Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Question
Chapter 61, Problem 20A
To determine
The area of the base of a right circular cone.
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7. Show that for R sufficiently large, the polynomial P(z) in Example 3, Sec. 5, satisfies
the inequality
|P(z)| R.
Suggestion: Observe that there is a positive number R such that the modulus of
each quotient in inequality (9), Sec. 5, is less than |an|/n when |z| > R.
9. Establish the identity
1-
1+z+z² +
2n+1
...
+z" =
1- z
(z1)
and then use it to derive Lagrange's trigonometric identity:
1
1+ cos cos 20 +... + cos no =
+
2
sin[(2n+1)0/2]
2 sin(0/2)
(0 < 0 < 2л).
Suggestion: As for the first identity, write S = 1+z+z² +...+z" and consider
the difference S - zS. To derive the second identity, write z =
eie in the first one.
8. Prove that two nonzero complex numbers z₁ and Z2 have the same moduli if and only if
there are complex numbers c₁ and c₂ such that Z₁ = c₁C2 and Z2 = c1c2.
Suggestion: Note that
(i≤
exp (101+0) exp (01-02)
and [see Exercise 2(b)]
2
02
Ꮎ
-
= = exp(i01)
exp(101+0) exp (i 01 - 02 ) = exp(102).
i
2
2
Chapter 61 Solutions
Mathematics for Machine Technology
Ch. 61 - A rectangular strip of steel 2 ft 4 in. long, 1 ft...Ch. 61 - In order to make a conical duct, a circular sheet...Ch. 61 - A square bar 78 in. on a side is to be milled from...Ch. 61 - Construct a regular hexagon 3 cm on a side. By...Ch. 61 - Two angles of a triangle measure 7318' and 4947'....Ch. 61 - Prob. 6ACh. 61 - Prob. 7ACh. 61 - Prob. 8ACh. 61 - Prob. 9ACh. 61 - Prob. 10A
Ch. 61 - Solve these exercises. Where necessary, round the...Ch. 61 - Prob. 12ACh. 61 - A vessel is in the shape of a right circular cone....Ch. 61 - Prob. 14ACh. 61 - Prob. 15ACh. 61 - A piece in the shape of a pyramid with a regular...Ch. 61 - Prob. 17ACh. 61 - Solve these exercises. Where necessary, round the...Ch. 61 - Prob. 19ACh. 61 - Prob. 20ACh. 61 - Prob. 21ACh. 61 - Solve these exercises. Where necessary, round the...Ch. 61 - Prob. 23ACh. 61 - Prob. 24ACh. 61 - Prob. 25ACh. 61 - The container is in the shape of a frustum of a...Ch. 61 - A steel forging is in the shape of a frustum of a...Ch. 61 - Find the volume of the frustum of a right circular...Ch. 61 - Prob. 29ACh. 61 - The side view of a tapered steel shaft is shown....Ch. 61 - A zinc casting is in the shape of a frustum of a...Ch. 61 - A piece in the shape of a frustum of a pyramid...Ch. 61 - Find the volume of a hollow machined steel piece...Ch. 61 - Prob. 34A
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- 1) Compute the inverse of the following matrix. 0 1 1 A = 5 1 -1 2-3 -3arrow_forward2) Consider the matrix M = [1 2 3 4 5 0 2 3 4 5 00345 0 0 0 4 5 0 0 0 0 5 Determine whether the following statements are True or False. A) M is invertible. B) If R5 and Mx = x, then x = 0. C) The last row of M² is [0 0 0 0 25]. D) M can be transformed into the 5 × 5 identity matrix by a sequence of elementary row operations. E) det (M) 120 =arrow_forward3) Find an equation of the plane containing (0,0,0) and perpendicular to the line of intersection of the planes x + y + z = 3 and x y + z = 5. -arrow_forward
- 1) In the xy-plane, what type of conic section is given by the equation - √√√(x − 1)² + (y − 1)² + √√√(x + 1)² + (y + 1)² : - = 3?arrow_forward3) Let V be the vector space of all functions f: RR. Prove that each W below is a subspace of V. A) W={f|f(1) = 0} B) W = {f|f(1) = ƒ(3)} C) W={ff(x) = − f(x)}arrow_forwardTranslate the angument into symbole from Then determine whether the argument is valid or Invalid. You may use a truth table of, it applicable compare the argument’s symbolic form to a standard valid or invalid form. pot out of bed. The morning I did not get out of bed This moring Mat woke up. (1) Cidt the icon to view tables of standard vald and braild forms of arguments. Let prepresent."The morning Must woke up "and let a represent “This morning I got out of bed.” Seled the cared choice below and II in the answer ber with the symbolic form of the argument (Type the terms of your expression in the same order as they appear in the original expression) A. The argument is valid In symbolic form the argument is $\square $ B. The angunent is braid In symbolic form the argument is $\square $arrow_forward
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