Calculus Max. and Min. Question

  • Thread starter Thread starter laker_gurl3
  • Start date Start date
  • Tags Tags
    Calculus Max
AI Thread Summary
To maximize the swimming area using 400m of rope, the optimal dimensions of the rectangle are 100m by 200m. With the added restriction that swimmers cannot be more than 50m from the shore, the dimensions change to 50m by 300m. The area is calculated using the formula S = a(400 - 2a), where 'a' represents the length parallel to the shore. By setting the derivative of the area function to zero, the maximum area can be determined. The discussion emphasizes the importance of correctly interpreting the problem as involving a rectangle, not a triangle.
laker_gurl3
Messages
94
Reaction score
0
The lifeguard at a public beach has 400m of rope available to lay out a rectangular restricted swimming area using the straight shoreline as one side of the triangle.
a.) If she wants to maximize the swimming area, what will the dimensions of the rectangle be?
b.)To ensure the safety of the swimmers, she decides that nobody should be more than 50m from shore. What should the dimensions of the swimming area be with this added restriction?...

What do i doo?

A is supposed to be 100m by 200m..and b is 50m by 300m...i can't get those at all though!
 
Physics news on Phys.org
First, repair the statement of your problem. The area is in the shape of a rectangle, not a triangle

a) Three sides of the rectangle are formed by the rope. Let x = the length of the side parallel to the shore. Figure out how to express the other two sides in terms of x. Express the area of the rectangle in terms of x. Maximize that area. You will need the derivative of the area set equal to zero.

b) This is a simple calculation based on your expression of the area in terms of x. What is the value of x in this case?
 
Last edited:
oops yah ur right, the last word of the problem should have been rectangle..
 
The rectangle has sides a,a,b,b.Okay?From the text of the problem u're given that

2a+b=400 and you're asked about the values of "a" and "b" to maximize the area,i.e.the product a\cdot b.

From the constraint,u find that b=400-2a and so the area function which needs to be maximized becomes

S=a(400-2a)

Find "a" for which the function S is maximum...

Daniel.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

MHB Lila Bird's question at Yahoo Answers regarding minimizing plot of land
Replies
1
Views
2K
Max and Min Problems: Solving with Calculus | Need Help & Explanation
Replies
8
Views
4K

Hot Threads

Recent Insights

Back
Top