Answer:
-45
Step-by-step explanation:
This question is incomplete.
Complete Question
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
280 tons of wood.
Step-by-step explanation:
From the above question:
To make 1 ship = we require 40 tons of wood.
1 ship = can accommodate 300 sailors.
Step 1
If :
300 sailors = 1 ship
2100 sailors = y ships
Cross Multiply
300 × y ships = 1 ship × 2100 sailors
y ships = 2100 / 300
y ships = 7
Hence, 2100 sailors can occupy 7 ships.
Step 2
We are told in the question that:
Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
If:
1 ship = 40 tons of wood
Since 7 ships can accommodate 2100 sailors,
7 ships =
7 × 40 tons of wood = 280 tons of wood.
Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.
I must assume that your graph is that of a straight line, and that the end points of the line are P and B, and (finally) that T is between P and B. If these assumptions are correct, then the length of the line segment PB connecting points P and B is 15 + 10, or 25.
![\frac{1}{x} +\frac{1}{y} = 5\\\\x^{-1}+y^{-1}=5\\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%2B%5Cfrac%7B1%7D%7By%7D%20%3D%205%5C%5C%5C%5Cx%5E%7B-1%7D%2By%5E%7B-1%7D%3D5%5C%5C)
Above, I changed the fraction form of x and y into exponential form so it is easier to see the differentiation. Now, we can differentiate:
![-1x^{-2}+-1y^{-2}\frac{dy}{dx}=5\\\\\frac{-1}{x^2}-\frac{1}{y^2}\frac{dy}{dx}=5\\\\-\frac{1}{y^2}\frac{dy}{dx}=5+\frac{1}{x^2}\\\\\frac{dy}{dx}=-5y^2-\frac{y^2}{x^2}](https://tex.z-dn.net/?f=-1x%5E%7B-2%7D%2B-1y%5E%7B-2%7D%5Cfrac%7Bdy%7D%7Bdx%7D%3D5%5C%5C%5C%5C%5Cfrac%7B-1%7D%7Bx%5E2%7D-%5Cfrac%7B1%7D%7By%5E2%7D%5Cfrac%7Bdy%7D%7Bdx%7D%3D5%5C%5C%5C%5C-%5Cfrac%7B1%7D%7By%5E2%7D%5Cfrac%7Bdy%7D%7Bdx%7D%3D5%2B%5Cfrac%7B1%7D%7Bx%5E2%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D-5y%5E2-%5Cfrac%7By%5E2%7D%7Bx%5E2%7D)
Now that we have dy/dx, we can plug in the x, which is 4, and the y, which is 4/19. We know these values of x and y because your question stated y(4) = 4/19.