Given that the angles of the two sectors are equal, we can find the relationship between the angles, radii, and the lengths of the arc
The length of the arc (S) is given by the formula
![S\text{ = }\frac{\theta}{360}\text{ x 2}\pi\text{ r}](https://tex.z-dn.net/?f=S%5Ctext%7B%20%3D%20%7D%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Ctext%7B%20x%202%7D%5Cpi%5Ctext%7B%20r%7D)
![\text{Since 2}\pi=360^0](https://tex.z-dn.net/?f=%5Ctext%7BSince%202%7D%5Cpi%3D360%5E0)
![S\text{ =}\theta\text{ r}](https://tex.z-dn.net/?f=S%5Ctext%7B%20%3D%7D%5Ctheta%5Ctext%7B%20r%7D)
Then we can make the angle the subject of the formula
![\theta\text{ =}\frac{S}{r}](https://tex.z-dn.net/?f=%5Ctheta%5Ctext%7B%20%3D%7D%5Cfrac%7BS%7D%7Br%7D)
For the first sector
![\begin{gathered} \text{with radius r}_1\text{ and angle }\theta_1 \\ \\ \theta_1\text{ =}\frac{S_1}{r_1} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bwith%20radius%20r%7D_1%5Ctext%7B%20and%20angle%20%7D%5Ctheta_1%20%5C%5C%20%20%5C%5C%20%5Ctheta_1%5Ctext%7B%20%3D%7D%5Cfrac%7BS_1%7D%7Br_1%7D%20%5Cend%7Bgathered%7D)
For the second sector
![\begin{gathered} \text{with radius r}_2\text{ and }\theta_2 \\ \theta_2=\frac{S_2}{r_2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bwith%20radius%20r%7D_2%5Ctext%7B%20and%20%7D%5Ctheta_2%20%5C%5C%20%5Ctheta_2%3D%5Cfrac%7BS_2%7D%7Br_2%7D%20%5Cend%7Bgathered%7D)
![\theta_{1\text{ =}}\text{ }\theta_2\text{ = }\theta\text{ =}\frac{S_1}{r_1}\text{ =}\frac{S_2}{r_2}](https://tex.z-dn.net/?f=%5Ctheta_%7B1%5Ctext%7B%20%3D%7D%7D%5Ctext%7B%20%7D%5Ctheta_2%5Ctext%7B%20%3D%20%7D%5Ctheta%5Ctext%7B%20%3D%7D%5Cfrac%7BS_1%7D%7Br_1%7D%5Ctext%7B%20%3D%7D%5Cfrac%7BS_2%7D%7Br_2%7D)
Simplifying the equation, we will obtain
Answer:
It can be both rational and irrational.
Step-by-step explanation:
Answer:
a) The absolute maximum is 401 and the absolute minimum is 9.
b) The absolute maximum is 349 and the absolute minimum is -99.
c) The absolute maximum is 401 and the absolute minimum is -99.
Step-by-step explanation:
The absolute minimum and absolute maximum values are determined with the help of the First and Second Derivative Tests:
FDT
![3\cdot x^{2} + 12\cdot x - 63 = 0](https://tex.z-dn.net/?f=3%5Ccdot%20x%5E%7B2%7D%20%2B%2012%5Ccdot%20x%20-%2063%20%3D%200)
The roots of the function are:
and
. Each point is evaluated in the second derivative of the function:
SDT
![f''(x) = 6\cdot x + 12](https://tex.z-dn.net/?f=f%27%27%28x%29%20%3D%206%5Ccdot%20x%20%2B%2012)
(Absolute minimum)
(Absolute maximum)
The values for each extreme are, respectively:
![f(x_{1}) = -99](https://tex.z-dn.net/?f=f%28x_%7B1%7D%29%20%3D%20-99)
![f(x_{2}) = 401](https://tex.z-dn.net/?f=f%28x_%7B2%7D%29%20%3D%20401)
Now, each interval is analyzed herein:
a) The absolute maximum is 401 and the absolute minimum is 9.
b) The absolute maximum is 349 and the absolute minimum is -99.
c) The absolute maximum is 401 and the absolute minimum is -99.
The equation that models the population of bats is 326,000 x (1.014)^X = Y, so the correct answer is A.
<h3><u>Equations</u></h3>
Given that a scientist is studying wildlife, and she estimates the population of bats in her state to be 326,000, and she predicts the population to grow at an average annual rate of 1.4%, to create an equation that models the population of bats, Y , after X years, the following calculation must be made:
- 326,000 x (1+ 1.4/100)^X = Y
- 326,000 x (1 + 0.014)^X = Y
- 326,000 x (1.014)^X = Y
Thus, in 3 years, the equation would operate as follows:
- 326,000 x 1.014^3 = Y
- 326,000 x 1.0425 = Y
- 339,884.58 = Y
Learn more about equations in brainly.com/question/2263981
We are given statement : The distance between Pittsburgh, Pennsylvania, and St. Louis, Missouri, is 17 miles less than 5 times the distance between Pittsburgh and Cleveland, Ohio.
The distance between Pittsburgh and Cleveland = d.
We need to write an expression for distance between Pittsburgh and St. Louis.
And it's "17 miles less than 5 times the d".
5 times of d is = 5d.
17 miles less than 5d = 5d -17.
Therefore, 5d -17 expression can you use to represent the distance between Pittsburgh and St. Louis.