Answers created by Barry H.

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• Help regarding this optimization problem to find dimensions?
  
• A large vase has a square base of side length 6 cm, and flat sides sloping outwards at an angle of 120◦ with the base. How to find the rate when height is rising?
  
• Find the rectangle with the maximum area, which can be turned in the corner. ?
  
• What is the derivative of tan(sin x)?
  
• An open-top rectangular box is constructed from a 10-in.- by-16-in. piece of cardboard by cutting squares of equal side length from the corners and folding up the sides. Find analytically the dimensions of the box of largest volume and the maximum volume?
  
• Find the extreme values of the function and where they occur? 1/x^2+1 i solve it as 0.5 is minimum at x= -1 but it is false!
  
• A gutter is to be made using a 5m long rectangular piece of metal that has to be bent to form the open topper gutter. the cross section of the gutter is an isosceles trapezoid with sides making angles 120 degrees with the base?
  
• Calculate Y' and Y'' at the point (2,6)?
  
• Pressure (p) and volume (v) given in eqn #pv^1.4=k# where k is constant. At certain instant pressure is #(25gm)/(cm^3# and volume is #32cm^3#. If volume is increasing at rate of #(5cm^3)/s#, how do you find the rate at which pressure is changing?
  
• How do you find the volume bounded by #y^2=x^3# and #y=x^2# revolved about the y-axis?
  
• A particle is moving along the curve whose equation is #8/5=(xy^3)/(1+y^2)#. Assume that the x-coordinate is increasing at the rate of 6 units/sec when the particle is at the point (1,2). At what rate is y-coordinate of the point changing at that instant?
  
• The graph of the equation 2x=y^2 from A (0,0) to B (2,2) is revolved about the x-axis. The surface area of the resulting solid( in square units and to three decimal places) is ?
  
• For what point on the curve of y = 9 x2(the 2 is a squared) - 2x is the slope of a tangent line equal to 34 ?
  
• Find the surface area of the solid of revolution obtained by rotating the curve y=4x^3 from x=1 to x=5 about the x-axis?
  
• At what point on the given curve is the tangent line parallel to the line 5x - y = 5? y = 4 + 2ex − 5x
  
• A box, open at the top is to be made from cardboard. The base of the box is a square of side x and its height is y. If the volume of the box is 32u^2, find the dimensions of the box if the area is to be least. Please help?
  
• Help pls...Question 22)b) ??
  
• What is the surface area produced by rotating #f(x)=x/pi^2, x in [-3,3]# around the x-axis?
  
• Water flows on to a flat surface at a rate of 5cm3/s forming a circular puddle 10mm deep. How fast is the radius growing when the radius is? 1cm? 10cm? 100cm?
  
• The volume of a cube is increasing at a rate of 10 cm^3/min. How fast is the surface area increasing when the length of an edge 90 cm?
  
• How to find the general solution for #x(x^2 + y^2)dy/dx = y(y^2-x^2)# using homogeneous ?
  
• Please help me with this calc question?
  
• A rancher wishes to create 4000 square meter rectangle enclosure. Two fences parallel to two of the sides will be used to create three equal areas. Find the dimensions of the fence that will require the least amount of fencing? Please help
  
• How do you write an equation of the line tangent to the graph of the circle whose equation is #x^2+y^2=16# at the point (0,4)?
  
• Find the derivative of sqrt(sin^2(x)) ? I can’t figure this out (using chain rule, product rule, etc)
  
• How do you express the concept of the rate of decay of a radioactive substance as a differential equation?
  
• How to find the function of this model?
  
• How do I find an equation for the tangent line to the graph of #f(x)=(sqrt(x))/(4x-8)# at the point #(3, f(3)#)?
  
• What is the equation of the line tangent to # f(x)=e^(x^2+x) # at # x=-1 #?
  
• What is the surface area of the solid created by revolving #f(x)=sqrt(x)# for #x in [1,2]# around the x-axis?
  
• How to find instantaneous rate of change for #y=4x^3+2x-3# at x=2?
  
• What is the arclength of #f(t) = (t^3-1,t^2-1)# on #t in [2,3]#?
  
• How do you find #(dy)/(dx)# given #cos(xy^2)=y#?
  
• State De Moivre's theorem and prove it for all integer values?
  
• The sum of two positive number is 16. Use optimization to find the smallest possible value of the sum of their squares?
  
• helpme please: A spring of 3 fts requires a force of 10 pounds to stretch it to a length of 3.5 fts a) Find the work required to stretch the spring from its natural length to a length of 5 fts?
  
• How to find h in terms of x?
  
