Mathematics For Elementary Teachers With Activities
5th Edition
ISBN: 9780134423401
Author: Sybilla Beckmann
Publisher: PEARSON
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Chapter 8.6, Problem 14P
To determine
To find: The exact decimal representation of
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Refer to page 15 for a problem involving evaluating a double integral in polar coordinates.
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Chapter 8 Solutions
Mathematics For Elementary Teachers With Activities
Ch. 8.1 - Johnny says that 3 is a multiple of 6 because you...Ch. 8.1 - Manuela is looking for all the factors of 90. So...Ch. 8.1 - Show how to find all the factors of the following...Ch. 8.1 - a. Write a word problem such that solving your...Ch. 8.1 - a. Write a problem about a realistic situation...Ch. 8.1 - Solve problems (a) and (b), and determine whether...Ch. 8.1 - a. If A and how are answer, B are counting numbers...Ch. 8.1 - * If A, B, and C are counting numbers and both A...Ch. 8.2 - Describe a way that the children in Mrs. Verner’s...Ch. 8.2 - Explain why an odd counting number can always be...
Ch. 8.2 - For each of the two designs in Figure 8.5, explain...Ch. 8.2 - Without determining the number of dots in the...Ch. 8.2 - If you add an even number and an even number, what...Ch. 8.2 - If you multiply an odd number and an odd number,...Ch. 8.2 - * If you multiply an even number by 3 and then add...Ch. 8.2 - * If you multiply an odd number by 3 and then add...Ch. 8.2 - * Suppose that the difference between two counting...Ch. 8.2 - * Suppose that the difference between two counting...Ch. 8.2 - * If you add a number that has a remainder of 1...Ch. 8.2 - * If you multiply a number that has a remainder of...Ch. 8.3 - Use the divisibility test for 3 to determine...Ch. 8.3 - According to the divisibility test for 10, to...Ch. 8.3 - According to the divisibility test for 5, to...Ch. 8.3 - Beth knows the divisibility test for 3. Beth says...Ch. 8.3 - What are all the different ways to choose the ones...Ch. 8.3 - Sam used his calculator to calculate...Ch. 8.3 - Explain how to modify the divisibility test for 3...Ch. 8.3 - For each of the numbers in (a) through (d), verify...Ch. 8.3 - a. Give a clear and complete explanation for why...Ch. 8.3 - a. Find a divisibility test for 25; in other...Ch. 8.3 - a. What are all the different ways to choose the...Ch. 8.3 - a. Find a divisibility test for 8. In other words,...Ch. 8.3 - a. Is it true that a whole number is divisible by...Ch. 8.3 - * Investigate the questions in the following parts...Ch. 8.3 - a. If you add 2 consecutive counting numbers (such...Ch. 8.4 - For which counting numbers, N, greater than 1, is...Ch. 8.4 - Use trial division to determine whether 251 is...Ch. 8.4 - For each of the numbers in (a) through (d),...Ch. 8.4 - Given that 792=23.32.11, find all the factors of...Ch. 8.4 - Without calculating the number 1923+1, explain why...Ch. 8.4 - Following Euclid’s proof that there are infinitely...Ch. 8.5 - Why do we not talk about a greatest common...Ch. 8.5 - Show how to use the definition of GCF to determine...Ch. 8.5 - Show how to use the definition of GCF to determine...Ch. 8.5 - Show how to use the definition of LCM to determine...Ch. 8.5 - Show how to use the definition of LCM to determine...Ch. 8.5 - Show how to use the slide method to determine the...Ch. 8.5 - Show how to use the slide method to determine the...Ch. 8.5 - Show how to use the slide method to determine the...Ch. 8.5 - Find the GCF and LCM of 25.32.5 and 23.34.7...Ch. 8.5 - Find the GCF and LCM of 34.52.75.11 and 37.53.73...Ch. 8.5 - Describe in general how to find the GCF and LCM of...Ch. 8.5 - Show all the details in the following...Ch. 8.5 - Show all the details in the following...Ch. 8.5 - Write a word problem that requires calculating the...Ch. 8.5 - Write a word problem that requires calculating the...Ch. 8.5 - Suppose you are teaching students about least...Ch. 8.5 - Kwan and Clevere are playing drums together,...Ch. 8.5 - At the zoo, the birds must be fed 12 cups of...Ch. 8.5 - There are periodical cicadas with 13-year life...Ch. 8.5 - In a clothing factory, a worker can sew 18 Garment...Ch. 8.5 - Keiko has a rectangular piece of fabric that is 48...Ch. 8.5 - A large gear will be used to turn a smaller gear....Ch. 8.5 - A large gear is used to turn a smaller gear. The...Ch. 8.6 - Use the standard division algorithm to determine...Ch. 8.6 - Use the standard division algorithm to determine...Ch. 8.6 - Use the standard division algorithm to determine...Ch. 8.6 - Write the following decimals as fractions. Explain...Ch. 8.6 - What is the 100th digit to the right of the...Ch. 8.6 - What is another way to write 1.824 as a decimal?...Ch. 8.6 - Without actually determining the decimal...Ch. 8.6 - Give an example of an irrational number, and...Ch. 8.6 - In your own words, prove that the square root of 5...Ch. 8.6 - Carl’s calculator displays only 10 digits. Carl...Ch. 8.6 - Fran has a calculator that shows at most 10...Ch. 8.6 - Tyrone used a calculator to solve a problem. The...Ch. 8.6 - * Show how to find the exact decimal...Ch. 8.6 - Prob. 14PCh. 8.6 - Prob. 15PCh. 8.6 - Prob. 16PCh. 8.6 - Prob. 17PCh. 8.6 - a. Use a calculator to calculate the decimal...Ch. 8.6 - a. Use a calculator to calculate the decimal...Ch. 8.6 - a. Suppose that a fraction AB where A and B are...
