C BUSINESS MATHEMATICS 15 February 2008 8.00AM ¨C 10.00AM Dewan Kuliah ¡°Z¡± Name:_______________________________ Matrix:_______________________________ INSTRUCTIONS This exam booklet contains five (5) questions (including one bonus question) Answer the FIRST FOUR questions; the bonus question is an option. Show all your works clearly. This booklet contains seven (7)
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