Questions asked by cherry

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• Consider the curve where a and b are constants. The normal to this curve at the point where x=4 is 4x+y=22. Find the values of a and b?
  
• Show the curve with equation does not have any horizontal tangents. for horizontal tangents make y=0 for y' means y'=0?
  
• The tangent to #y=x^2e^x# at #x=1# cuts the #x# and #y#-axes at #A# and #B# respectively. Find the coordinates of #A# and #B#.?
  
• Find the coordinates of the turning point of the curve y=8x+(1/2x^2) and determine whether this point is a maximum or minimum point?
  
• Plz help Solve for x?
  
• Given that,#y=sqrt(4x-7)-2/3(x-4)#, find dy/dx and show that. Hence find the maximum point of the curve?
  
• Given that,#y=sqrt(4x-7)-2/3(x-4)# find #dy/dx# and show that#(d^2y)/dx^2=(-4)/((4x-7)sqrt(4x-7)#. Hence find the maximum point of the curve?
  
• The position of a particle moving along the x-axis is given by #x(t)=t^3-9t^2+24t# meters where t is in seconds, #t>=0# a) Draw a sign diagram for the particle's velocity and acceleration functions.?
  
• The roots of q quadratic #x^2-sqrt(20x)+2=0# are c and d. Without using calculator show that #1/c+1/d=sqrt(5)#?
  
• A radioactive substance decays according to the formula #W=20e^(-kt)# grams where t is the time in hours. Find the rate of radioactive decay at : i) t=100 hours ii) t=1000 hours?
  
• The temperature of a liquid after being placed in a refrigerator is given by #T=5+95e^(-0.123t)# degree Celsius where t is the time in minutes Show that #(dT)/dt=c(T-5)# for some constant c. Find the value of c?
  
• In the conversion of sugar solution to alcohol, the chemical reaction obeys the law #A=10(1-e^(-0.231t))#, #t>=0# where t is the number of hours after the reaction commences, s is the sugar concentration (%), and A is the alcohol produced in litres.?
  
• If the rate of change of x is 2 unit #s^-1#, Find the rate of change of y in #y=3/((2x-3)^3# when x=2?
  
• Find the perimeter and the area of the rectangle ABCD where #A(4,5),B(4,-2),C(-3,-2)# and #D(-3,5)# ?
  
• The figure shows the curve #y=x^2# and the point D(-1,0). P(p,0) is a variable point on the x-axis and PQ is parallel to the y-axis. Express the area,A, of the triangle DPQ in terms of p. ?
  
• A cylindrical jar, of radius 3 cm, contains water to a depth of 5 cm. The water is then poured at a steady rate into an inverted conical container with its axis vertical. ?
  
• Help plz how to find the antiderivative of #y=e^x#???
  
• Given that #int_1^3f(x)dx=3# and #int_3^6f(x)dx=5#, find: #int_1^3[f(x)+x]dx# ?
  
• Find the constant of integration #c# given that #f'(x)=2cosx-3sinx# and #f(pi/4)=1/sqrt2#? i already solved it and im getting #c=-4/sqrt2# but the answer is #c=-2sqrt2#
  
• Find the constant of integration #c# given that #f''(x)=2x# and the points #(1,0)# and #(0,5)# lie on the curve ?
  
• Three points have coordinates #A(1,2)#, #B(9,0)# and #C(6,t)#. Calculate the value(s) of t if : (a) #angleABC=90^@# (b) AC is perpendicular to BC?
  
• Three points have coordinates A(6,6), B(-3,3) and C(9,k). The foot of the perpendicular from A to BC is the midpoint of BC. Calculate the possible values of k?
  
• How to find x, #x^5=9#?
  
• The diagram shows a trapezium ABCD in which AD=7cm and #AB=(4+sqrt5)cm#. AX is perpendicular to DC with DX=2cm and XC= x cm. Given that the area of trapezium ABCD is #15(sqrt5+2)cm^2#, obtain an expression for x in the form of #a+bsqrt5#.?
  
• The points A(-2,2), B(4,4) and C(5,2) are the vertices of a triangle. The perpendicular bisector of AB and the line through A parallel to BC intersect at the point D. Find the area of the quadrilateral ABCD.?
  
• Find the function of #int(x^2+1)^3dx# ?
  
• Suppose #f'(x)=p sin(1/2x)# where #p# is a constant, #f(0)=1# and #f(2pi)=0#. Find p and hence find f(x).?
  
• The function #f(x)=4e^-x+2#, for #x inRR# and #g(x)=2e^x-4#, for #x inRR# using the substitution #t=e^x# , solve #g(x)=f(x)#?
  
• Without using a calculator evaluate #sin45^o/(cos30^o +sin60^o#?
  
• Express #4x^2+32x+55# in the form #(ax+b)^2+c#, where a, b and c are constants and a is positive?
  
• How to solve #cosx-2sinx=1# for #0<=x<=2pi#?
  
• Given that #4<=y<=6#, find the value of y for which #2cos((2y)/3)+sqrt3=0#?
  
• Find the function of the integral #y=2-1/sqrtx#?
  
• Find the area of the region enclosed by #y=x^2-2x# and #y=3#?
  
• Determine the area of the region enclosed by #y=sqrtx# and #y=x^2#?
  
• Find the area of the region bounded by #y=2e^x#, #y=e^(2x)# and #x=0#?
  
• Given that y<4, find the largest value of y such that #5tan(2y+1)=16#?
  
• The diagram shows four straight lines AD, BC, AC, and BD. lines AC BD intersect at O such that angle AOB is #pi/6radians#. AB is an arc of the circle, centre O and radius 10cm, and CD is an arc of the circle, centre O and radius 20cm?
  
• Find the area enclosed by the function y=f(x) and x-axis for #f(x)=-x(x-2)(x-4)#?
  
• Simplify #(x-2)/(x^2+6x+9)-(x+2)/(2x^2-18)#?
  
• How many numbers between 2000 and 5000 can be made from the digits 1, 2, 4, 5, 7 and 8 if each digit is used only once?
  
• Show that #(8x^2)^(8-r)(1/(2x))^r=2^(24-4r)(x^(16-3r))#?
  
• A curve has the equation #y=(x+2)sqrt(x-1)#. show that #dy/dx=(kx)/(sqrt(x-1))#, where k is a contant and state the value of k.?
  
• I really need help with this plz i) Find #d/dx(x^3lnx)# ii) Hence find #intx^2lnxdx# ?
  
• Help plz.!! Given that #y=e^(x^2)#, find #dy/dx# Hence find #int xe^(x^2)dx#?