Equations Reducible to Quadratic Equations Exercise 4.2 Solve the following equations: 1. x 4 − 6 x 2 + 8 = 0 Solution: x4 − 6 x2 + 8 = 0 Let y = x 2 and y 2 = x 4 The above equation becomes: y 2 − 6 y + 8 = 0 y2 − 6 y + 8 = 0 y2 − 4 y − 2 y + 8 = 0 y ( y − 4) − 2( y − 4) = 0 ( y − 2)( y − 4) = 0 y − 2 = 0 and y − 4 = 0 y=2 y=4 2 As‚ y = x x2 = 2 x2 = 4 x = ±2 x=± 2 solution set = { 2‚ − 2‚ 2‚ −2} 2. x −2 − 10 = 3 x−1 Solution: x −2 − 10 = 3 x −1 x −2 − 3 x −1 − 10 = 0 Let
Premium Quadratic equation
Name __________________ Balloons and Buoyancy Simulation Go to HYPERLINK "http://phet.colorado.edu/simulations/sims.php?sim=Balloons_and_Buoyancy" http://phet.colorado.edu/simulations/sims.php?sim=Balloons_and_Buoyancy and click on Run Now. Determine what factors make a hot air balloon or a helium balloon float Student Instructions: 1. Why does a hot air balloon float even though it is so heavy? Hot air balloons float because the buoyancy force of the hot air is more that the
Premium Hot air balloon Airship Temperature
Lab #1: Projectile Motion Purpose: To determine experimentally the initial and final velocities of an air powered projectile. Hypothesis: If the angle of the rocket is launched at 45 degrees than the distance and velocity will maximize. Materials: Rocket launching platform Rocket launcher Rocket body Air pump Safety goggles Rubber washer Nose cone 40‚ 45‚ 50‚ 55 and 60 angle wooden blocks Measuring wheel Procedure: 1. The rocket was assembled by the rocket launcher
Premium Rocket Hypothesis
A superconductor is a metallic alloy that conducts electricity without resistance‚ below a certain temperature. Once in motion‚ an electrical current will flow in a closed loop within a superconducting material. This is the closest to scientists of a perpetual motion machine. In 1911‚ Heike Kamerlingh Onnes first observed superconductivity. He used mercury and cooled to four degrees Kelvin. When the mercury reached that temperature‚ the resistance disappeared. That meant that the electrical current
Premium Superconductivity Magnetic field Electric current
Laboratory simulation: Refraction Name:______SummerAbdullah______________________________ Class:______12G________ Learning goals Familiarize with simulations of physical processes. Log raw data and plot graphs. Partially familiarize with the scientific method (phenomenon‚ prediction‚ experiment‚ and conclusion). Derive the dependence of the angle of refraction on the angle of incidence and the index of refraction. Simulation used “Refraction of light” (“bending-light_el.jar”): http://phet
Premium Refraction Snell's law Total internal reflection
1. A single disturbance that moves from point to point through a medium is called a ___. a. period b. periodic wave c. wavelength d. pulse Answer: D A wave is a continuous and repeating disturbance of a medium and a pulse is a single disturbance. 2. If the particles of the medium are vibrating to and fro in the same direction of energy transport‚ then the wave is a ____ wave. a. longitudinal b. sound c. standing d. transverse Answer: A In longitudinal waves‚ particles of the medium
Premium Wave Frequency Sound
Midterm Study Questions: The following are the types of questions you can expect on the Midterm. The questions on the midterm‚ however are NOT limited to these questions. The following questions do not include the material in the California Supplement‚ or matters we may have discussed in class. Anything in chapters 1-3 and 5 in the California Supplement and anything we have discussed in class is covered in the midterm. CIVIL LITIGATION CHAPTER 1 True/False 1. Most aspects of civil
Premium Jurisdiction Court Civil procedure
Flight is a phenomenon that has long been a part of the natural world. Birds fly not only by flapping their wings‚ but by gliding with their wings outstretched for long distances. Smoke‚ which is composed of tiny particles‚ can rise thousands of feet into the air. Both these types of flight are possible because of the principles of physical science. Likewise‚ man-made aircraft rely on these principles to overcome the force of gravity and achieve flight. Lighter-than-air craft‚ such as the hot
Premium Wing Force Aircraft
Miriam Yanez Physics 018-01 Literature Review 25 April 2012 Biophysics and protein dynamics have shaped our lives when it comes down to advancements in medicine. In living cells‚ proteins are the main components that keep the organism running at its best with every single protein and enzyme having their own function. The discovery of DNA‚ RNA‚ and other protein synthesis became the structures of life in a new perspective in the smallest ways leading to the continuing studies to uncover more
Premium DNA Gene Protein
1. A book is at rest on a tabletop. A free-body diagram for this situation looks like this: Return to Questions Return to Info on Free-body diagrams Return to on-line Force Description List 2. A girl is suspended motionless from the ceiling by two ropes. A free-body diagram for this situation looks like this: Return to Questions Return to Info on Free-body diagrams Return to on-line Force Description List 3. An egg is free-falling from a nest in a tree. Neglect air resistance. A
Premium Friction Force