Find the value of 25½(1) 25-3/2(2) Answer ANSWER Explanation Explanation Given that y = 2×5 + 7 + 1/x³, x≠0 find, in their simplest form, dy/dx(3) \(\int\)y dx4) Answer ANSWER Explanation Explanation The points...
Find the value of 16-¼(2) Simplify x(2x-¼)4(2) Answer ANSWER Explanation Explanation Find \(\int \) (12×5 ā 3×2 + 4×3 )dx giving each term in its simplest form. (5) Answer ANSWER Explanation Explanation Simplify 5...
Express 7cosx ā 24sin x in the form R cos (x + α) where R>0 and 0<α<π/2 . Give the value of α to 3 decimal places. (3) Hence write down the minimum value...
Find the set of values of x for which 3/x + 3 > x – 4/x (7) Answer ANSWER Explanation Explanation d²y/dx²= ex(2ydy/dx + y² + 1) Show that d³y/dx³= ex[2yd²y/dx² + 2(dy/dx)² +...
A car of mass 1000 kg moves with constant speed V m sā1 up a straight road inclined at an angle θ to the horizontal, where sin θ = 1/30. The engine of the...
A cyclist starts from rest and moves along a straight horizontal road. The combined mass of the cyclist and his cycle is 120 kg. The resistance to motion is modelled as a constant force...
A disease occurs in 3% of a population. State any assumptions that are required to model the number of people with the disease in a random sample of size n as a binomial distribution.(2)...
Express 2/(2r + 1)(2r + 3) in partial fractions.(2) Using your answer to (a), find, in terms of n, [IMAGE] Give your answer as a single fraction in its simplest form. (3) ANSWER z...
9x²/(x – 1)²(2x + 1) = A/(x – 1) + B/(x – 1)² + C/(2x + 1) Find the values of the constants A, B and C. (4) ANSWER f(x) = 1/√(9 + 4x²)...
Use integration to find the exact value of \(\int_{\frac{\pi}{2}}{0} \)xsin2x dx (6) ANSWER The current, I amps, in an electric circuit at time t seconds is given by I = 16 ā 16(0.5)t, t≥0...
