The problem is an optimization problem in mathematics where one must use algebra and calculus to maximize the area of a rectangular parking lot with a given amount of fencing along three sides. By setting up a function for the area in terms of width and differentiating, the maximum area can be found.
Explanation:The problem presented involves finding the maximum area of a rectangular parking lot given a certain amount of fencing, when one side of the rectangle requires no fencing. This is a classic optimization problem in mathematics which involves the use of algebra and calculus. By setting up a function for the area of the rectangle in terms of one variable and differentiating to find the maximum value, we can determine the solution.
Lets assume that the length of the lot that is along the busy street doesn't require fencing, and let the width of the lot be w and the length be l. Since fencing is only required for three sides, and we have 2,200 feet of fencing, the perimeter equation is 2w + l = 2,200. Solving for l, we get l = 2,200 - 2w. The area A of the parking lot will be given by the equation A = w * l. Substituting the expression for l into the area equation, we get A = w(2,200 - 2w) or A = 2,200w - 2w^2. To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Once the width is found, we can find the length using the perimeter equation and thus calculate the maximum area of the lot.
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A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x−2)=48 x(x-2)=48 What is the length, x, of the garden? The length is _____ feet.
Answer:
The length is [tex]8[/tex] feet.
Step-by-step explanation:
we know that
the area of the rectangle is equal to
[tex]A=xy[/tex]
where
x is the length side of rectangle
y is the width side of rectangle
In this problem we have
[tex]A=48\ ft^{2}[/tex]
so
[tex]48=xy[/tex] ----> equation A
[tex]y=x-2[/tex] ------> equation B
substitute equation B in equation A
[tex]48=x(x-2)[/tex]
[tex]x^{2}-2x-48=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2}-2x-48=0[/tex]
so
[tex]a=1\\b=-2\\c=-48[/tex]
substitute in the formula
[tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-48)}} {2(1)}[/tex]
[tex]x=\frac{2(+/-)\sqrt{4+192}} {2}[/tex]
[tex]x=\frac{2(+/-)14} {2}[/tex]
[tex]x=\frac{2+14} {2}=8\ ft[/tex] -----> the solution
[tex]x=\frac{2-14} {2}=-6[/tex]
at the bake sale connie bought 4 chocolate cookies kevin bought 4 brownies and luis bought 6 sugar cookies in simplest form what fraction represents the number of cookies bought
if the area of the triangle is 84 inches squared what is the value of x
[tex]84[/tex]
[tex] \sqrt{84} [/tex]
Xy=30
3x-y=-9
Solve by the substitution method
Find the x-intercepts of the parabola with vertex (-3,-18) and y-intercept at (0,0)
To find the x-intercepts of the parabola given its vertex and y-intercept, we can first determine the equation of the parabola. Then, we set y equal to zero and solve for x. In this case, the x-intercepts are 0 and -6.
Explanation:The x-intercepts of a parabola can be found by setting the y-coordinate to zero and solving for x. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex. In this case, the vertex is (-3, -18), so the equation of the parabola is y = a(x + 3)^2 - 18. Since the y-intercept is at (0, 0), we can substitute these values into the equation to solve for a. Plugging in the values gives: 0 = a(0 + 3)^2 - 18. Solving for a, we get a = 2. Therefore, the equation of the parabola is y = 2(x + 3)^2 - 18. To find the x-intercepts, we set y equal to zero and solve for x: 0 = 2(x + 3)^2 - 18. Simplifying, we have 2(x + 3)^2 = 18. Dividing both sides by 2 gives (x + 3)^2 = 9. Taking the square root of both sides, we get x + 3 = ±3. Solving for x gives the x-intercepts as x = 0 and x = -6.
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A theater can seat 144 people. The number of rows is 7 less than the number of seats in each row. How many rows of seats are there?
To determine the number of rows in the theater, we use the given information to create the equation x * (x - 7) = 144 where x is the number of seats per row. Factoring out, we find 16 and 9 as a suitable pair, leading to the conclusion that there are 9 rows of seats in the theater.
