If the garden is to be 1250 square feet, and the fence along the driveway costs $6 per foot while on the other three sides it costs only $2 per foot, find the dimensions that will minimize the cost.
Answers
So, the minimum cost is $400.
Area of the rectangle:
The area of a rectangle is the region occupied by a rectangle within its four sides or boundaries.
And the formula is,
Given that,
Area of the garden=1250 square feet.
Let, the length be and the breadth be
then,
The total cost of the fence is,
Now, differentiating the obtained equation we get,
Therefore the length is 25 ft
And breadth is 50ft
Now, calculating the minimum cost,
Learn more about the area of the rectangle:
Answer:
Dimensions of rectangular garden:
x = 25 feet ( sides along the driveway)
y = 50 feet
Step-by-step explanation:
Rectangular area is:
A(r) = x*y (1)
if we call x one the driveway side the cost of that side will be
6*x
The cost of the other side parallel to driveway side is 2*x and cost of the others two sides are 4*y
Total costs: C = 6*x + 2*x * 4*y (2)
From equation (1)
A(r) = 1250 = x*y ⇒⇒ y = 1250/ x
Plugging that value in equation (2) we get costs as a function of x
that is:
C(x) = 6*x + 2*x + 4* 1250/x
Taking derivatives on both sides of the equation
C´(x) = 6 + 2 - 5000/x²
C´(x) = 8 - 5000 /x²
C´(x) = 0 ⇒ 8 - 5000 /x² = 0
8*x² -5000 = 0
x² = 5000/8
x² = 625
x = 25 feet
and y = 1250/ 25
y = 50 ft
C(min) = 50*2*2 + 6*25 + 2*25
C(min) = 200 + 200
C(min) = 400 $
Related Questions
The sum of the lengths of is 24.62 cm. The length of is 3 cm and the length of is 17.8 cm. What is the length of and what kind of triangle is this?A. 3.82 cm; scaleneB. 3.82 cm; isoscelesC. 3.92 cm; scaleneD. 3.92 cm; isosceles
Is the quotient 2.7 ÷ 3 greater than or less than 1? Explain plzz!!!
I need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which of the following is least like the others? Exit Test A road B street C highway D trail
x|y
-2|2
1|5
3|7
---- ----
A. y = x + 4
B. y = -x
C. y = x - 4
D. y = 4 - x
Answers
Answer:
y = x + 4
Step-by-step explanation:
y = mx + b (m = slope; b = y-intercept)
I used 2 points (-2 , 2) and (1 , 5) to calculate the slope of the line
m= (y₂ - y₁)/(x₂ - x₁)
(5-2)/(1--2) = 3/3= 1
y = 1x + b
using point (1, 5)
5 = 1(1) + b
5 = 1 + b
b = 5-1
b=4
y= 1x + 4 or simply y= x + 4
Answer:
A y = x + 4
yeh i did the test
Step-by-step explanation:
Writen in base 10
Answers
Answers
Answer:
266
Step-by-step explanation:
Red marbles = 4
Green marbles = 1
Lavender marbles = 1
Yellow marbles = 3
Orange marbles = 2
To pick 5 marbles with at most 1 yellow, we can pick 5 non-yellow marbles or (4 non-yellow marble and 1 yellow marble).
Picking 5 non-yellow marbles
There are 4 + 1 + 1 + 2 = 8 non-yellow marbles.
The number of ways of picking any 5 is
Picking 4 non-yellow marble and 1 yellow marble
The number of ways of picking any 4 non-yellow marbles is
The number of ways of picking any 1 yellow marble from 3 is
Number of ways for both =
Total number of picking 5 marbles with at most 1 yellow
Therefore, total number of ways = 56 + 210 = 266
Answers
The area of rectangle with length 12.75 cm and the width 3.64 cm with 4 significant figures is 46.41 cm².
What is a quadrilateral?
quadrilateral is a plane mathematical closed figure consist of four side and four edges. There are 7 types of quadrilateral.
Trapezium, Parallelogram, Rectangle, Rhombus, Square, Kite.
Here, it is given that :
the lengthl of a rectangle is = 12.75 cm
the breadthb of a rectangle is = 3.64 cm
Now, let us calculate the area of this rectangle using area formula :
area of rectangle A = length x breadth
A = 12.75 x 3.64
A = 46.41 cm²
Therefore, the area of rectangle with length 12.75 cm and the width 3.64 cm with 4 significant figures is 46.41 cm².
check and know more about quadrilateral here :
#SPJ2
Answer:
3200
Step-by-step explanation:
3r + 11
9x-14
Answers
(11 plus -19) = -8.
12x -8
divide both sides by 12 and you will have your answer!
20
20.8
20.86
20.9
Answers
Answer:
20.9 is the answer because To round 20.86 to the nearest tenth consider the hundredths’ value of 20.86, which is 6 and equal or more than 5. Therefore, the tenths value of 20.86 increases by 1 to 9. 20.86 rounded to the nearest tenth = 20.9