You should have drawn1 - x-axis and y-axis in light pencil.2 - graphed a down-facing parabola with the top of the frown on the y-axis at y = 2. It should be crossing the x-axis at ±√2. This should be in dark pencil or another color.3 - In dark pencil or a completely new color, draw a rectangle with one of the horizontal sides sitting on top of the x-axis and the other horizontal side touching the parabola at each of the top corners of the rectangle. The rectangle will have half of its base in the positive x-axis and the other half on the negative x-axis. It should be split right down the middle by the y-axis. So each half of the base we will say is "x" units long. So the whole base is 2x units long (the x units to the right of the y-axis, and the x units to the left of the y-axis) I so wish I could draw you this picture... In the vertical direction, both vertical edges are the same length and we will call that y. The area that we want to maximize has a width 2x long, and a height of y tall. So A = 2xy This is the equation we want to maximize (take derivative and set it = 0), we call it the "primary equation", but we need it in one variable. This is where the "secondary equation" comes in. We need to find a way to change the area formula to all x's or all y's. Since it is constrained to having its height limited by the parabola, we could use the fact that y=2 - x2 to make the area formula in only x's. Substitute in place of the "y", "2 - x2" into the area formula. A = 2xy = 2x(2 - x2) then simplify A = 4x - 2x3 NOW you are ready to take the deriv and set it = 0 dA/dx = 4 - 6x2 0 = 4 - 6x2 6x2 = 4 x2 = 4/6 or 2/3 So x = ±√(2/3) Width remember was 2x. So the width is 2[√(2/3)]Height is y which is 2 - x2 = 2 - 2/3 =4/3
10+18=28
17+11=28
OR
2x=28 where x=14
4x where x=7
<em>V = 120 in^3</em>
<u><em>Here is why:</em></u>
The volume formula for a pyramid is:
The B stands for the area of the base, which in this case is a right triangle. We will find the area of the right triangle first, then plug it into the equation.
The area formula for a triangle is:
Plug in the numbers.
A = 45
Now we have found the area of B, we can plug it into the volume formula for the pyramid.
V = 120 in^3
Answer:
The price: 16.5
The total payment: 18.82
=> The amount of tax: 18.82-16.5 = 2.32
=> Tax rate = The amount of tax / The price = 2.32/16.5 = 0.14 = 14%
Answer:
Choice C is the answer.
Known information:
a = adult $
s = student $
We have 2 adults and 3 students.
Step-by-step explanation:
To find the total price of tickets given a # of students and adults, multiply a by the # of adults and multiply s by the # of students. Therefore, it would look like this:
2a + 3s = price
Therefore, choice C is the answer.
Hope this helps!
