Her time was 0.02 seconds short of being equal to the 2nd fastest time. In conclusion, no, she was slower.
Step-by-step explanation:
Below is an attachment containing the solution.
Answer:
From given, we have,
Paul says he is 16 inches shorter than 1 1/2 times Theresa's height.
Steve says he's 6 inches shorter than 1 1/3 times Theresa's height.
Let the height of Theresa be "x" inches.
So, we get,
For Paul, 1 1/2 x - 16 = T
⇒ 3/2 x - 16 = T ......(1)
For Steve, 1 1/3 x - 6 = T
⇒ 4/3 x - 6 = T .........(2)
equating equations (1) and (2), we get,
3/2 x - 16 = 4/3 x - 6
6 - 16 = 4/3 x - 3/2 x
-10 = (8 - 9)/6 x
-60 = -x
x = 60 inches.
Therefore, Theresa is 60 inches tall.
Answer:
common ratio: 1.155
rate of growth: 15.5 %
Step-by-step explanation:
The model for exponential growth of population P looks like: 
where
is the population at time "t",
is the initial (starting) population
is the common ratio,
and
is the rate of growth
Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:
![P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\](https://tex.z-dn.net/?f=P%28t%29%3DP_i%281%2Br%29%5Et%5C%5C13000%3D2300%2A%281%2Br%29%5E%7B12%7D%5C%5C%5Cfrac%7B13000%7D%7B2300%7D%20%3D%20%281%2Br%29%5E12%5C%5C%5Cfrac%7B130%7D%7B23%7D%20%3D%20%281%2Br%29%5E%7B12%7D%5C%5C1%2Br%3D%5Csqrt%5B12%5D%7B%5Cfrac%7B130%7D%7B23%7D%20%7D%20%3D1.155273%5C%5C)
This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155
We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:

So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %

Differentiate both sides with respect to <em>x</em>, assuming <em>y</em> = <em>y</em>(<em>x</em>).




Solve for d<em>y</em>/d<em>x</em> :



If <em>y</em> ≠ 0, we can write

At the point (1, 1), the derivative is
