If 270º <x< 360º , show that √(2+√(2+2cosx)) = 2 sin x/4. Thank You! :)
If 270º <x< 360º , show that √(2+√(2+2cosx)) = 2 sin x/4. Thank You! :)
Prove that cos6x + sin6x = (5+3cos4x)/8 Thank You! :)
Prove that tanx = cotx - 2 cot 2x. Hence show that 2tan20º + 4tan40º + 8tan80º = 9(cot 10º-tan10º) Thank You!:)
Given that tan A =2/3 where pi<A<3pi/2, find, without using a calculator, the value of tan (1/2 A). Ans: (-3-√13)/2 Thank You! :)
The mass, m milligrams , of a radioactive substance, present at time t years after first being observed, is given by m=300e-0.85t . Given that p milligrams is the amount of the substance that...
Factorize the expression 2 sinx cosx -cosx +4sinx -2 . Ans:(cosx+2)(2sinx-1) Thank you! :)
Solve for 0°<x<180° for the following equations. 8cosec 2x cot 2x =3 Ans: 35.3°, 144.7° Thank You! :)
The rates of return from firms A, B and C are x%, y% and 5% respectively. Firm A's rate differs from firm B's rate by half the difference in the rates between firm B and firm C. Find the possible...
The curve y=axn-23 passes through (3,4), (9,220) and (-1,k). Find the values of a, n and k. Ans: a=3, n=2 and k=-20 Thank You!:)
Fenitoine is administered intravenously through a bolus injection. The concentration, C µg/ml , of the drug in the blood, t hours after administration is given by C=4.86e-0047t . State the concentration...
B is any point on the curve y2=2x and A is a fixed point with coordinates (2,6). Find the equation of the curve trace by the mid-point of AB. Ans: y2-6y-x+10=0 Thank...
(i) Given that the line y=mx, where m is a positive integer, does not intersect the circle x2+ y2 -4mx +3=0, find the value of m. (ii) A line parallel to y=mx is a tangent parallel...
A curve has the equation y= (x-a)[√(x-b)] for x≥b, where a and b are constants. It intersects the x axis at the point A with x=b+1. Show that the gradient of the curve at A is 1. Thank...
A curve has the equation y=3e2x. Find the value of d2y/dx2 at the point where the gradient is 3. Ans:6 Thank You! :)
The number of crimes, C, in a particular country between 2000 and 2010 was given by the function C=11.9+ 0.1t + ln(t+1), where t is the number of years passed since 2000. Show that C...
Differentiate the following with respect to x. cos(x+π)/sin3x Ans: [sin(x+π)sin3x +3cos(x+π)cos3x]/ sin23x Thank you! :)
The function f is defines by f(x)=sinx + cosx , for 0≤x≤2π. Find (i) The range of values of x for which f(x) is increasing (ii) The range of values...
Two variables x and y are related by y= ln(2+e-x) for x >0. Given that x is increasing at a rate of 3 units per second, find, in terms of e, the rate of change of y when x=1. Ans:...
Differentiate with respect to x. ln[ (x+3)3 cos3x / sin x ] Thank You ! :) Ans : 3/(x+2) -3tan3x -cotx
Differentiate with respect to x. ln ((√x2 +1) -x) . Thank you! :) Ans: -1/(√x2+1)