Answers created by Costas C.

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• A soft tennis ball is dropped onto a hard floor from a height of 1.25 m and rebounds to a height of 1.05 m?
  
• A triangle has corners at `(5 ,6 )`, `(4 ,3 )`, and `(2 ,2 )`. What is the area of the triangle's circumscribed circle?
  
• An object with a mass of `2 kg`, temperature of `315 ^oC`, and a specific heat of `12 (KJ)/(kg*K)` is dropped into a container with `37 L` of water at `0^oC`. Does the water evaporate? If not, by how much does the water's temperature change?
  
• Question #a540a
  
• How do you solve `5x^2+98=0` using the quadratic formula?
  
• What is `f(x) = int -cos6x -3tanx dx` if `f(pi)=-1`?
  
• Does temperature increase during melting?
  
• What is the density of the solid in the following problem?
  
• If `f(x) = sqrt(1+x)` and `g(x) = (3x^2)/(x^2+1)`, what is `g[f(x)]`?
  
• Question #bc6c7
  
• What is the limit of `ln(x+1)/x` as x approaches `oo`?
  
• How do you solve `lnx+ln(x-2)=1`?
  
• How do you find the absolute maximum and absolute minimum values of f on the given interval: `f(t) =t sqrt(25-t^2)` on [-1, 5]?
  
• For what values of x is `f(x)= x-x^2e^-x` concave or convex?
  
• Question #2566c
  
• What is `f(x) = int x/(x-1) dx` if `f(2) = 0`?
  
• Question #7fb29
  
• Question #6bd6c
  
• An object is at rest at `(4 ,5 ,8 )` and constantly accelerates at a rate of `4/3 m/s^2` as it moves to point B. If point B is at `(7 ,9 ,2 )`, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
  
• How do you find the first and second derivative of `sin^2(lnx)`?
  
• How do you simplify `log_4 8`?
  
• Question #a4844
  
• The kinetic energy of an object with a mass of `1 kg` constantly changes from `243 J` to `658 J` over `9 s`. What is the impulse on the object at `3 s`?
  
• What is the derivative of `f(x) = (x^3-(lnx)^2)/(lnx^2)`?
  
• Question #c446e
  
• How do you find the limit of `sin((x-1)/(2+x^2))` as x approaches `oo`?
  
• Question #962b9
  
• How do you balance `BaCl_2 + Al_2S_3 -> BaS + AlCl_3`?
  
• The force applied against an object moving horizontally on a linear path is described by `F(x)=x^2-3x + 3`. By how much does the object's kinetic energy change as the object moves from `x in [ 0 , 1 ]`?
  
• How are distance and changing velocity related to limits?
  
• How do you graph `f(X)=ln(2x-6)`?
  
• What steps would you take to determine the density of a rubber eraser?
  
• How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `F(x)=x^2- 4x -5`?
  
• How do you find f'(x) using the definition of a derivative `f(x) =sqrt(x−3)`?
  
• What are the critical values, if any, of `f(x)= x^3/(x+4)+x^2/(x+1)-x/(x-2)`?
  
• How do you simplify the expression `3sqrt(2x^2y)`?
  
• How do you find the asymptotes for `y= (x+1)^2 / ((x-1)(x-3))`?
  
• An object with a mass of `90 g` is dropped into `750 mL` of water at `0^@C`. If the object cools by `30 ^@C` and the water warms by `18 ^@C`, what is the specific heat of the material that the object is made of?
  
• Rob left Mark's house and drove toward the dump at an average speed of 45 km/h James left later driving in the same direction at an average speed of 75 km/h. After driving for 3 hours James caught up. How long did Rob drive before James caught up?
  
• A balanced lever has two weights on it, the first with mass `8 kg` and the second with mass `24 kg`. If the first weight is `2 m` from the fulcrum, how far is the second weight from the fulcrum?
  
• What is the Cartesian form of `r-theta = -2sin^2theta-cot^3theta`?
  
• What is the maximum number of mols of copper (III) sulfide that can be formed when 8.0 mols of copper reacts with 9.0 mols of sulfur?
  
• What is `int xln(x)^2`?
  
• How do you convert `4=(x+8)^2+(y-5)^2` into polar form?
  
• How do you graph and solve `|2x-5| >= -1`?
  
• What is the equation of the line tangent to `f(x)=x^2 + sin^2x` at `x=pi`?
  
• How do you evaluate the integral of `int (dt)/(t-4)^2` from 1 to 5?
  
• How do you find the points where the graph of the function `f(x)=sin2x+sin^2x` has horizontal tangents?
  
• Using charles' law and understanding of what is happening at the particle level, explain why a marshmallow expands in size when you microwave it?
  
• How do you graph using the intercepts for `y=-6x-9`?
  
