Answer:
=
with T₁ = 5000
Step-by-step explanation:
There is a common ratio r between consecutive terms in the sequence, that is
r =
=
=
= ![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
This indicates the sequence is geometric with recursive rule
= r ![T_{n-1}](https://tex.z-dn.net/?f=T_%7Bn-1%7D)
Here tr =
, thus
=
, T₁ = 5000
Answer:
![L = -1.5 \frac{in}{hr} t + 11.2](https://tex.z-dn.net/?f=%20L%20%3D%20-1.5%20%5Cfrac%7Bin%7D%7Bhr%7D%20t%20%2B%2011.2)
Step-by-step explanation:
For this case we need to define some notation:
represent the remaining length of the candle in inches
represent the time in hours that have elapsed since the candle was lit.
For this case we assume that L and f are related so then we can write this like that:
L is a function of t.
And for this case we have a constant rate given of:
![m = \frac{\Delta L}{\Delta t}= -1.5 \frac{in}{hr}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B%5CDelta%20L%7D%7B%5CDelta%20t%7D%3D%20-1.5%20%5Cfrac%7Bin%7D%7Bhr%7D)
And we know a initial condition ![L(2) = 8.2 in](https://tex.z-dn.net/?f=%20L%282%29%20%3D%208.2%20in)
So then since we have a constant rate of change we can use a linear model given by:
![L = m t +b](https://tex.z-dn.net/?f=%20L%20%3D%20m%20t%20%2Bb)
Where m is given and we need to find b. If we use the initial condition we have this:
![8.2 = -1.5 \frac{in}{hr} (2) +b](https://tex.z-dn.net/?f=%208.2%20%3D%20-1.5%20%5Cfrac%7Bin%7D%7Bhr%7D%20%282%29%20%2Bb)
And solving for b we got:
![b = 8.2 +1.5*2=11.2 in](https://tex.z-dn.net/?f=%20b%20%3D%208.2%20%2B1.5%2A2%3D11.2%20in)
So then our lineal model would be given by:
![L = -1.5 \frac{in}{hr} t + 11.2](https://tex.z-dn.net/?f=%20L%20%3D%20-1.5%20%5Cfrac%7Bin%7D%7Bhr%7D%20t%20%2B%2011.2)
The mode would be 30 and the median cannot be determined i believe in this one
i hope that helps
Answer:
11/24 - 6/24 = 5/24
Step-by-step explanation:
Common denominator is 24
24 * 1 = 24 11 * 1 = 24 11/24
4 * 6 = 24 1 * 6 = 24 6/24
New fractions are 11/24 and 6/24
Subtract them
11/24 - 6/24 = 5/24
Answer:
![y\geq -6](https://tex.z-dn.net/?f=y%5Cgeq%20-6)
Step-by-step explanation:
we know that
The graph of the figure represent a vertical parabola open upward
The vertex represent a minimum
The vertex of the quadratic equation is the point (h,k)
The range of the quadratic equation is the interval for y [k,∞)
![y\geq k](https://tex.z-dn.net/?f=y%5Cgeq%20k)
Looking at the graph
The vertex is the point (0,-6)
therefore
The range is the interval [-6,∞)
![y\geq -6](https://tex.z-dn.net/?f=y%5Cgeq%20-6)