Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 33, Problem 5A
To determine
Convert the given percentage in decimal form.
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Q4.
a)
A periodic waveform f(t) is shown in Figure 2
f(t)
Vo
Figure 2
T
with f(t+mT) = f(t) and m is an integer. Also, V₁ = 3, t = 1, T = 2.
(i)
(ii)
Derive the formulae for the complex Fourier coefficients c for f(t).
Sketch the amplitude spectrum of ƒ (t) (including the components up to
n = ±3).
PLease solve handwritten, dont use AI.
please solve the question handwritten without AI
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- (a) (b) Let A, B be disjoint subsets of a set X. Show that AC Bc. Use proof by contradiction to show that for any a, b = R, if a is rational and b is irrational then ba is irrational.arrow_forward(d) Consider the sequences (xn), (yn) defined recursively as follows: Xn+1 = xn2yn, i. ii. n, Yn+1=Yn2xn for n ≥ 1, x1 = 1, y₁ = 2. Calculate x2, y2 and x3, Y3. - Show using induction or otherwise that for any natural number - Xn+Yni = (1+2i)". Hence or otherwise, show that for any natural number n, iii. Zn = (V5)” cos(n arctan2), n = (V5)” sin(n arctan 2).arrow_forward2. (a) For each of the following functions, decide whether it is injective, and whether it is surjective. Justify your answers. i. f: Z → 22 Z 3z +1 ii. 9: C→ 22 Re(z) + Im(z)arrow_forward
- Not use ai pleasearrow_forward2. Given f(0) = (2 cos 0)² - 3sin²0. 1 a. Show that f(0) = ½ + ½ 7 + - cos cos 20. 2 2 b. Hence, find the exact value of √² 0 ƒ (0) do.arrow_forward2. Given f(0) = (2 cos 0)² - 3sin²0. 1 a. Show that f(0) = ½ + ½ 7 +-cos cos 20. 2 2 b. Hence, find the exact value of √ ƒ (0) d0.arrow_forward
- Not use ai pleasearrow_forward1 Solve for (x, y, z) in the set of linear, inhomogeneous equations: x-y+2x=5 2x + 3y - z = 4 2x-2y+4z6.arrow_forwardThe sides of a triangular prism base measures 6cm, 8cm and 10cm while it's height is 12cm. Determine the total surface area of the prism in square cmarrow_forward
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