Contemporary Abstract Algebra
9th Edition
ISBN: 9781337249560
Author: Joseph Gallian
Publisher: Cengage Learning US
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Chapter 9, Problem 2E
Prove that
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1. Given that h(t) = -5t + 3 t². A tangent line H to the function h(t) passes through
the point (-7, B).
a. Determine the value of ẞ.
b. Derive an expression to represent the gradient of the tangent line H that is
passing through the point (-7. B).
c. Hence, derive the straight-line equation of the tangent line H
2. The function p(q) has factors of (q − 3) (2q + 5) (q) for the interval -3≤ q≤ 4.
a. Derive an expression for the function p(q).
b. Determine the stationary point(s) of the function p(q)
c. Classify the stationary point(s) from part b. above.
d. Identify the local maximum of the function p(q).
e. Identify the global minimum for the function p(q).
3. Given that m(q)
=
-3e-24-169 +9
(-39-7)(-In (30-755
a. State all the possible rules that should be used to differentiate the function
m(q). Next to the rule that has been stated, write the expression(s) of the
function m(q) for which that rule will be applied.
b. Determine the derivative of m(q)
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Chapter 9 Solutions
Contemporary Abstract Algebra
Ch. 9 - Let H={(1),(12)} . Is H normal in S3 ?Ch. 9 - Prove that An is normal in Sn .Ch. 9 - Let H={[ab0d]|a,b,dR,ad0} .IsH a normal subgroupof...Ch. 9 - Let G=GL(2,R) and let K be a subgroup of R*. Prove...Ch. 9 - Viewing 3and12 as subgroups of Z, prove that 3/12...Ch. 9 - Prove that if H has index 2 in G, then H is normal...Ch. 9 - Prove that a factor group of a cyclic group is...Ch. 9 - Prove that a factor group of an Abelian group is...Ch. 9 - Prob. 17ECh. 9 - Determine the order of (ZZ)/(2,2) . Is the group...
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- In simplest terms, Sketch the graph of the parabola. Then, determine its equation. opens downward, vertex is (- 4, 7), passes through point (0, - 39)arrow_forwardIn simplest way, For each quadratic relation, find the zeros and the maximum or minimum. a) y = x 2 + 16 x + 39 b) y = 5 x2 - 50 x - 120arrow_forwardIn simplest terms and step by step Write each quadratic relation in standard form, then fi nd the zeros. y = - 4( x + 6)2 + 36arrow_forward
- In simplest terms and step by step For each quadratic relation, find the zeros and the maximum or minimum. 1) y = - 2 x2 - 28 x + 64 2) y = 6 x2 + 36 x - 42arrow_forwardWrite each relation in standard form a)y = 5(x + 10)2 + 7 b)y = 9(x - 8)2 - 4arrow_forwardIn simplest form and step by step Write the quadratic relation in standard form, then fi nd the zeros. y = 3(x - 1)2 - 147arrow_forward
- Step by step instructions The path of a soccer ball can be modelled by the relation h = - 0.1 d 2 + 0.5 d + 0.6, where h is the ball’s height and d is the horizontal distance from the kicker. a) Find the zeros of the relation.arrow_forwardIn simplest terms and step by step how do you find the zeros of y = 6x2 + 24x - 192arrow_forwardStep by step Find the zeros of each quadratic relation. a) y = x2 - 16xarrow_forward
- In simplest step by step terms, how do you find the zeros of y = x2 - 16arrow_forwardIn simplest terms, Describe the shape and position of the parabola relative to the graph of y = x 2 y = - 80( x + 9) 2 + 10.8arrow_forwardas a Identify each equation Parabola, circle, ellipse perbola without completio the square. x²-6x-14 y = 33-y² 14y ofarrow_forward
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