Answer:
the population after 52 days is $34,804.27
Step-by-step explanation:
Given that
There is a population of the rabbits i.e. 192
And, the growth rate is 10%
We need to find out the population after 52 days
So,
= 192 × e^(0.10 × 52)
= $34,804.27
hence, the population after 52 days is $34,804.27
<span>There are 100 possible pairs of numbers.
Half of them start with an even number so only 50 have a first odd number.
Of those remaining 50, half of those have an odd second number.
Leaving 25 of the original 100 to have two odd numbers.
P= 25/100=1/4</span>
Answer:
if you want it as dollars and cents it is $77.50 but in nearest whole number it would be 78 dollars
Step-by-step explanation:
step 1: multiply the 2 by 5 and you get 10%
step two: you put 10 over 100 and multiply 77,500
10/100 x 77,500/1= $77.50
but when you roung it off you get 78 dollars
Answer:
k = 9
length of chord = 2/3
Step-by-step explanation:
Equation of parabola: ![y=k (x-\frac13)^2](https://tex.z-dn.net/?f=y%3Dk%20%28x-%5Cfrac13%29%5E2)
<u />
<u>Part 1</u>
If the curve passes through point
, this means that when
, ![y = 1](https://tex.z-dn.net/?f=y%20%3D%201)
Substitute these values into the equation and solve for
:
![\implies 1=k \left(\dfrac23-\dfrac13\right)^2](https://tex.z-dn.net/?f=%5Cimplies%201%3Dk%20%5Cleft%28%5Cdfrac23-%5Cdfrac13%5Cright%29%5E2)
![\implies 1=k \left(\dfrac13 \right)^2](https://tex.z-dn.net/?f=%5Cimplies%201%3Dk%20%5Cleft%28%5Cdfrac13%20%5Cright%29%5E2)
Apply the exponent rule
:
![\implies 1=k \left(\dfrac{1^2}{3^2} \right)](https://tex.z-dn.net/?f=%5Cimplies%201%3Dk%20%5Cleft%28%5Cdfrac%7B1%5E2%7D%7B3%5E2%7D%20%5Cright%29)
![\implies 1=\dfrac{1}{9}k](https://tex.z-dn.net/?f=%5Cimplies%201%3D%5Cdfrac%7B1%7D%7B9%7Dk)
![\implies k=9](https://tex.z-dn.net/?f=%5Cimplies%20k%3D9)
<u>Part 2</u>
- The chord of a parabola is a line segment whose endpoints are points on the parabola.
We are told that one end of the chord is at
and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:
![\implies 1=9 \left(x-\dfrac13 \right)^2](https://tex.z-dn.net/?f=%5Cimplies%201%3D9%20%5Cleft%28x-%5Cdfrac13%20%5Cright%29%5E2)
![\implies \dfrac19 = \left(x-\dfrac13 \right)^2](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac19%20%3D%20%5Cleft%28x-%5Cdfrac13%20%5Cright%29%5E2)
![\implies \sqrt{\dfrac19} = x-\dfrac13](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7B%5Cdfrac19%7D%20%20%3D%20x-%5Cdfrac13)
![\implies \pm \dfrac13 = x-\dfrac13](https://tex.z-dn.net/?f=%5Cimplies%20%5Cpm%20%5Cdfrac13%20%20%3D%20x-%5Cdfrac13)
![\implies x=\dfrac23, x=0](https://tex.z-dn.net/?f=%5Cimplies%20x%3D%5Cdfrac23%2C%20x%3D0)
Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)
To calculate the length of the chord, find the difference between the x-coordinates:
![\implies \dfrac23-0=\dfrac23](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac23-0%3D%5Cdfrac23)
**Please see attached diagram for drawn graph. Chord is in red**