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- Refer to page 9 for a problem requiring finding the tangent plane to a given surface at a point. Instructions: Use partial derivatives to calculate the equation of the tangent plane. Show all calculations step-by-step. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 8 for a problem involving solving a second-order linear homogeneous differential equation. Instructions: Solve using characteristic equations. Show all intermediate steps leading to the general solution. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 17 for a problem requiring solving a nonlinear algebraic equation using the bisection method. Instructions: Show iterative calculations for each step, ensuring convergence criteria are satisfied. Clearly outline all steps. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forward
- Problem: The probability density function of a random variable is given by the exponential distribution Find the probability that f(x) = {0.55e−0.55x 0 < x, O elsewhere} a. the time to observe a particle is more than 200 microseconds. b. the time to observe a particle is less than 10 microseconds.arrow_forwardThe OU process studied in the previous problem is a common model for interest rates. Another common model is the CIR model, which solves the SDE: dX₁ = (a = X₁) dt + σ √X+dWt, - under the condition Xoxo. We cannot solve this SDE explicitly. = (a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler scheme to simulate a trajectory of the CIR process. On a graph, represent both the trajectory of the OU process and the trajectory of the CIR process for the same Brownian path. (b) Repeat the simulation of the CIR process above M times (M large), for a large value of T, and use the result to estimate the long-term expectation and variance of the CIR process. How do they compare to the ones of the OU process? Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000. 1 (c) If you use larger values than above for the parameters, such as the ones in Problem 1, you may encounter errors when implementing the Euler scheme for CIR. Explain why.arrow_forwardRefer to page 1 for a problem involving proving the distributive property of matrix multiplication. Instructions: Provide a detailed proof using matrix definitions and element-wise operations. Show all calculations clearly. Link [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
- Refer to page 30 for a problem requiring solving a nonhomogeneous differential equation using the method of undetermined coefficients. Instructions: Solve step-by-step, including the complementary and particular solutions. Clearly justify each step. Link [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 5 for a problem requiring finding the critical points of a multivariable function. Instructions: Use partial derivatives and the second partial derivative test to classify the critical points. Provide detailed calculations. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 3 for a problem on evaluating limits involving indeterminate forms using L'Hôpital's rule. Instructions: Apply L'Hôpital's rule rigorously. Show all derivatives and justify the steps leading to the solution. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forward
- 3. Let {X} be an autoregressive process of order one, usually written as AR(1). (a) Write down an equation defining X₁ in terms of an autoregression coefficient a and a white noise process {} with variance σ². Explain what the phrase "{} is a white noise process with variance o?" means. (b) Derive expressions for the variance 70 and the autocorrelation function Pk, k 0,1,. of the {X} in terms of o2 and a. Use these expressions to suggest an estimate of a in terms of the sample autocor- relations {k}. (c) Suppose that only every second value of X is observed, resulting in a time series Y X2, t = 1, 2,.... Show that {Y} forms an AR(1) process. Find its autoregression coefficient, say d', and the variance of the underlying white noise process, in terms of a and o². (d) Given a time series data set X1, ..., X256 with sample mean = 9.23 and sample autocorrelations ₁ = -0.6, 2 = 0.36, 3 = -0.22, p = 0.13, 5 = -0.08, estimate the autoregression coefficients a and a' of {X} and {Y}.arrow_forward#8 (a) Find the equation of the tangent line to y = √x+3 at x=6 (b) Find the differential dy at y = √x +3 and evaluate it for x=6 and dx = 0.3arrow_forwardRefer to page 96 for a problem involving the heat equation. Solve the PDE using the method of separation of variables. Derive the solution step-by-step, including the boundary conditions. Instructions: Stick to solving the heat equation. Show all intermediate steps, including separation of variables, solving for eigenvalues, and constructing the solution. Irrelevant explanations are not allowed. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
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