Abstract Algebra Answers

Consider the function f : Z4 → Z12 defined by f(x) = 3x. Show that f(x) does
NOT preserve multiplication.

Prove that 5Z is both a prime and maximal ideal of Z

Show that sin b

find two straight lines tangent to y=x^3 and they pass through point (2,8)

a 180 pound person burns 284 calories playing basketball for 25 minutes.at this rate,how many calories would the person burn in 45 minutes to the nearest whole number

A wall of a house is in th shape of trapezoid. Find th number of square feet of area. If a one-gallon can o paint covers approximately 200ft sq, how many cans must be purchased?
20ft, 22ft, and 8ft.

Find each of the following for the circle.
Radius
Diameter
Circumference formula
Circumference of the circle

Through this chapter,you will be using and comparing fractions and decimals.Cicle all of the fractions below that are equal to 1/2.
6/12 15/30 4/7 5/10 1/3 2/3 9/12 7/14

I have to use mathcad to solve this question A flexible wire P QRS, of total length 12 metres, is bent into a three-edged planar shape, and its ends P, S are placed against a disc of radius 9 metres with centre O, as shown in the diagram below. (The arc P S is not part of the wire.) The end-segments P Q and RS of the wire lie along straight lines through O, while the arc QR forms part of a circle with centre O and subtends an angle x (in radians) at O. This question concerns the area A enclosed between the wire and the edge of the disc, which is shown shaded below. This area can be expressed by A = f(x), where f(x)=9x(4 − 3x)(16 + 3x) / 2(2+x)^2  0 ≤ x ≤4/3 (a) (i) Plot the graph of the function f(x). Your graph should cover the interval [0, 1.33] in the x-direction and [0, 20] in the y-direction. (ii) By using the ‘Trace’ facility (and also, if you wish, the ‘Zoom’ facility), estimate to two decimal places the coordinates of the point on this graph at which y = f(x) takes its maximum value. (iii) On the same graph, plot the line y = 8. Using the ‘Trace’ facility, estimate to two decimal places both solutions of the equation f(x) = 8. (These solutions give the values of x for which the shaded area is 8 m2 .)

in a triangle ABC the lengths of the sides, in cm, are AB=c BC=a AC=b the angle ACB=120 show that c^2=a^2+b^2+ab