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`?