Other Math Answers

A seller sells 2 types of sugar packets, white sugar and brown sugar. The seller can sell up to a

maximum of 1000 units of sugar packets with the condition that she must sell at least 200 units

of white sugar packets and 360 units of brown sugar packets. The seller gets RM0.40 for every

unit of white sugar packet sold and RM0.8 for every unit of brown sugar packet sold. Given

the seller sold x units of white sugar packet and y units of brown sugar packet and the profit

obtain is at least RM400.

(a)

Find the objective function and formulate the system of inequalities satisfying the given

constraints.

(b)

Sketch the graph and shade the feasible region, R satisfying the system of inequalities

in part (a).

(c)

Determine the number of white sugar packet and brown sugar packet that the seller

should sold to maximize the profit obtained. Hence, determine the maximum profit

obtained by the dealer.

A sinking fund is created for redemption of debentures of Rs. 2,00,000 at the

end of 10 years. Contributions to the fund are to be made at the end of each quarter.

Find the amount of each quarterly deposit if rate of interest is 9% p.a. compounded

quarterly.

Mr. X plans to send his son for higher studies abroad after 10 years. He expects

the cost of these studies to be Rs.1,00,000. How much should he save at the beginning

of each year to accumulate this amount at the end of 10 years, if the interest rate is 8%

compounded annually.

A uniform beam ab of length 6m and mass 20kg rest on support paid q placed in front of each . Each end of the beam masses of 10kg and 8kg are place at a and b respectively calculate the reactions at p and q (take g=9.8ms-1)

11.solve in |R:

(a) (2x+3)x/-x+1<or=0

(b) 2x-1/5x+3>0

12.solve in|R:

(a) x+5/x+7=4-x/5-x

(b) 24/x-3+24/x-3=6

13.solve in |R:

(a) 1/m-1 - 1/m+1=1/24

(b) k-5/k+1 + 2/k = 2/k(k+1)

14.solve in |R:

(a) 2m²+m=0

(b) t²-6t+5=0

15.solve in |R:

(a) 5-x-(1-3x)<2(x+1)-1

(b) 2t+3>or=2(t-5).

5.solve simultaneously for real values of x:

(a) x+5>or=2 (b) x+6>10

x-3<7 x-5<or=5

6.eliminate the parameter to obtain an equation connecting x and y:

(a) x=3sinα (b) x=t+1

y=4cosα y=1/t+1

7.eliminate the parameter to obtain an equation connecting x and y:

(a) x=3t (b) x=2+10t

y=t² y=-3+10^-t

8.solve for real value of x and discuss with respect to parameter m:

(a) (m-1)x-3<0 (b) 1-mx<or=0

9.solve for real value of x and discuss with respect to parameter m:

(a) (2+m)(2-m)x+m+2=0.

(b) m(m+2)x-2m=0.

10.solve |R:

(a) (2x-3)(5-3x)>or=0

(b) x(x-1)(x+1)<0

1. Find the values of my for which the system is not a Cramer's system.

(a)-2x+m²y=m

x-my=1-m

(b) mx+y=2

x+my=-2

2.solve graphically and shade the unwanted region:

(a) x+y-2>0

(b) x-y+1<or=0

3.solve for real values of x and y:

(a) 5x+3y=12 (b) x-2y=3

7x+2y=19 -3x+6y=-9

4.solve for real numbers values of x and y:

(a) 4y-3x=2 (b) x+2y=40

2y+1=2x 3x=60-y

5.solve simultaneously for real values of x:

(a) x+5>or=2 (b) x+6>10

x-3<7 x-5<or=5

Explain general motion simple pendulum

Two particles move in concentric circles, of center O and radii a, b (a < b), with uniform speeds u, v in the same sense. Let P, Q be the positions of the particles at a moment when their relative velocity is along the line joining them. 

(a) Obtain expressions for the ratios b : a and v : u in terms of α and β, where α = ∠OQP 

and β = ∠OPQ.

(b) Show further that if θ = ∠POQ, 

cos θ = (au + bv) / (bu+av)