Find two different sets of parametric equations for the given rectangular equation (there are many correct solutions)

zlopas [31]

Answer:

Vertex = (12,64)

The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.

X-intercepts: 4 and 20

The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.

Step-by-step explanation:

To find the vertex we can use the formula for the x-coordinate of the vertex:

x_v = -b/2a

Where a and b are coefficients of the quadratic equation (in this case, a = -1 and b = 24)

So we have that:

x_v = -24 / (-2) = 12

The vertex is 12 cups of coffee. Now we apply this value to find the y-coordinate of the vertex:

f(x) = -12^2 + 24*12 - 80 = 64

So the vertex is (12,64). The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.

To find the x-intercepts, we need to make f(x) = 0 and find the values of x:

-x2 + 24x - 80 = 0

Delta = 24^2 - 80*4 = 256

sqrt(Delta) = 16

x1 = (-24 + 16)/(-2) = 4

x2 = (-24 - 16)/(-2) = 20

The x-intercepts are 4 and 20. The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.

5 0

3 years ago

Spruce budworms are a major pest that defoliates balsam fir. They are preyed upon by birds. A model for the per capita predation

xenn [34]

Answer:

f'(N) = a(k² - N²)/(k² + N²)

The function increases in the interval

(-k < N < k)

And the function decreases everywhere else; the intervals given as

(-∞ < N < -k) and (k < N < ∞)

Step-by-step explanation:

f(N)=aN/(k²+N²)

The derivative of this function is obrained using the quotient rule.

Then to determine the intervals where the function is increasinumber and decreasing,

The function increases in intervals where f'(N) > 0

and the function decreases in intervals where f'(N) < 0.

This inequality is evaluated and the solution obtained.

The solution is presented in the attached image.

Hope this Helps!!!

8 0

3 years ago

Can you please help and show work

Setler79 [48]

What do you need answered?

3 0

4 years ago

Josiah downloads 44 songs including 16 songs by his favorite band. Express as a decimal the number of songs by his favorite band

marin [14]

Using a calculator, 16/44 = 0.363636363636363636... it goes on and on. It is repeating. If it was terminating, you would see the end.

There are a few ways to report the number, I'm not sure which one you need. A common way to show a repeating decimal is to put a line above it, I will upload a picture of what I mean.

Otherwise, you can round it.

4 0

3 years ago

Read 2 more answers

The sum of an integer and its square is 72. Find the greatest possible integer.

givi [52]

$x + x^2 = 72$

$x^2 + x - 72 = 0$

$(x -8)(x+9) = 0$

$x = -9, 8$

Greatest Possible Integer: 8

4 0

3 years ago