Potential energy<span> is the </span>energy<span> possessed by an object because of its position.
So it is D the highest point of the trajectory. </span>
12:45Answer:
Part A: 9 hours 45 minutes
Part B: $126.1575
Step-by-step explanation:
Part A,
From 7:45 to 12:15 is 4 hours and 30 minutes
From 12:45 which he clocked back in to 6:00 is 5 hours and 15 minutes.
4 hours and 30 minutes plus 5 hours and 15 minutes = 9 hours and 45 minutes.
Part B, 9 hours and 45 minutes can be represented as 9.45
And since he gets 15.35 "per" hour shows we can multiply.
15.35 x 9.45 = 126.1575
Therefor he earned 126.15.
Answer:
Length = 18.099 ft
Width = 11.049 ft
Step-by-step explanation:
let the length of the field be x ft
and the width be y ft
as per the condition given in problem
x=2y-4 -----------(A)
Also the area is given as 200 sqft
Hence
xy=200
Hence from A we get
y(2y-4)=200
taking 2 as GCF out
2y(y-2)=200
Dividing both sides by 2 we get
![y(y-2)=100](https://tex.z-dn.net/?f=y%28y-2%29%3D100)
![y^2-2y=100](https://tex.z-dn.net/?f=y%5E2-2y%3D100)
subtracting 100 from both sides
![y^2-2y-100=0](https://tex.z-dn.net/?f=y%5E2-2y-100%3D0)
Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Here in our case
a=1
b=-1
c=-100
Putting those values in the formula and solving them for y
![y=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-%28-2%29%2B%5Csqrt%7B%28-2%29%5E2-4%20%5Ctimes%20%28-1%29%20%5Ctimes%20100%7D%7D%7B2%20%5Ctime%201%7D)
![y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-%28-2%29-%5Csqrt%7B%28-2%29%5E2-4%20%5Ctimes%20%28-1%29%20%5Ctimes%20100%7D%7D%7B2%20%5Ctime%201%7D)
Solving first
![y=\frac{2+\sqrt{4+400}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%2B%5Csqrt%7B4%2B400%7D%7B2%7D)
![y=\frac{2+\sqrt{404}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%2B%5Csqrt%7B404%7D%7B2%7D)
![y=\frac{2+20.099}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%2B20.099%7D%7B2%7D)
![y=\frac{22.099}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B22.099%7D%7B2%7D)
![y=11.049](https://tex.z-dn.net/?f=y%3D11.049)
Solving second one
![y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-%28-2%29-%5Csqrt%7B%28-2%29%5E2-4%20%5Ctimes%20%28-1%29%20%5Ctimes%20100%7D%7D%7B2%20%5Ctime%201%7D)
![y=\frac{2-\sqrt{4+400}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2-%5Csqrt%7B4%2B400%7D%7B2%7D)
![y=\frac{2-\sqrt{404}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2-%5Csqrt%7B404%7D%7B2%7D)
![y=\frac{2-20.099}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2-20.099%7D%7B2%7D)
![y=\frac{-18.99}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-18.99%7D%7B2%7D)
![y=-9.045](https://tex.z-dn.net/?f=y%3D-9.045)
Which is wrong as the width can not be in negative
Our width of the field is
y=11.099
Hence the length will be
x=2y-4
x=2(11.049)-4
x=22.099-4
x=18.099
Hence our length x and width y :
Length = 18.099 ft
Width = 11.049 ft
let's firstly convert the mixed fractions to improper fractions and then proceed.
![\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B9%7D%7B2%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B5%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\begin{array}{ccll} miles&hours\\ \cline{1-2} \frac{9}{2}&\frac{5}{4}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{9}{2}~~}{x}=\cfrac{~~ \frac{5}{4}~~}{1}\implies \cfrac{~~ \frac{9}{2}~~}{\frac{x}{1}}=\cfrac{5}{4}\implies \cfrac{9}{2}\cdot \cfrac{1}{x}=\cfrac{5}{4} \\\\\\ \cfrac{9}{2x}=\cfrac{5}{4}\implies 36=10x\implies \cfrac{36}{10}=x\implies \cfrac{18}{5}=x\implies 3\frac{3}{5}=x](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccll%7D%20miles%26hours%5C%5C%20%5Ccline%7B1-2%7D%20%5Cfrac%7B9%7D%7B2%7D%26%5Cfrac%7B5%7D%7B4%7D%5C%5C%5B1em%5D%20x%261%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B~~%20%5Cfrac%7B9%7D%7B2%7D~~%7D%7Bx%7D%3D%5Ccfrac%7B~~%20%5Cfrac%7B5%7D%7B4%7D~~%7D%7B1%7D%5Cimplies%20%5Ccfrac%7B~~%20%5Cfrac%7B9%7D%7B2%7D~~%7D%7B%5Cfrac%7Bx%7D%7B1%7D%7D%3D%5Ccfrac%7B5%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B9%7D%7B2%7D%5Ccdot%20%5Ccfrac%7B1%7D%7Bx%7D%3D%5Ccfrac%7B5%7D%7B4%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B9%7D%7B2x%7D%3D%5Ccfrac%7B5%7D%7B4%7D%5Cimplies%2036%3D10x%5Cimplies%20%5Ccfrac%7B36%7D%7B10%7D%3Dx%5Cimplies%20%5Ccfrac%7B18%7D%7B5%7D%3Dx%5Cimplies%203%5Cfrac%7B3%7D%7B5%7D%3Dx)
Each room would be 1 hour because it say that two rooms get painted in two hours <span />