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
g100num [7]
3 years ago
11

A hardware store wants to enclose a 800 square foot rectangular area adjacent to its store to display gardening equipment. One s

ide will be formed by the wall of the store. The side opposite the store will be constructed with steel fencing costing $6 per foot and the other two sides will be constructed with wood fencing costing $3 per foot. What are the dimensions that will minimize cost
Mathematics
1 answer:
inna [77]3 years ago
8 0

Answer:

x = 20√2 ft and y = 40/√2 ft

Step-by-step explanation:

Let; x = length of steel fencing

y = length of a wood fence that is perpendicular to the store

Thus, since area is 800 ft², then;

xy = 800

Length of fence; L = x + 2y

From earlier, xy = 800

y = 800/x

Thus;

L = x + 2(800/x)

L = x + 1600/x

Now, steel fencing costing $6 per foot and the other two sides will be constructed with wood fencing costing $3 per foot. Thus, total cost is;

C(x) = 6x + 3(2y)

But y = 800/x. Thus;

C(x) = 6x + 3(1600/x))

C(x) = 6x + 4800/x

C'(x) = 6 - 4800/x²

At C'(x) = 0, the cost is minimized.

Thus=

6 - 4800/x² = 0

6x² = 4800

x² = 4800/6

x² = 800

x = √800

x = 20√2

When 0 < x < 20√2, C'(x) < 0, so we say that C(x) is decreasing

When x > 20√2, C'(x) > 0, so we say that C(x) is increasing

Thus, the cost is minimized when x = 20√2

Thus, putting 20√2 for x in y = 800/x, we have;

y = 800/(20√2)

y = 40/√2

Thus, dimensions that will minimize cost are;

x = 20√2 ft and y = 40/√2 ft

You might be interested in
What is the probability of drawing a black ace followed by a heart out
Verdich [7]

Correct option C) 0.98%

<u>Step-by-step explanation:</u>

We know that  , there are 2 black ace cards out of 52 cards in a deck & 13 hearts out of 52 cards . Here we have to tell What is the probability of drawing a black ace followed by a heart out  of a deck when the cards aren't replaced . Let's find out:

Firstly , a black ace is drawn , so probability :

⇒ P(Black) = \frac{2}{52}

Now , A heart is drawn out of 51 cards ( as one black ace is already drawn !):

⇒ P(Heart) = \frac{13}{51}

So , Probability of occurring both events is :

⇒ P(Black)(P(Heart))

⇒ \frac{2}{52} (\frac{13}{51} )

⇒ 0.0098

Percentage = 0.0098(100) = 0.98%

Therefore , Correct option C) 0.98%

7 0
3 years ago
Add ma insta yurrr.jazzy
cupoosta [38]

Answer:

lol nooooooooooooooooo

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Which of the following describes the “p/2” in the expression above?
julia-pushkina [17]

Option B. Quotient is the right answer

Step-by-step explanation:

Given expression is:

p/2 +4(7+p)

Let us look at the options one by one

<u>A. factor</u>

p/2 is not a factor as the factor is always multiplied with another factor

<u>B. quotient</u>

This is the right answer as p is being divided by 2. The quotient of both will be used for further calculations

Hence,

Option B. Quotient is the right answer

Keywords: MCQs, Expressions

Learn more about polynomial expressions at:

  • brainly.com/question/12896802
  • brainly.com/question/12973601

#LearnwithBrainly

5 0
3 years ago
How to solve 6x+3=5x+10
laila [671]
6x+3=5x+10 \\\\ 6x-5x=10-3 \\\\ \boxed{x=7}
7 0
3 years ago
Read 2 more answers
Which expression is equivalent to -2 (5x-.75)
GrogVix [38]

Answer:

-10x + 1.5

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • C=(4+y)h Solve for y
    5·1 answer
  • 2.21*10^11 in standard notation
    14·1 answer
  • suppose you go to a concert and purchase three identical t-shirts and a hat that hat cost $21 and you spend $60 an hour how much
    7·2 answers
  • Simplify. <br>√3/10 <br><br><br>A. √15/5 <br><br>B. √30/10 <br><br>C. √3/10 <br><br>D. √3/5
    6·1 answer
  • A bus is traveling at a speed of 55 miles per hour. Which statement is correct?
    6·2 answers
  • An insurance agent receives 16% commission on every premium paid. How much commission is paid on a policy with a premium of $497
    8·2 answers
  • Evaluate the following expression. Round your answer two decimal places. Log3(10)
    11·2 answers
  • Write a 2 paragraphs telling me how you have used algebra in your life outside of school
    14·1 answer
  • Write an exponential function in the form y=ab^x 0,6 2,96
    11·1 answer
  • What is an equation of the line that passes through the points (6, 4) and(6,−6)?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!