Answer:
The x-coordinate of the point changing at ¼cm/s
Step-by-step explanation:
Given
y = √(3 + x³)
Point (1,2)
Increment Rate = dy/dt = 3cm/s
To calculate how fast is the x-coordinate of the point changing at that instant?
First, we calculate dy/dx
if y = √(3 + x³)
dy/dx = 3x²/(2√(3 + x³))
At (x,y) = (1,2)
dy/dx = 3(1)²/(2√(3 + 1³))
dy/dx = 3/2√4
dy/dx = 3/(2*2)
dy/dx = ¾
Then we calculate dx/dt
dx/dt = dy/dt ÷ dy/dx
Where dy/dx = ¾ and dy/dt = 3
dx/dt = ¾ ÷ 3
dx/dt = ¾ * ⅓
dx/dt = ¼cm/s
The x-coordinate of the point changing at ¼cm/s
Add all the minutes together, then divide by the number of students:
21+35+77+48+24+29+37+98+30+7 = 406 total minutes
10 students.
Average = 406 / 10 = 40.6 minutes per week.
The answer is A.
The pharmacy should charge $201.6 for the entire bottle
Cost price refers the price the seller bought the product
Selling price refers to the price the seller sells to the consumer.
Profit refers to the money earned by the seller above the cost price
Loss refers to the money paid by the seller above the cost price.
Profit= SP-CP
CP=30X$4.60=$138
TOTAL EXPENSES=$138+30X$1.40
= $180
FOR PROFIT OF 12%,the seller must sell in= $180(1+12/100)
=$201.6
Therefore,the pharmacy should charge $201.6 for the entire bottle to make a profit of atleast 12%
Learn more about profit and loss,
brainly.com/question/19104371
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Answer:- a.The given expression is equivalent to 
Given expression:- ![[\frac{(3xy^{-5})^3}{(x^{-2}y^2)^{-4}}]^{-2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%283xy%5E%7B-5%7D%29%5E3%7D%7B%28x%5E%7B-2%7Dy%5E2%29%5E%7B-4%7D%7D%5D%5E%7B-2%7D)
![=[\frac{(3)^3x^3y^{-5\times3}}{x^{-2\times-4}y^{2\times-4}}]^{-2}.........(a^m)^n=a^{mn}](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B%283%29%5E3x%5E3y%5E%7B-5%5Ctimes3%7D%7D%7Bx%5E%7B-2%5Ctimes-4%7Dy%5E%7B2%5Ctimes-4%7D%7D%5D%5E%7B-2%7D.........%28a%5Em%29%5En%3Da%5E%7Bmn%7D)
![=[\frac{27x^3y^{-15}}{x^8y^{-8}}]^{-2}](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B27x%5E3y%5E%7B-15%7D%7D%7Bx%5E8y%5E%7B-8%7D%7D%5D%5E%7B-2%7D)
![=[27x^{3-8}y^{-15-(-8)}]^{-2}............\frac{a^m}{a^n}=a^{m-n}](https://tex.z-dn.net/?f=%3D%5B27x%5E%7B3-8%7Dy%5E%7B-15-%28-8%29%7D%5D%5E%7B-2%7D............%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D)
![=[27x^{-5}y^{-7}]^{-2}=(27)^{-2}(x^{-5})^{-2}(y^{-7})^{-2}.........(a^m)^n=a^{mn}](https://tex.z-dn.net/?f=%3D%5B27x%5E%7B-5%7Dy%5E%7B-7%7D%5D%5E%7B-2%7D%3D%2827%29%5E%7B-2%7D%28x%5E%7B-5%7D%29%5E%7B-2%7D%28y%5E%7B-7%7D%29%5E%7B-2%7D.........%28a%5Em%29%5En%3Da%5E%7Bmn%7D)
Thus a. is the right answer.
