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Answers by John R.

word problem (answer)

Hi Carolyn,   Since Martha can rake the yard in 4 hours, her rate is 1 yard in 4 hours or 1/4 yds/hr. Her brothers rate is 1/7 yds/hr. So the total amount raked is:    Area = 1/4*t + 1/7*t   For just 1 yard, the equation becomes   1 = 1/4*t...

You first need to find out the velocity of the spacecraft using conservation of momentum   m1v1 = m2v2   (the spacecraft will move off in the opposite direction)   then use the kinematic equation    x=vt   where v is the...

Hi Chris,   1. First draw a free-body diagram of the airplane at the top of the loop. 2. The only forces acting on the plane is gravity (mg) and the force on the wing. Neglect the thrust and friction in this case. Or if you include them they will cancel. 3. The acceleration...

Hi Kyle,   Distance is simply the speed times the time (d = vt), however, in this case the speed varies with time which makes it a little more difficult. In either case the answer is the value of the area under the curve. (note that the x axis is time and the y axis is speed). So plot...

The potential energy of the pinecone before it drops is mgh (given the ground is used as the zero potential energy reference). After if falls the energy is all kinetic energy or (1/2)mv^2 Equating these gives v^2 = 2gh. Note that you can now determine the energy loss due to air friction by the difference...

What is f(x)? (answer)

f(x) is a notation for a "function of x." Usually it is written as f(x)= "something", which is an expression with x as what we call the independent variable. Many times f(x) and y are the same thing. In solving a quadratic equation you are looking for the roots of the expression in the form of a^2...

The x coordinates are measured to the right of origin (or y axis) and y values are measured up from the origin (or the x axis).

First recall the formulas -(a - b) = (b - a) and x^2 + a^2 = (x + a)(x - a). If you rearrange the equation with these formulas in mind you get: 1/(x-3) + 2/(x-3) = 4/[(x + 3)(x - 3)] Now you can add the terms on the left hand side and multiply through by [(x + 3)(x - 3)]. That should give you...

Recall that the square root of a number is a number when squared equals the first number. mathematically if b = sqrt(a) then b^2 = a. So what you are looking for is the square root of 19. It turns out that this is an irrational number (a number continues in its decimal places forever) and usually...