Answer:
1 cm
Step-by-step explanation:
We know that the formula for perimeter is<u> 2(l+w) or l+l+w+w</u>
We know that the height is 5 cm so that means <em><u>w= 5</u></em> also that there is 5 cm on both sides of the rectangle. So 5+5=10 so that means that the length of the rectangle is <em><u>1 cm</u></em> if you add the length together you 2 when you add the width you get 10. <em>10+2=12.</em>
Answer:
maximum revenue is 114005
Step-by-step explanation:
for the function R(p) to attain its maximum value R'(p) must be 0.
that is the slope of R(p) must be 0.
R(p) = ![-5p^{2} + 1510p](https://tex.z-dn.net/?f=-5p%5E%7B2%7D%20%2B%201510p)
R'(p) = ![-10p + 1510](https://tex.z-dn.net/?f=-10p%20%2B%201510)
therefore ![-10p + 1510 = 0](https://tex.z-dn.net/?f=-10p%20%2B%201510%20%3D%200)
therefore R(p) is maximum when p = 151
therefore R(151) = ![-5(151^{2} )+1510(151)](https://tex.z-dn.net/?f=-5%28151%5E%7B2%7D%20%29%2B1510%28151%29)
= 114005
Answer: half year
Step-by-step explanation:
The formula to find the simple interest is given by :-
, , where P is the principal amount , r is the rate of interest and t is the time in year.
Given : I=420 ; r=14%=0.14 and P =$6000
Then, we have the following equation :-
![420=6000\times0.14 \times t\\\\\Rightarrow\ t=\dfrac{420}{6000\times0.14}=0.5](https://tex.z-dn.net/?f=420%3D6000%5Ctimes0.14%20%5Ctimes%20t%5C%5C%5C%5C%5CRightarrow%5C%20t%3D%5Cdfrac%7B420%7D%7B6000%5Ctimes0.14%7D%3D0.5)
It means the duration of the loan is half year .
D because you would subtract the initial value from the finals value and you get 250, than you would divide it by the initial value and get .25, than you would multiply it by 100 and you would get 25%
Answer:
Part 1 : ![I_A = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=I_A%20%3D%205.77%20e%5E%7B0.01055t%7D)
Part 2 : In 2069 the population would be 12 millions.
Step-by-step explanation:
Part 1 : Given function that shows the population( in millions ) of Israel after t years since 2000,
![I_A = A_0 e^{kt}](https://tex.z-dn.net/?f=I_A%20%3D%20A_0%20e%5E%7Bkt%7D)
If t = 0,
![I_A = 5.77](https://tex.z-dn.net/?f=I_A%20%3D%205.77)
![\implies 5.77 = A_0 e^{0}\implies A_0 = 5.77](https://tex.z-dn.net/?f=%5Cimplies%205.77%20%3D%20A_0%20e%5E%7B0%7D%5Cimplies%20A_0%20%3D%205.77)
If t = 77 years,
The population in 2077,
![I_A = A_0 e^{77k}=5.77 e^{77k}](https://tex.z-dn.net/?f=I_A%20%3D%20A_0%20e%5E%7B77k%7D%3D5.77%20e%5E%7B77k%7D)
According to the question,
Population in 2077 = 13 millions
![13 = 5.77 e^{77k}](https://tex.z-dn.net/?f=13%20%3D%205.77%20e%5E%7B77k%7D)
![\frac{13}{5.77} = e^{77k}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B5.77%7D%20%3D%20e%5E%7B77k%7D)
Taking ln both sides,
![\ln(\frac{13}{5.77}) = \ln(e^{77k})](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B13%7D%7B5.77%7D%29%20%3D%20%5Cln%28e%5E%7B77k%7D%29)
![\ln(\frac{13}{5.77}) = 77k](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B13%7D%7B5.77%7D%29%20%3D%2077k)
![\implies k = 0.010549\approx 0.01055](https://tex.z-dn.net/?f=%5Cimplies%20k%20%3D%200.010549%5Capprox%200.01055)
Hence, the required function would be,
![I_A = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=I_A%20%3D%205.77%20e%5E%7B0.01055t%7D)
Part 2 : If ![I_A = 12](https://tex.z-dn.net/?f=I_A%20%3D%2012)
![12 = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=12%20%3D%205.77%20e%5E%7B0.01055t%7D)
![\frac{12}{5.77} = e^{0.01055t}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B5.77%7D%20%3D%20e%5E%7B0.01055t%7D)
Taking ln both sides,
![\ln(\frac{12}{5.77}) = \ln(e^{0.01055t})](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B12%7D%7B5.77%7D%29%20%3D%20%5Cln%28e%5E%7B0.01055t%7D%29)
![\ln(\frac{12}{5.77}) =0.01055t](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B12%7D%7B5.77%7D%29%20%3D0.01055t)
![\implies t\approx 69](https://tex.z-dn.net/?f=%5Cimplies%20t%5Capprox%2069)
∵ 2000 + 69 = 2069
Hence, in 2069 the population would be 12 millions.