1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
blondinia [14]
3 years ago
6

A rectangular area of 36 f t2 is to be fenced off. Three sides will use fencing costing $1 per foot and the remaining side will

use fencing costing $3 per foot. Find the dimensions of the rectangle of least cost. Make sure to use a careful calculus argument, including the argument that the dimensions you find do in fact result in the least cost (i.e. minimizes the cost function).
Mathematics
1 answer:
OLga [1]3 years ago
7 0

Answer:

x = 8,49 ft

y  = 4,24  ft  

Step-by-step explanation:

Let  x be the longer side of rectangle   and  y  the shorter

Area of rectangle     =    36 ft²     36  =  x* y   ⇒ y =36/x

Perimeter of rectangle:

P  =  2x   +   2y    for convinience we will write it as    P  = ( 2x + y ) + y

C(x,y)   =  1 * ( 2x  +  y  )  +  3* y

The cost equation as function of x is:

C(x)  =  2x  + 36/x   + 108/x

C(x)  =  2x  + 144/x

Taking derivatives on both sides of the equation

C´(x)  = 2  - 144/x²

C´(x)  = 0         2  - 144/x² = 0       ⇒  2x²  -144 = 0    ⇒  x² =  72

x = 8,49 ft       y  = 36/8.49    y  = 4,24  ft    

How can we be sure that value will give us a minimun

We get second derivative

C´(x)  = 2  - 144/x²      ⇒C´´(x)  = 2x (144)/ x⁴

so C´´(x) > 0

condition for a minimum

You might be interested in
Please help with this question! i'm really struggling :(
Dmitriy789 [7]

Answer:

Step-by-step explanation:

You need to learn about Interpreting graphs,x-intercepts and y-intercepts And Translating functions

4 0
2 years ago
Solve and get brainliest!!<br>please be sure of your answer!!!!​
laila [671]

Answer:

hope this helps youuuuu

4 0
3 years ago
Solve the right triangle, ΔABC, for all the missing side and angles to the nearest tenth given sides a = 10.6 and b = 19.2.
Aliun [14]

Answer:

Part 1) c=21.9\ units

Part 2) B=61.1\°

Part 3) A=28.9\°

Part 4) C=90\°

Step-by-step explanation:

step 1

Find the length side c

Applying the Pythagoras Theorem

c^{2}=a^{2}+b^{2}

substitute the given values

c^{2}=10.6^{2}+19.2^{2}

c^{2}=481

c=21.9\ units

step 2

Fin the measure of angle B

we know that

In the right triangle

tan(B)=b/a

substitute the given values

tan(B)=19.2/10.6

B=arctan(19.2/10.6)=61.1\°

step 3

Find the measure of angle A

we know that

The measure of interior angles in a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

Remember that in a right triangle the measure of angle C is 90 degrees

we have

B=61.1\°

C=90\°

substitute

A+61.1\°+90\°=180\°

A=28.9\°

4 0
3 years ago
Plz help will mark brainliest :)
shepuryov [24]

Answer:

an odd    an even

Step-by-step explanation:

plz mark as brainliest. my first answer

3 0
3 years ago
Which of the following is the equation of a line parallel to 3y=6x+5 that passes through (2,3)?
Verdich [7]

Answer:

The answer is C y= 2x-1

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • What is the discounted price of a guitar for 95.00 and the discount is 15%
    11·2 answers
  • Pomocy!!!!!!<br> Klasa 5 pomocy nie rozumiem<br> Zad 6
    15·2 answers
  • Ty has 5 goats and 19 carrots. He gives each goat the same number of carrots, and he uses as many carrots as he can. How many ca
    15·1 answer
  • How many quarter hours are in 5 hours
    14·1 answer
  • WILL AWARD A MEDAL AND FIVE STARS!!!!
    14·1 answer
  • Are 1/2 and 12/24 and 13/26 equivalent?
    8·1 answer
  • Rearrange the fractions in ascending order:<br> 1/3, 3/11, 6/19, 5/8
    14·1 answer
  • Help please, i'll give the crown thing if I can
    14·1 answer
  • Y=2x-2<br> y=-2x-6 solve
    11·2 answers
  • 8. Math on the Spot Write an equation in slope-intercept form for the line that passes
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!