Answer:
Negative
Step-by-step explanation:
Answer:
Step-by-step explanation:
Length = x
width = x - 7
height = x - 10
volume = 600 in^3
Volume = L * w * h
600 = x * (x - 7)*(x - 10)
600 = x * (x^2 - 17x + 70)
600 = x^3 - 17x^2 + 70x
x^3 - 17x^2 + 70x - 600 = 0
There is a genius somewhere that could solve this using algebra. The rest of us have 2 choices. We can graph it (see below) or we could use a program that solves it for us. I'll do both for you.
a = 1
b = - 17
c = 70
d = - 600
There is only 1 real solution: x = 15
L = 15
w = 8
h = 5
That has to be one of the ugliest graphs made. It does into the hundreds of thousands and it still looks like a straight line. Trust me. It's not.
Answer:
3/4
Step-by-step explanation:
You can do this two different ways. Both include picking two points where the line crosses a corner. I'm using (0,-1) and (4,2). Now here you can either use
Slope=
or
If you use the first one start at point (0,-1) and go to point (4,2) and count how many it goes up (rise) and then put that over how many it goes to the right (run).
If you use the second one then plug in the numbers.
y2=second y point
y1=first y point
x2=second x point
x1=first x point
Now just solve.

Answer:

Step-by-step explanation:
The logistic equation is the following one:

In which P(t) is the size of the population after t years, K is the carrying capacity of the population, r is the decimal growth rate of the population and P(0) is the initial population of the lake.
In this problem, we have that:
Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. This means that
.
The number of fish tripled in the first year. This means that
.
Using the equation for P(1), that is, P(t) when
, we find the value of r.









Applying ln to both sides.


This means that the expression for the size of the population after t years is:

(2, 8)
Because you cannot divide by 0, which 2 would do to the bottom.