Answer:
The derivative is
![\frac{dy}{dx} = 2 - \frac{2\sqrt3}{\sqrt x}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20-%20%20%5Cfrac%7B2%5Csqrt3%7D%7B%5Csqrt%20x%7D%5C%5C)
Step-by-step explanation:
The function is given by
![y = 2x - 1 - \sqrt {3x}](https://tex.z-dn.net/?f=y%20%3D%202x%20-%201%20-%20%5Csqrt%20%7B3x%7D)
Differentiate with respect to x, we get
![\frac{dy}{dx} = 2 - 0 - \frac{2\sqrt3}{\sqrt x}\\\\\frac{dy}{dx} = 2 - \frac{2\sqrt3}{\sqrt x}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20-%200%20-%20%5Cfrac%7B2%5Csqrt3%7D%7B%5Csqrt%20x%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20-%20%20%5Cfrac%7B2%5Csqrt3%7D%7B%5Csqrt%20x%7D%5C%5C)
Michael's initial investment is $45.80, the cost of the share.
Michael Receives $1.71 in dividends.
He receives $47.50 for the stock when he sells it.
His profit on the sale of the stock is $47.50 - 45.80 = $1.70.
His total return on the stock is his total earnings, the dividends plus his profits on the sale of the stock, divided on what he paid initially, $45.80:
(1.71 + 1.70) ÷ 45.80 = .0744 = 7.45%
7.45% return on investment in less than a year, not bad!
Closest answer is 7.7%, not sure why it isn't exactly 7.45 or 7.5%.
Answer is B) 7.7%
Answer: a) 1977060966, b) 146581344.
Step-by-step explanation:
Since we have given that
There are 10 numbers,
There are 26 lower case letters,
There are 26 upper case letters,
Since the first 3 characters have to be digits and next 6 can be upper or lower.
So, a) repetitions are allowed:
![10^3\times (26+26)^6\\\\=10^3\times 52^6\\\\=1977060966](https://tex.z-dn.net/?f=10%5E3%5Ctimes%20%2826%2B26%29%5E6%5C%5C%5C%5C%3D10%5E3%5Ctimes%2052%5E6%5C%5C%5C%5C%3D1977060966)
b) repetitions are not allowed:
![^{10}P_3\times ^{52}C_6\\\\=720\times 20358520\\\\=146581344](https://tex.z-dn.net/?f=%5E%7B10%7DP_3%5Ctimes%20%5E%7B52%7DC_6%5C%5C%5C%5C%3D720%5Ctimes%2020358520%5C%5C%5C%5C%3D146581344)
Hence, a) 1977060966, b) 146581344.
Step-by-step explanation:
It is given that,
Initial speed of the car, u = 40 m/s
Final speed of the car, v = 25 m/s
Time taken, t = 3.5 s
(a) We need to find the magnitude and direction of the car’s acceleration as it slows down. It can be calculated using formula as :
The acceleration is in the opposite direction of motion i.e. west.
(b) Let s is the distance the car travel in the 3.5-s time period. It can be calculated using the third equation of motion as
![s=\dfrac{v^2-u^2}{2a}](https://tex.z-dn.net/?f=s%3D%5Cdfrac%7Bv%5E2-u%5E2%7D%7B2a%7D)
![s=\dfrac{25^2-40^2}{2\times (-4.28)}](https://tex.z-dn.net/?f=s%3D%5Cdfrac%7B25%5E2-40%5E2%7D%7B2%5Ctimes%20%28-4.28%29%7D)
s = 113.9 meters
Hence, this is the required solution.
Answer:
100
Step-by-step explanation:
The population is changing linearly. This means that the population is increasing by a particular value n every year.
From 2009 to 2017, there are 8 increases and so, the population increases by 8n.
The population increased from 1700 to 2500. Therefore, the population increase is:
2500 - 1700 = 800
This implies that:
8n = 800
=> n = 800/8 = 100
The average population growth per year is 100.