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1. Big O analysis

Homework Statement 4. Give a c > 0 and an integer n0 ≥ 1 such that, for all n ≥ n0. b. 16n log (n²) ≤ cn² The answer (from the sheet) is c = 32 Homework Equations .. The Attempt at a Solution When I attempt to solve such an equation I start at n=1, then go to n=2. but that way I get the...
2. Probability Question

Homework Statement In a population of children 60% are vaccinated against the 'waterpokken'. The probablilities of contracting 'waterpokking' are 1/1000 if the child is vaccinated and 1/100 if not. a: Find the probability that a child selected at random will contract 'waterpokken'. Homework...
3. Linear Algebra Question

Homework Statement How to convert an implicit representation to a parametric Homework Equations Implicit: ax + by + cz = d. Parametric: (x,y,z) = (xp, yp, zp) + s(xv,yv,zv,) + t(xw,yw,wz) The Attempt at a Solution For parametric to implicit it would look like this: (x,y,z) = (0, 7, 6)T +...
4. Find the linear transformation matrix

Homework Statement Suppose that a linear transformation maps a point (2,3) to (0,1) and maps a point (9,7) to (1,0). Find the matrix for this linear transformation. 2. Solution (answersheet) Observe that the two point that are the result of the mapping are the two base vectors. If our...
5. Find k if (4,1,k) & (5,1,-3) are perpendicular?

Homework Statement Vectors find k if (4,1,k)τ & (5,1,-3)τ are perpendicular? From the answer sheet I know the answer is k = 7 Homework Equations I believe I need these two but I'm not certain: Dot-product: v*w = v1w1 + v2w2 + ... vdwd cos θ = v*w / ||v|| * ||w|| The Attempt at...

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7. Derivative 1/x³

how to compute the ANTI derivative of 1 / x^3 I think I need the formula: f(x) = 1/x^n than f'(x) = -n/x^n+1 but I'm not sure and don't know how to use it. I know the answer is: -0.5 * x^-2 but have no idea why. could someone explain this to me please?