Search results

"Find the coordinates of 3 points on the parabola x^2 = 4ay such that the normals through these 3 points pass through the point (-12,15)" Is there a better way than forming 3 equations in 3 unknowns?

need help with 2 problems: 1) "in how many ways can 4 people be accommodated if there are 4 rooms available" [ans 256] and... 2) "in how many ways can 8 oarsmen be seated in an eight-oared boat if 3 can row only on the stroke and 3 can row only on the bow side" [ans 1152] For question 1...

"Solve the equation 6x^4 - 11x^3 - 26x^2 + 22x +24 = 0 given that the product of 2 of the roots is equal to the product of the other two." what would be a good way to approach this question? i tried using the relationship between coefficients but didnt seem to get the answer after several...

Prove that if P(x)=ax^4 + bx^3 +cx^2 + dx + e is even, then b=d=0. I know its obvious from just looking at it but how would you prove it?

How do you integrate 1/{[sqrt(x)][1+x]}??

how do you find the inverse of y=x^3 +3x. this is my working so far, but its wrong when you graph it... x=y^3 +3y x=y(y^2 +3) xy=y^2 +3 y^2 - xy +3 = 0 y^2 - xy = -3 y^2 - xy + (x/2)^2 = -3 + (x/2)^2 (y - x/2)^2 = [(x^2 - 12)/4] y - x/2 = +or- sqrt[(x^2 - 12)/4] y = x/2 +or- sqrt[(x^2 -...

"a tank contains 100L of brine whose concentration is 3g/L. 3L of brine whose concentration is 2g/L flow into the tank each minute and at the same time 3L of mixture flow out each minute. Derive the equation Q=200+100e^(-0.03t)" let Q be quantity of salt at time t dQ/dt= rate of inflow -...

"a body, initially at room temperature 20% is heated so that its temperature would rise by 5degrees/min if no cooling took place. Cooling does occur in accordance with Newton's law of cooling and the maximum temperature the body could attain is 120degrees. How long would it take to reach a...

"A batsman hits a cricket ball 'off his toes' towards a fieldsman who is 65m away. They ball reaches a maximum height of 4.9m and the horizontal component of its velocity is 28m/s. Find the constant speed with which the fieldsman must run forward starting at the instant the ball is hit, in order...