Abstract Algebra Answers

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

Jess, Kathy, and Linda work on the math club's newspaper. One is the editor, one is the reporter, and one is the writer. Linda does not participate in sports. Jess and the editor play tennis together. Linda and the reporter are cousins. What is each persons job?

The probability that Peter is late for school is 0,15.
Calculate the probability that Peter is not late for school.

A piece of string is cut into two pieces at a randomly selected point. What is the probablility that the longer piece is at least x times as long as the shorter piece

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
.)

Define a closed set.

ABCDEFGH is a regular octagon. A and E are opposite vertices of the octagon. A frog starts jumping from vertex to vertex, beginning from A.& From any vertex of the octagon except E, it may jump to either of the two adjacent vertices.& When it reaches E, the frog stops and stays there.& Let a(n) be the number of distinct paths of exactly n jumps ending in E. Then what is the value of a(2n – 1)?

Given the following point; A(3,1) B(-1,1) C(7,3) D(1,2) E(3,-4) F(-1,-5).
(1)plot all these points on the same graph sheet.

(2)find the length of the following line using the three main methods. AB,AC,AD,AE,AF,BC,BD,BE,BF,CD,CE,CF,DE,DF,EF
(3)find the gradient of each of the line above

(4)measure the angle which each of the lines above makes with the positive direction of x-axis .y2-y1/x2-x1.

(5)find the equation of each of the lines above

(6)find the tangent of each of the angles measured above

(7)compare the gradient of each line calculated above with the tangent of the angles calculated above