• A closed rectangular storage bin is to be made so that it has a square base. The volume of the bin must be 8m^3. The material to make the sides costs twice as much as that for the top and the bottom. Find the dimensions of the box that will (- cont.)?
  
• If an isosceles triangle has perimeter P, how long must the legs of the triangle be to maximize its area? (Your answer may depend on P).
  
• Can you help me to solve this? thanks for help
  
• How do you find the derivative of #f(x)=7^(2x)#?
  
• If the slope of the tangent to #4x^2+cx+2e^y=2# at x=0 is 4, then what is the value of c?
  
• What is the equation of the tangent line of #f(x)=1/absx# at #x=4#?
  
• A square plate of metal is expanding under the action of heat, and its side is increasing at the uniform rate of 0.1 cm per hour. What is the rate of increase of its area at the moment when the side is 16cm long?
  
• How to solve this very difficult volume problem involving integration?
  
• How do you find dy/dx of #y^2 = ln x# and evaluate it at the point (e, 1)?
  
• What is the volume of the solid produced by revolving #f(x)=1/x, x in [1,4] #around the x-axis?
  
• How do solve applications of differentiation?
  
• What is the distance between the following polar coordinates?: # (3,(12pi)/8), (9,(5pi)/8) #
  
• A particle is released from rest at point O at time t= 0 and it falls vertically that its acceleration at is given g-kv,where k is positive constant, g is gravity,v is instantaneous velocity at time t.Express v in terms of g,k and t?
  
• Gasoline is pumped from the tank of a tanker truck at a rate of 20L/s. If the tank is a cylinder 2.5m in diameter and 15m long, at what rate is the level of gasoline falling when the gasoline in the tank is 0.5m deep?
  
• Find the volume using disk/washer method of region bound by curves y=e^-x/2, y=ln(9)? The solid is generated when R is revolves around x-axis. The boundaries are ln(9) and 0. I just need help setting up the integral. Thank you.
  
• Find the volume of the cone of maximum value that can be inscribed in a sphere of radius R?
  
• How do you use implicit differentiation to find the slope of the line tangent to #y+ lnxy=4# at (.25, 4)?
  
• What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 125 #cm^3#?
  
• A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is minimum?
  
• How do you implicitly differentiate #15=x^2/y+y^2#?
  
• Y=logx? Give it's derivation.
  
• How do you find the area of the surface generated by rotating the curve about the x-axis #y=1/3x^3, 0<=x<=1#?
  
• A viscous liquid is poured onto a flat surface it forms a circular patch whose area grows at a steady rate of 5cm^2s^-1 find in term of pi (a) the radius of patch 20 sec after pouring has commenced (b) the rate of increase of the radius at this instant?
  
• What is the equation of the line tangent to the curve x^2 + y^3 = 9 at the point (-1, 2)? I am thrown off because it's no longer a circle. Does it matter?
  
• A conical tank has a circular base with radius 5 ft and height 12 ft. If water is flowing out of the tank at a rate of 3 ft^3/min, how fast is the height of the water changing when the height is 7 ft?
  
• Find the dimensions of the rectangle of maximum area that can be inscribed in a right triangle with base 6 units and height 4 units?
  
• A stone is dropped into a still pond sends out a circular ripple who’s radius increases at a constant rate of 2 m/sec. How rapidly is the area enclosed by the ripple increasing at the end of 20 sec?
  
• A point moves along the curve y= x^2+1 in such way that when x=4 the x-coordinate is increasing at the rate of 5ft/sec at what rate is the y coordinate changing at that time?
  
• How do you find an equation of the tangent line to the curve #xe^y+ye^x = 1# at the point (0,1)?
  
• Population y grows according to the equation dy/dx=ky, where k is constant and t is measured in years. If the population doubles every 10 years, then what is the value of k?
  
• What is the general formula for exponential growth of a population?
  
• A bacteria population grows such that growth rate is proportional to population. At t=0 there are 100000 bacteria. At 48 hours there are 300000. How many bacteria will there be at t=72 hours?
  
• How do you find the slope of #2x+3y-3=0#?
  
• How do you solve the following system: #x + y = 16, 2x + 3y = 12#?
  
• A piece of wire #26m# long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square in order to minimize the total area?
  
• Solve #x.dy/dx-y=2x^2y#?
  
• Find y' ?? please help
  
• Question #4d69c
  
• Question #494b1
  
• How do you differentiate #f(t)=sin^2(e^(sin^2t))# using the chain rule?
  
• How do you differentiate #y = 3x cos^2 (x)#?
  
• Question #1f1cc
  
• Question #994ee
  
• How do you find the derivative using the difference quotient f ( x ) = 1 / x + 2 ?
  
• Question #7d637