Answer:
i'm pretty sure it's c
Step-by-step explanation:
<h3>
Answer: Choice C) 40 </h3>
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Work Shown:
Plug in x = 0
![g(x) = 3^{2x}\\\\g(0) = 3^{2*0}\\\\g(0) = 3^{0}\\\\g(0) = 1\\\\](https://tex.z-dn.net/?f=g%28x%29%20%3D%203%5E%7B2x%7D%5C%5C%5C%5Cg%280%29%20%3D%203%5E%7B2%2A0%7D%5C%5C%5C%5Cg%280%29%20%3D%203%5E%7B0%7D%5C%5C%5C%5Cg%280%29%20%3D%201%5C%5C%5C%5C)
This indicates that (0,1) is on the curve. This is the y intercept.
Do the same for x = 2
![g(x) = 3^{2x}\\\\g(2) = 3^{2*2}\\\\g(2) = 3^{4}\\\\g(2) = 81\\\\](https://tex.z-dn.net/?f=g%28x%29%20%3D%203%5E%7B2x%7D%5C%5C%5C%5Cg%282%29%20%3D%203%5E%7B2%2A2%7D%5C%5C%5C%5Cg%282%29%20%3D%203%5E%7B4%7D%5C%5C%5C%5Cg%282%29%20%3D%2081%5C%5C%5C%5C)
So we know that (2,81) is another point on this curve.
We need to find the slope of the line through (0,1) and (2,81) to get the slope of the secant line we want.
![m = \text{slope}\\\\m = \frac{\text{rise}}{\text{run}}\\\\m = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{g(2)-g(0)}{2-0}\\\\m = \frac{81-1}{2-0}\\\\m = \frac{80}{2}\\\\m = 40\\\\](https://tex.z-dn.net/?f=m%20%3D%20%5Ctext%7Bslope%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B%5Ctext%7Brise%7D%7D%7B%5Ctext%7Brun%7D%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B%5Ctext%7Bchange%20in%20y%7D%7D%7B%5Ctext%7Bchange%20in%20x%7D%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7Bg%282%29-g%280%29%7D%7B2-0%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B81-1%7D%7B2-0%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B80%7D%7B2%7D%5C%5C%5C%5Cm%20%3D%2040%5C%5C%5C%5C)
The slope of the line through (0,1) and (2,81) is m = 40. This value of m is exactly the slope of the secant line your teacher is asking for. This is why the answer is choice C.
G(h(x))
g(x^2 -2)
4(x^2 - 2) + 1
4x^2 - 8 + 1
4x^2 - 7
Answer:
The population size after four days is calculated as 168.
Step-by-step explanation:
Let the population size be P
t be the time variable which is measured in hours
Therefore,
by the differential equation
= 0.8329P
So,by solving and expifying the equation on both sides, we get
P = Ae^0.8329t
Therefore,from the first equation we get
P(0) = 6,
A = 6.
Therefore the population size after four days is
P(4) =![{6}\times{e^0.8329(4)}](https://tex.z-dn.net/?f=%20%7B6%7D%5Ctimes%7Be%5E0.8329%284%29%7D)
= 168( rounded to nearest whole number)
Answer:
From the circumference you can determine the radius. Once you have the radius, you calculate the area as πr^2
The answer will be
A=201cm^2
Step-by-step explanation: