전체 글102 CH.1& 2 VECTORS & 1D KINEMATICS (General Physics) [HW] 1.shows the components of F-> , Fx and Fy , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system's orientation, the key being the angle between the vector and the coordinate axes, often designated θ . θtheta is measured to the vector from the x axis, and counterclockwise is positive. Express Fx and Fy in terms of the lengt.. 2023. 1. 16. W1. Introduction to IOE (Discussion) Brief introduction to Technical Communication + Professionalism & Online Etiquette I. A few email dos and don’ts 1. Be wary of hitting ‘reply all’ and over ccing 2. Provide a clear and specific subject line 3. Indicate a clear purpose early in your email 4. If you have action items, make them clear (including ‘due dates’ for each) 5. Avoid humor, overfamiliarity 6. Keep length manag.. 2023. 1. 11. L1. Introduction The Tree of Life The cell theory and the theory of evolution by natural selection imply that all species are descended from a single common ancestor at the root of a family tree of all organisms - the tree of life. Phylogeny I. Reading a phylogenetic tree 1. The evolutionary relationships between organisms can be determined by comparing genetic information. ex) Humans and dogs have more similar .. 2023. 1. 11. General Chemistry Lecture Notes Ch.E Essentials Unit, Measurement & Problem Solving Ch.1 Atoms Ch.2 The Quantum-Mechanical Model of the Atom Ch.3 Periodic Properties of the Elements Ch.4 Molecules and Compounds Ch.5 Chemical Bonding I Ch.6 Valance Bond Theory and Molecular Orbital Theory Ch.7 Reaction Stoichiometry Ch.8 Aqueous solutions and reactions in aqueous solution Ch.9 Thermochemistry Ch.10 Gases Ch.11 Liquids, Solids, .. 2023. 1. 11. Calculus 1 Summary Notes [Chapter 1. FOUNDATION FOR CALCULUS: FUNCTIONS & LIMITS] 1.1 Functions and Change 1.2 Exponential Functions 1.3 New Functions from Old 1.4 Logarithmic Functions 1.5 Trigonometric Functions 1.6 Powers, Polynomials, and Rational Functions 1.7 Introduction to Limits and Continuity 1.8 Extending the Idea of a Limit [Chapter 2. KEY CONCEPT: THE DERIVATIVE] 2.1 How Do We Measure Speed? 2.2 The Derivat.. 2022. 12. 13. [Notes & HW Answers] 6.2 Constructing Antiderivatives Analytically [Prepwork 6.2] Q1. If 𝐹(𝑥) is an antiderivative of 𝑓(𝑥), what is the most general antiderivative? A: The most general antiderivative = F(x) + C Q2. Using the properties of antiderivatives in theorem 6.1 to find ∫(3cos(𝑥)+2sin(𝑥))𝑑𝑥 A: ∫(3cos(𝑥)+2sin(𝑥))𝑑𝑥= 3sin(x) - 2cos(x) + C Q3. Use the Fundamental Theorem to calculate the following integral exactly: A: ∫^(𝜋/3)_0 (2/cos^2𝜃) 𝑑𝜃= 2tan(𝜋/3) - 2t.. 2022. 12. 8. [Notes & HW Answers] 6.1 Antiderivatives Graphically and Numerically [Prepwork 6.1] Q1. Enter two different antiderivatives of 𝑓=2𝑥. A: Antiderivative 1 = x^2+1 Antiderivative 2 = x^2+2 Q2. Suppose that the graph of 𝑓′f′ is given below. At what 𝑥 value does 𝑓 cease being linear? 𝑥= 1 At what 𝑥 value does the maximum value of 𝑓 occur? 𝑥= 3 Q3. Suppose that 𝐹′(𝑡)=𝑡cos(𝑡) and 𝐹(0)=3. Use the data and method from example 5 in the text to estimate each of the followin.. 2022. 12. 8. [Notes & HW Answers] 5.4 Theorems about Definite Integral [Prepwork 5.4] Q1. For some function f, suppose that for some a∫^b_a f(x) dx=7 and ∫^c_a f(x) dx=9. Find each of the following. A: ∫^a_b f(x) dx= −7 ;∫^c_b f(x) dx= 2 Q2. Use the technique of example 2 in the text to evaluate the integral ∫^2_(−2) (|2x|+3) dx exactly. A: ∫^2_−2 (|2x|+3) dx = 20 Q3. Using a calculator to evaluate the appropriate integral, find the average value of P = f(t) = 2.03.. 2022. 12. 6. [Notes & HW Answers] 5.3 The Fundamental Theorem of Calculus [Prepwork 5.3] Q1. Around the beginning of the 1800’s, the population of the U.S. was growing at a rate of about 1.37t million people per decade, with t being measured in decades from 1810.If the population P(t) was 7.2 million people in 1810, estimate the population in 1820 (one decade later) by considering the work in example 2. A: P(1)= 8.375309 Q2. Given the CO2 addition rate shown in exampl.. 2022. 12. 6. [Notes & HW Answers] 5.2 The Definite Integral [Prepwork 5.2] Q1. Following example 1 in the text, suppose we considered n=4 to approximate the integral. What are each of the following? A: Δt= 0.25; f(t2)= 1/1.5 Q2. Find the exact value of the following integral. A: ∫^2_(-2) (4-x^2)^(1/2) dx = 2π Estimate the total area between f(x)=cos(x4) and the x-axis for (0≤x≤π)^(1/4)(Note: you will want to sketch the curve y=f(x). Shade the regions be.. 2022. 12. 6. [Notes & HW Answers] 5.1 How Do We Measure Distance Traveled? [Prepwork 5.1] Q1. Consider the velocity data for the car shown in table 5.1. Find lower and upper estimates for the distance it travels between 𝑡=4 and 𝑡=8. A: lower = 164 upper = 184 Write the difference between these as the following product: difference = (Δ𝑡)(Δ𝑣)= (2) (10) Q2. The velocity of a bicycle is given by v(t) = 4t feet per second, where t is the number of seconds after the bike sta.. 2022. 12. 6. [Notes & HW Answers] 4.6 Related Rates [Prepwork 4.6] Q1. In example 4, how fast is the fuel consumption changing if instead the car is moving 30 mph and decelerating at a rate of 3000 miles/hr^2? Answer: Decreasing at a rate of approximately (choose the closest answer) 600 mpg/hr. Q2. A spherical snowball is melting. Its radius decreases at a constant rate of 3 cm per minute from an initial value of 100 cm. How fast is the volume de.. 2022. 12. 6. 이전 1 2 3 4 5 6 7 ··· 9 다음
