Let the original fraction be
Now let's increase both numerator and denominator by 2:
This produces a 1/12 increase:
The left hand side can be rearranged as
Invert both sides:
Solve the quadratic equation:
So, in the first case, the original fraction is
In the second case, we have
Answer:
The condensed log equation is:
Step-by-step explanation:
We use these following logarithm properties to solve this question:
In this question:
So
Becomes:
Now applying the addition and subtraction properties, we have:
The condensed log equation is:
You can cross multiply to find the answer. Start by setting up your equation:
45/30 = 60/x (30 represents half an hour)
Next, cross multiply, 45 times x, and 60 times 30:
45x = 1800 you must isolate the "x" value by using the opposite operation it is involved in. Here we have 45x (x is multiplied to 45) so we must divide 45, which will cancel itself out, leaving us with "x."
What you do on one side of the equation, you must do on the other, so divide 1800 by 45 as well, which will leave you with 40.
Working it out on paper, your equation should now look like this: x=40, which represents the amount of time it will take to fill a 60 gallon tube.
Answer: It will take 40 minutes to fill a 60 gallon tube.
Sears Tower is 114 stories tall
The equation is
P = 200 / (1 + 20000 e^-0.549t)
TO get the rate of epidemic growth, we differentiate the equation with respect to t
dP/dt = -200(1 + 2000 e^-0.549t)^-2 (20000)(-0.549)
Substitute t = 10 and you will get the epidemic growth rate after 10 years