Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 1, Problem 6A
Express as thirty-seconds.
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c.
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e.
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g.
h.
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d((x, y), (z, w)) = |xz|+|yw|, show that whether d is a metric on
R² or not?.
Q3/Let R be a set of real number and d: R² x R² → R such that
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d((x, y), (z, w)) = max{\x - zl, ly - w} show that whether d is a metric
on R² or not?.
Q4/Let X be a nonempty set and d₁, d₂: XXR are metrics on X let
d3,d4, d5: XX → R such that
d3(x, y) = 4d2(x, y)
d4(x, y) = 3d₁(x, y) +2d2(x, y)
d5(x,y) = 2d₁ (x,y))/ 1+ 2d₂(x, y).
Show that whether d3, d4 and d5 are metric on X or not?
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Chapter 1 Solutions
Mathematics for Machine Technology
Ch. 1 - Write the fractional part that each length, A...Ch. 1 - A welded support base is cut into four pieces as...Ch. 1 - Prob. 3ACh. 1 - Reduce to halves. a. 48 b. 918 c. 100200 d. 121242...Ch. 1 - Prob. 5ACh. 1 - Express as thirty-seconds. a. 14 b. 34 c. 118 d....Ch. 1 - Express as equivalent fractions as indicated. a....Ch. 1 - Prob. 8ACh. 1 - Prob. 9ACh. 1 - Express the following mixed numbers as improper...
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- Complex Analysis 2 First exam Q1: Evaluate f the Figure. 23+3 z(z-i)² 2024-2025 dz, where C is the figure-eight contour shown in C₂arrow_forwardQ/ Find the Laurent series of (2-3) cos around z = 1 2-1arrow_forward31.5. Let be the circle |+1| = 2 traversed twice in the clockwise direction. Evaluate dz (22 + 2)²arrow_forward
- Using FDF, BDF, and CDF, find the first derivative; 1. The distance x of a runner from a fixed point is measured (in meters) at an interval of half a second. The data obtained is: t 0 x 0 0.5 3.65 1.0 1.5 2.0 6.80 9.90 12.15 Use CDF to approximate the runner's velocity at times t = 0.5s and t = 1.5s 2. Using FDF, BDF, and CDF, find the first derivative of f(x)=x Inx for an input of 2 assuming a step size of 1. Calculate using Analytical Solution and Absolute Relative Error: = True Value - Approximate Value| x100 True Value 3. Given the data below where f(x) sin (3x), estimate f(1.5) using Langrage Interpolation. x 1 1.3 1.6 1.9 2.2 f(x) 0.14 -0.69 -0.99 -0.55 0.31 4. The vertical distance covered by a rocket from t=8 to t=30 seconds is given by: 30 x = Loo (2000ln 140000 140000 - 2100 9.8t) dt Using the Trapezoidal Rule, n=2, find the distance covered. 5. Use Simpson's 1/3 and 3/8 Rule to approximate for sin x dx. Compare the results for n=4 and n=8arrow_forward1. A Blue Whale's resting heart rate has period that happens to be approximately equal to 2π. A typical ECG of a whale's heartbeat over one period may be approximated by the function, f(x) = 0.005x4 2 0.005x³-0.364x² + 1.27x on the interval [0, 27]. Find an nth-order Fourier approximation to the Blue Whale's heartbeat, where n ≥ 3 is different from that used in any other posts on this topic, to generate a periodic function that can be used to model its heartbeat, and graph your result. Be sure to include your chosen value of n in your Subject Heading.arrow_forward7. The demand for a product, in dollars, is p = D(x) = 1000 -0.5 -0.0002x² 1 Find the consumer surplus when the sales level is 200. [Hints: Let pm be the market price when xm units of product are sold. Then the consumer surplus can be calculated by foam (D(x) — pm) dx]arrow_forward
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