• In the reaction `2NaOH+H_2SO_4 -> 2H_2O+Na_2SO_4`, how many grams of sodium sulfate will be formed if you start with 200.0 grams of sodium hydroxide and you have an excess of sulfuric acid?
  
• What is the domain and range of `sqrt((5x+6)/2)`?
  
• How do you differentiate `f(x)=sqrt(ln(1/sqrt(xe^x))` using the chain rule.?
  
• A projectile is shot at an angle of `pi/12` and a velocity of `4 m/s`. How far away will the projectile land?
  
• How do you simplify `(x^-1y^-2z^3)^-2 (x^2y^-4z^6)`?
  
• How do you find the area bounded by the curves `y = -4sin(x)` and `y = sin(2x)` over the closed interval from 0 to pi?
  
• How do you convert `-xy=-x^2+4y^2` into a polar equation?
  
• How do you factor `y= x^2-x-20` ?
  
• Circle A has a center at `(3 ,2 )` and a radius of `6`. Circle B has a center at `(-2 ,1 )` and a radius of `3`. Do the circles overlap? If not, what is the smallest distance between them?
  
• What is the equation of the tangent line of `f(x)=14x^3-4x^2e^(3x)` at `x=-2`?
  
• Cups A and B are cone shaped and have heights of `32 cm` and `12 cm` and openings with radii of `18 cm` and `6 cm`, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
  
• An object with a mass of `3 kg` is traveling in a circular path of a radius of `7 m`. If the object's angular velocity changes from `3 Hz` to `29 Hz` in `3 s`, what torque was applied to the object?
  
• What is the average speed of an object that is still at `t=0` and accelerates at a rate of `a(t) =t+3` from `t in [2, 4]`?
  
• How do you insert parentheses to make `18+2*1+3^2 =38` true?
  
• How would you simplify `sqrt48 + sqrt3`?
  
• Given `f(x)=8x-1`, and `g(x)=x/2` how do you find fog(x)?
  
• A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/6`, the angle between sides B and C is `(7pi)/12`, and the length of B is 11, what is the area of the triangle?
  
• How do you differentiate `f(x)=8e^(x^2)/(e^x+1)` using the chain rule?
  
• How do you find the intercepts for `y=x^2-9x+20`?
  
• How do you write an exponential equation that passes through (0, -2) and (2, -50)?
  
• How do you simplify `5sqrt(-75) - 9sqrt(-300)`?
  
• Is `f(x)=(x+3)^3-4x^2-2x` increasing or decreasing at `x=0`?
  
• How do you differentiate `e^((ln2x)^2)` using the chain rule?
  
• How do you solve `x^(2/3) - 3x^(1/3) - 4 = 0`?
  
• How do you find the inverse of `1-ln(x-2)=f(x)`?
  
• How do you find general form of circle centered at (2,3) and tangent to x-axis?
  
• What is the derivative of `f(t) = (t^2-sint , 1/(t-1) )`?
  
• Question #dbd28
  
• How do you differentiate `f(x) = (sinx)/(sinx-cosx)` using the quotient rule?
  
• How do you solve `3 log x = 6 - 2x`?
  
• What is the surface area of the solid created by revolving `f(x) = xe^-x-xe^(x) , x in [1,3]` around the x axis?
  
• Using the limit definition, how do you differentiate `f(x)=(3x)/(7x-3)`?
  
• The diameter of a circle is 8 centimeters. A central angle of the circle intercepts an arc of 12 centimeters. What is the radian measure of the angle?
  
• Question #07304
  
• How do I find the limits of trigonometric functions?
  
• Question #f9cc1
  
• How would you determine the equation of the circle which passes through the points D(-5,-5), E(-5,15), F(15,15)?
  
• Can a function be continuous and non-differentiable on a given domain??
  
• If `f(x)= cos5 x` and `g(x) = e^(3+4x )`, how do you differentiate `f(g(x))` using the chain rule?
  
• What is the slope-intercept form of `15x+12y=9`?
  
• How do you solve `log_4x=2.5`?
  
• What is the formula for time from a changing velocity?
  
• How do you solve `5^(4x) = 2115`?
  
• How do you find the derivative of `1/(x-5)`?
  
• Is `f(x)=xe^x-3x` increasing or decreasing at `x=-3`?
  
• What is the average speed of an object that is still at `t=0` and accelerates at a rate of `a(t) =t/6` from `t in [0, 1]`?
  
• What happens to a saturated solution of sugar in water when the temperature of the solution is suddenly lowered by 10°C?
  
• What are the first and second derivatives of `f(x)=ln(-2e^(-6x^3)+x^2)`?
  
• What is the average speed of an object that is not moving at `t=0` and accelerates at a rate of `a(t) =6t-9` on `t in [3, 5]`?
  
• A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6` and the angle between sides B and C is `pi/12`. If side B has a length of 1, what is the area of the triangle?
  
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