Hi Tiffany,   The slope of the new line is the same as the sloe of the given line. Which is -1/9.   Now the new line is, so far:   y = -1/9 x + b   and it must satisfy the point (-5,-7), so   -7 = (-1/9)*(-5) + b   Just...

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 Jay,   The question can be rephrased to what maked the denominator zero. It would be where sin x = 0. What angle would this be in the interval given?

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...

The area of the mirror is:   Area = width x height      or   A = wh   So the height is   h = A/w   h = 225/13.75   h = 16.36 inches   Doesn't look like it will fit.

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...

Using a graphing function would be the easiest. I don't think this one can be solved explicitly. At least not very easily.

You're on the right track,   Use long division, divide the equation for the volume by x-3, then divide this answer by x+1.

Hi Gabriele,   This explanation may be a little more sophisticated than you need so I welcome others to contribute.   This requires using the polar form of complex numbers as follows:   A complex number may be represented in the polar form by using Euler's...

Let x equal the number of hours at the pharmacy and y equal the number of hours babysitting. Then 15x +10y = 90 Now the last part of your question did not show up above but I am assuming that the total hours where specified, let call that T. So the second equation is: x +...

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...

Just in case you are not taking a calculus level class, the position can be deterimined by the area under the curve of the velocity graph up to the time in question. If the graph drops below the x axis, count this as negative area.

We know from the first part that the distance is equal to the speed multiplied by the time d = st, or d = (45 mi/hr)t we also know from the last part this same distance is d = (60 mi/hr)(43 mi - 10 mi - t), or (60 mi/hr)(33 hr - t). Now elliminate the d (45...

If A is the original amout deposited, the account balanece, B, after 1 period is B = A(1 + i), where i is the interest for the period. After two periods, B = A(1 + i)(1 + i) or A(1 + i)^2. And carrying this out to n periods you will obtain B = A(1 + i)^n. This is the formula...