Answer:
132
ft²
Step-by-step explanation:
First we shall work out the area of 1 skylight. one skylight is 15/8 feet so 15/8 x 15/8 = 3.515625 feet. x this by 2 as there is 2 skylights. So in total, there is 7.03125 feet^2 covered by the skylights. Take this from the original area 140ft - 7.03125 ft = 132.96875 ft^2 or as a mixed number 132
ft²
Answer:
![U_{n+1}=U_{n}-4](https://tex.z-dn.net/?f=U_%7Bn%2B1%7D%3DU_%7Bn%7D-4)
Next term = -16
Step-by-step explanation:
![\text{let} \ \left( U_{n}\right) \text{be the sequence which we are looking for}](https://tex.z-dn.net/?f=%5Ctext%7Blet%7D%20%5C%20%20%5Cleft%28%20U_%7Bn%7D%5Cright%29%20%20%5Ctext%7Bbe%20the%20sequence%20which%20we%20are%20looking%20for%7D)
0-4 = -4
(-4)-0 = -4
(-8)-(-4) = -4
(-12)-(-8) = -4
It’s clear that Un is an arithmetic sequence of common difference r = -4
Then
![U_{n+1}=U_{n}-4](https://tex.z-dn.net/?f=U_%7Bn%2B1%7D%3DU_%7Bn%7D-4)
Next term :
![U_{6}=U_{5}-4 = -12-4=-16](https://tex.z-dn.net/?f=U_%7B6%7D%3DU_%7B5%7D-4%20%3D%20-12-4%3D-16)
![\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies -6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=-6(x-3) \\\\\\ y-1=-6x+18\implies y=-6x+19](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B3%7D~%2C~%5Cstackrel%7By_1%7D%7B1%7D%29~%5Chspace%7B10em%7D%20slope%20%3D%20m%5Cimplies%20-6%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-1%3D-6%28x-3%29%20%5C%5C%5C%5C%5C%5C%20y-1%3D-6x%2B18%5Cimplies%20y%3D-6x%2B19)
bearing in mind that
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
then we'd end up with 6x + y = 19.
This is like the equation of a line where y is the area, x is the time, and 8.5% is your slope. So you have y=0.085x+b (reason why I switched 8.5% into 0.085 is because that is how you write a percent as a decimal).So now you need to find what b is. So you know orignally the area is 2400km^2 at x=0 years (this is what it is initially).If you plug those numbers in you have:2400=0.085(0)+bThen after solving for b, you can write your equation as:y=0.085x+(whatever you found b to be)Then plug 13 in for x and you have your answer. y=-.085(13)+2400