Algebra Answers

Solve the linear system
x+2y=4, 3x-y=2 by substitution.
If 4x+y=c, ax+by=3 is a system having the same solution set as previously equation find a,b,c.

Prove that 2^n>1+ n*√(2^(n-1)) for all n>2 using the inequalities.

Apply Cramer's rule to solve the following system of equations:
2x+ y+z=4
x-y+2z=2
3x-2y-z=0

As a contrast between the old and the modern and between the large and the small, consider the following: In old rural England 1 hide (110 acres) was the area of land needed to sustain one family with a single plough for one year. (An area of 1 acre is equal to 4047 m2.) Also, 1 wapentake was the area of land needed by 100 such families. In quantum physics, the cross-sectional area of a nucleus (defined in terms of the chance of a particle hitting and being absorbed by it) is measured in units of barns, where 1 barn is 1 × 10-28 m2 (exactly). (In nuclear physics jargon, if a nucleus is “large,” then shooting a particle at it is like shooting a bullet at a barn door, which can hardly be missed.) What is the ratio of 22 wapentakes to 16 barns?

The following equation; Q = r - kP, depicts -------

The population (in millions) of a certain country can be approximated by the function: p(x) = 50 ∙ 1.05^x Where x is the number of years after 2000. Which of the following calculations will tell in what year the population can be expected to reach 200 million?

f(x)=1-x^ g(x)=1+x find the function of f o g

3 major projects P1, P2, P3 are being funded by 3 voluntary agencies V1,V2,V3. V1,V2,V3 are willing to pay Rs. 8000, Rs. 4000, Rs. 2000, respectively per person on the project P1; Rs. 4000, 3000, 4000 respectively per person on P2; and Rs. 3000, 5000, 8000 respectively on the project P3. Further, the amount that V1,V2,V3 have kept aside for paying people on these projects is Rs. 217000, 142000 and 132000 respectively. How many people should each project employ so that the total money available is utilised?

Use the principle of induction to prove the statement:
2^n>1+n*√{2^(n-1)} for all n > 2

Write the converse of the statement:
If p and q are the only roots of a polynomial f over C , then deg f=2.