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AlgebraQuestion and Answers: Page 93
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Question and Answers Forum |
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AlgebraQuestion and Answers: Page 93 |
| Simplify by using law of algebra (a) [p∨(p∧q)]→∼p (b)(p∧q)→q |
| Determine whether the following proposition is true or not [(p→∼q)∧(q∨r)∧p]→r |
| (m/n) = (k/p) and (m/n) = (k/p) = 1,5 Find (m/n) + (k/p) = ? |
| If acosh x+bsinh x=c show that. x=ln [((c±(√(c^2 +b^2 −a^2 )))/(a+b))] |
| (2x^3 y+3xy−5x^2 y^2 +12)÷(2x−4) Divide it using compound division |
| Express sinh^(−1) x−ln x in terms of natural logarithms.Hence find the limit as x→∞ |
| evaluate Σ_(k=1) ^n k e^(kx) |
| Find a∈R Such that x_1 ^(16) + x_2 ^(16) + x_3 ^(16) = 30 Where x_1 ,x_2 ,x_3 − are the roots of the equation: x^3 + ax + 1 = 0 |
| show that p⇒((p⇒q)⇒q) is tautology |
| Let the points ABC form a triangle on the cartesian plane, whose area is 20. Let the coordinates of said points be A(8, 6) B(2, 4) and C(x, y) If ∣AC∣=∣BC∣, find the coordinates of point C. |
| if a+b+c+d+e=8 and a^2 +b^2 +c^2 +d^2 +e^2 =16, what is the maximal value of a ? |
| Show that when x is small ln (cosh x)≈(x^2 /2)−(x^4 /(12))+... and that when x is large ln (cosh x)≈x−ln 2 |
| Given that sinh^(−1) x=sech^(−1) x show x=(√((((√5)−1)/2) )) |
| Solve simultaneous sinh x+cosh y=5 sinh^2 x+cosh^2 y=13 |
| Show that cosh x>sinh x |
| Show that the minimum value of sinh x+ncosh x is (√(n^2 −1)) and this occurs x=0.5ln (((n−1)/(n+1))) |
| What is the absolute error for the measurements: (a) 250m to the nearest 10m. (b) 143m to three sig. figures. (c) 41500cm to the nearest 100. |
| Let f(x)= (ax+1)^5 .(1+bx)^4 ; a,b ∈ N if times of x equal 62 so what are possible values of the sum a, b? |
| Let S= {1, 2, ..., 9, 0} A: How many multiples of eight of four digits can be formed from S B: The same question for different digits |
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| solve (x^2 −5)^2 −x=5 |
| ((a^(n+1) + b^(n+1) )/(a^n + b^n )) = (√(ab)) find n=? |
| How many different words of 4 letters can be formed from the word Flat earth |
| Let S= {1, 2, 3, 4, ..., 28, 29, 30} How many subgroups of 3 elements are in the S so that their sum is a multiple of 3 The answer is 1 360 subgroups |
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