Hi Sidney,
Let's begin by writing the Revenue Function, R(x), we have to maximize. It will be based upon the number of units (x) less than the initial 110 units with a corresponding increase in revenue dollars of 10x above the initial revenue of $46,200 (110 x 420):
...

Hi Ekene,
A nice passel of problems !!
We'll consider each one in turn, below:
Problem #1:
(pi/6)(180/pi) = 180/6 = 30 degrees
The angle (-pi/6) or (-30 degrees) lies in quadrant IV where x is positive and y is...

Hi Tan,
For "at least" and "at most" combination problems - it's easier to start with the total possible combinations and then subtract the cases we don't want:
1. Total Possible Combinations:
...

Hi Bianca,
Let's begin by assigning a letter to represent our unknown:
x = hours all three pipes open to fill tank
Next, let's write expressions in terms of our unknown (x) for the portion each pipe either adds to or takes away from a completed (whole)...

Hi Courtney,
Let's begin by writing the Compound Interest formula and identifying the variables and their values as given in the problem:
F = P[1 + (r/p)]pt
F (future value) = $34,299.49
...

Hi Ryan,
Let's begin by representing the number of production units for each model in terms of the number of production units for model "C":
x = # of model "C" units
4x = # of model "A" units (4 times # of model "C"...

Hi Nathan,
Let's begin by representing algebraically each person's time to do the job alone:
x = Sandy's time to do the job alone
x - 2 = Dave's time to do the job alone
Next, let's write an equation to express the sum of each person's...

Hi Ryan.
Let's begin by assigning a letter to represent our unknown:
x = miles from airport
Next, let's write an equation to express the total cost of the taxi ride from the airport and then solve it for our unknown (x):
Flat Fee...

Hi Haley,
Let's begin by writing the quadratic function in standard form
(ax2 + bx + c):
h(t) = -16t2 + 40t + 5 (a = -16; b = 40; c =5)
Next, let's find the time (t) needed for the ball to reach its maximum height using the axis...

Hi Jessi,
Since we are given the focus and the directrix of the parabola, we'll first determine the vertex form of its equation and then transform it into the standard form.
Let's begin by writing the vertex form of the equation for a parabola and identifying its properties:
...

Hi Haley,
Before we get to solving for the time asked in our problem, let's first determine the key information concerning the flight path of the toy rocket.
Let's begin by writing the Height Function, h(t), in standard quadratic form (ax2 + bx + c):
...

Hi Haley,
Let's begin by writing the Profit Function, P(x), in standard quadratic form (ax2 + bx + c):
P(x) = -2x2 + 2500x (a = -2; b = 2500; c = 0)
Now let's use the axis of symmetry formula (x = -b/2a) for a parabola
to calculate...

Hi Amber,
Let's begin by writing algebraic expressions to represent the two rates:
x = Pedro's rate (mph)
3x = Pablo's rate (mph)
Next, let's write an equation to express the relationship between the two times using the given distance...

Hi Dan,
Let's begin by writing algebraic expressions to represent the amount invested at each profit percentage:
x = amount invested at 6% profit
15,000 - x = remainder invested at 10% profit
Now let's write an equation using our...

Hi Badi,
You were on the right track trying to express a relationship in terms of sin2A (2sinAcosA):
(2/2)(1/8)[sin(29.5)][cos(29.5)] = [2sin(29.5)cos(29.5)]/16
[2sin(29.5)cos(29.5)]/16 = sin[2(29.5)]/16
sin[2(29.5)]/16...

Hi Ginger,
Let's begin by factoring completely both the numerator and the denominator of our function, g(x):
g(x) = (x3-2x2+x)/(x2-1)
g(x) = [x(x2-2x+1)]/[(x-1)(x+1)]
g(x) = [x(x-1)(x-1)]/[(x-1)(x+1)]
...

Hi Jenna,
Let's begin by showing a table giving us our answer:
Year Population Calculation
2000 1,000 initial population
2015 3,000 ...

Hi Amber,
Let's begin by writing algebraic expressions to represent the amount invested in each account:
x = invested amount in account earning 3.9% interest annually
50000 - x = remainder invested in other account earning 10.5% interest annually
Next,...

Hi Evelyn,
Let's begin by writing algebraic expressions to represent the amount invested at each interest rate:
x = amount invested at 8%
5000 - x = remainder invested at 5%
Next, let's write the Simple Interest formula and identify...

Hi Mario,
Let's begin by writing our given ratio to make 1 cup of the glob mixture:
1 cup glob = 3 parts glue / 2 parts corn starch
To make 85 cups of the glob mixture, we simply multiply the fraction (3/2) for 1 cup by (85/85) to scale up the components...