Solutions to Graded Problems Math 200 Section 1.6 Homework 2 September 17‚ 2010 20. In the theory of relativity‚ the mass of a particle with speed v is m = f (v) = m0 1 − v 2 /c2 where m0 is the rest mass of the particle and c is the speed of light in a vacuum. Find the inverse function of f and explain its meaning. Solution. We simply solve for v: m= m0 1− v 2 /c2 =⇒ m 1 − v 2 /c2 = m0 =⇒ m2 1 − v2 c2 = m2 0 m2 v2 =⇒ 1 − 2 = 0 c m2 =⇒ v2 m2 =1− 0 c2 m2 m0 m m0 m 2 =⇒
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Using Polynomials in the “Real World” Polynomial functions are used in our everyday lives in a few different ways‚ this includes art‚ architecture‚ construction‚ financial planning‚ and manufacturing. We can also calculate how long it will take one person to do a job alone when we know how long it takes a group to get it done as well. Farmers on crop farms work dawn to dusk through the growing season to produce the grains‚ fruits‚ and vegetables that feed the country. These equations help them
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A Honda Civic travels in a straight line along a road. It’s distance x from a stop sign is given as a function of time t by the equation‚ where and. Calculate the velocity of the car for each of the time given: (a) t = 2.00s; (b) t = 4.00s; (c) What will be the time when the acceleration is equal to zero? Solution: By getting the derivative of the distance as a function of time we can get the velocity as a function of time. Substitute the values of α and β
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EXPERIMENT 2: BATCH DISTILLATION AT CONSTANT REFLUX OBJECTIVE: To operate a batch distillation unit at constant reflux. To examine the change in top and bottom composition over time in a batch distillation. PROCEDURES: 1. Perform the general start-up procedures (Section 4). Refer appendix 1. 2. Record initial volume and refractive index of the liquid mixture in the reboiler. 3. Set the heater power to 1.5kW. 4. Set reflux timer to 10 second for set 1 and 30 second for set 2. ( Note: Set 1:
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Sonya Kovalevsky was born on January 15‚ 1850 in Moscow‚ Russia. She grew up in a very intellectual family. Her father was a military officer and a landholder; her mother was the granddaughter of a famous Russian astronomer and an accomplished musician. She grew up living a lavish life‚ and was first educated by her uncle‚ who read her fairy tales‚ taught her chess‚ and talked about mathematics. She even bumped into the subject of trigonometry while studying elementary physics. She achieved
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Student Activity A Generic Function Use the generic graph of f(x) with domain [–6‚ –3] and [–2‚ 6] to answer the questions below. 7 Y 6 5 4 3 2 1 X -7 -6 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 1. What is the range of f(x)? 2. What is the domain? 3. On what intervals is f(x) decreasing? 4. On what intervals will the following statements be true? a) As x increases‚ y increases. b) As x increases
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CS 159 – HW #01 5 Points Possible Due: September 6‚ 2010 at 11:00pm. Problem: Given the coordinates of two points‚ determine the shortest distance between the two points (green line) and the rectilinear distance (red‚ blue‚ and yellow lines all represent the same distance). All inputs are integer values. You are permitted to use mathematical functions for square root‚ power‚ and absolute value as necessary. Example Execution #1: Example Execution #2: Enter the first point: 0 0
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Functions 1 Functions A function f from a set A to a set B is an assignment of exactly one element of B to each element of A. We write f(a) = b if b is the unique element of B assigned by the function f to the element a of A. If f is a function from A to B‚ we write f: AB (note: Here‚ ““ has nothing to do with if… then) 2 Functions If f(A)=B‚ we say that A is the domain of f If f(a) = b‚ we say that b is the image of a. The range of f(A)=B is the set of all images of elements of A. We say that
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I saw her lying on the floor in a pool of blood‚ her eyes still opened but rolled back. My sight of her became blurred‚ I noticed after awhile. Wet‚ hot tears were starting to roll down my face. I could not catch my breath. My body quivered‚ I was beginning to fall. The last thing I remembered was a tattered book lying on the floor a few centimeters from her hand. It was a bright sunny Friday morning. The birds were singing‚ rays of sunshine shone into my room and the air was fresh with a tint
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Continuing professional development According to http://www.tda.gov.uk/teachers/continuingprofessionaldevelopme nt/what_is_cpd.aspx Continuing Professional Development or CPD for short involves activities that are reflective which is designed to improve a person’s characteristics‚ understanding‚ knowledge and skills also to support their needs and develop on their professional practice. “CPD is a combination of approaches‚ ideas and techniques that will help you manage your own learning
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