Joint variation final
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Here are the answers to the activity questions on page 216 of the study guide in one whole sheet of paper: 5. Kinetic energy (KE) varies jointly as mass (m) and the square of velocity (v2). KE = kmv2 Given: Mass (m) = 8 g Velocity (v) = 5 cm/s KE = 100 ergs Find k: 100 ergs = k(8 g)(5 cm/s)2 100 ergs = k(8)(25) 100 ergs = 200k k = 100/200 = 1/2 KE = kmv2 Given: Mass (m) = 6 g
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The document defines direct variation and provides examples of how to determine if a relationship is direct variation. It explains that direct variation can be represented by an equation in the form of y=kx, where k is the constant of variation. It gives examples of determining the constant of variation from tables of x and y values and using the constant to find unknown values. It also provides examples of solving word problems using direct variation.
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Pc 1.10 notes
Mathematical modeling and variation describes direct, inverse, and joint variation. Direct variation means that as one variable increases, the other increases proportionally. Inverse variation means that as one variable increases, the other decreases proportionally. Joint variation occurs when two variables increase or decrease together but not necessarily at the same rate.
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Cyclic groups are common in everyday life and appear in patterns found in nature, geometry, and music. The document discusses several applications of cyclic groups, including:
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This document presents a solution to the Klein-Gordon equation for a modified screened Coulomb potential plus inversely quadratic Yukawa potential using the formula method. The formula method provides simple formulas to find bound state solutions to quantum mechanical wave equations. This method is applied to solve the radial part of the Klein-Gordon equation for the combined modified screened Coulomb plus inversely quadratic Yukawa potential. Bound state energy eigenvalues and wave functions are obtained through this approach.
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Bound State Solution of the Klein–Gordon Equation for the Modified Screened C...
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We present solution of the Klein–Gordon equation for the modified screened Coulomb potential (Yukawa) plus inversely quadratic Yukawa potential through formula method. The conventional formula method which constitutes a simple formula for finding bound state solution of any quantum mechanical wave equation, which is simplified to the form; 2122233()()''()'()()0(1)(1)kksAsBscsssskssks−++ψ+ψ+ψ=−−. The bound state energy eigenvalues and its corresponding wave function obtained with its efficiency in spectroscopy.
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Solution of ps02 cmth03apr13
This document contains the exam for the course Mathematics M.Sc. Semester II held on 29 April 2013. It has 4 questions. Question 1 contains 8 multiple choice questions. Question 2 contains 9 short answer questions related to differential geometry topics like curves on surfaces, fundamental forms, geodesics, etc. Question 3 has 2 longer proof-based questions, one about constructing a curve with a given curvature and the other characterizing curves with constant curvature and torsion. Question 4 asks to show that a local diffeomorphism is an isometry if and only if the first fundamental forms of the domain and range surfaces are the same.
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Joint variation final
- 2. Jointly Proportional. When we say z is jointly proportional to a set of variables, it means that z is directly proportional to each variable taken one at a time. If z varies jointly with respect to x and y, the equation will be of the form z = kxy (where k is a constant).
- 3. Examples: 1. If z varies jointly x and y when z=12, x=9 and y=3. Find the equation of variation. Sol’n: z=kxy 12=k(9)(3) 12 27 = 27𝑘 27 k= 4 9 ∴ The equation of variation is z= 𝟒 𝟗 xy.
- 4. 2. If p varies jointly as q and squared of r, and p = 225 when q = 4 and r = 3, find p when q = 6 and r = 8. Sol’n: p=kqr2 p=kqr2 225=k(4)(3)2 p= 25 4 (6)(8)2 225=k(4)(9) p= 25 4 (6)(64) 225 36 = 36𝑘 36 p= 25 4 (384) k= 25 4 p= 9600 4 p=2400
- 5. 3. The volume of a cone varies jointly as its height and the square of its radius. A cone with a radius of 6 inches and a height of 10 inches has a volume of 120π cubic inches. Find the volume of a cone having a radius of 15 inches and a height of 7 inches. Sol’n: v=khr2 v=khr2 120𝜋 = k 10 6 2 v= 𝜋 3 (7)(15)2 120𝜋 360 = 360𝑘 360 v= 1575𝜋 3 7in k= 𝜋 3 v=525𝜋 cubic inches 15 in
- 6. Activity(Board work) Column A Column B “a varies jointly as b and c” 1. Translate the statement above into mathematical equation. 2. If a=6, b=6 and c=2. What is k? 3. What is a when b=9 and c=2? “ area(a) varies jointly as length(l) and width(w)” 4. Translate the statement above into mathematical equation. 5. If area is 12cm2, length is 2 and width is 4, then what is k? 6. What is a when l=8cm and w=3cm? j. a= 𝑘 𝑏𝑐 u. 1 2 a. 36cm2 e. 9 d. k= 3 2 h. a=kbc n. a=klw
- 7. Answer: _ __ __ __ __ __ 1 2 3 4 5 6
- 8. Direction: Answer and illustrate what is being asked. Encircle the final answer.(NR×5) 1. Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and a velocity of 5 centimeters per second has a kinetic energy of 100 ergs. Find the kinetic energy for a mass of 6 grams and a velocity of 9 centimeters per second. 2. Wind resistance varies jointly as an object’s surface area and velocity. If an object traveling at 40 mile per hour with a surface area of 25 square feet experiences a wind resistance of 225 Newtons, how fast must a car with 40 square feet of surface area travel in order to experience a wind resistance of 270 Newtons?
- 9. Assignment: In your study guide page 216 answer activity numbers 5and 6. Write it in a one WHOLE sheet of paper.