Explanation:The student's question involves finding the number of rows of seats in a theater given certain constraints. To solve this problem, let's designate x as the number of seats in each row. According to the question, the number of rows of seats is 7 less than the number of seats in a row, which can be written as x - 7. Since we know the theater can seat 144 people in total, we can create the following equation to represent the total number of seats:
x imes (x - 7) = 144
Solving this quadratic equation by factoring will give us the value of x, which will then allow us to calculate x - 7 for the number of rows. By factoring 144, we find that 16 and 9 are factors that satisfy the equation (16 imes 9 = 144) and also meet the condition that one factor is 7 less than the other (16 - 7 = 9). Therefore, the number of seats in each row is 16, and the number of rows is 16 - 7 which gives us 9 rows in the theater.
here is another question 2/5 divided by 1/6
write the equation of a line perpendicular to 9x+8y=3 that passes through the point (8,-7). Type an equation using slope- intercept form or using the given point in point- slope form. use integers or simplified fractions for any numbers in the equation.
Claire picked some apples. She used 2/5 of the apples to make jam, She gave 1/3 of the remainder to her neighbor. What fraction of the apples did she give to her neighbor? Can someone please explain step by step please
A car rental cost $80 per day, for the first 250 miles, plus $0.20 for each additional mile. If Sonya's rental cost was $124 for one-day rental, how many miles did she drive?
A wheel of radius 1.9 feet is moving forward at 12 feet per second. How fast is the wheel turning?
frieda has 12 red apples and 15 green apples she is going to share equally among8 people and keep any extra apples for herself.how many apples will frieda keep for herself
Frieda will keep 3 apples to herself after sharing
ProportionsFrom the given question, we are told that frieda has 12 red apples and 15 green apples. The total number of fruit is expressed as:
Total = 12 + 15Total = 27 fruitIf she is going to share equally among 8 people, then the remainder when 27 is divided by 8 will be the remaining fruit
Taking the ratio
Ratio = 27/8
Ratio = 3 remainder 3
Frieda will keep 3 apples to herself after sharing
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At his grandfather's funeral, rick cries, "grandpa's not coming back." approximately how old is rick?
Rick's age cannot be determined based on his statement at his grandfather's funeral.
Explanation:Rick's age cannot be determined based solely on his statement at his grandfather's funeral. Crying and expressing grief at a funeral is a normal response regardless of age. It is important to remember that people of all ages experience loss and express their emotions in different ways. Age is a complex and multifaceted characteristic influenced by a variety of factors. Therefore, it is not possible to accurately determine Rick's age based on the given information.
If the actual length of the bridge is 4200 feet, then what is the scale of the diagram of the bridge?
the product of two consecutive even positive integers is 782 more than the sum of the two integers. Find the integers
To find the consecutive even positive integers, we set up an equation based on the given information and solve for the variables.
Explanation:Let's assume the first even positive integer is x. Therefore, the next consecutive even positive integer will be x + 2. According to the problem, the product of these two integers is 782 more than their sum. We can set up the equation as x(x + 2) = x + x + 2 + 782.
Simplifying the equation, we get x^2 + 2x = 2x + 784.
By solving this quadratic equation, we find that the value of x is 26. Therefore, the consecutive even positive integers are 26 and 28.
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Is one period a complete cycle of a graph?
2500 kilobytes in 5 minutes
3. Jones of New York sold a fax machine for $400 to Ron Stationery of Boston. Terms of the sale on July 29 are 2/10 EOM FOB New York. Jones agreed to prepay the freight of $25. Assume Ron pays on September 4. How much will it pay Jones?
From a standard desk of 52 card, 5 card are draw.What are the odds of each even occurring?
a) 5 aces
b) 5 face cards
The price of a DVD is $19 . The price is 12% lower than last week.
What was the price of the DVD last week?
Round your answer to the nearest cent.
Need answer in less than 10 mins. plz
The interest on 6000 at 6% compounded semiannually for eight years is?
What is greater 7/12 0.75 or 5/6
find the radian measure of an angle at the center of a circle with radius 67.0 cm that intercepts an arc length of 118 cm
One student is selected at random from group of 12 freshmen, 16 sophomores, 20 juniors, and 2 seniors. Find the probability that the person selected is
A scientist is working with 0.9m of gold wire. How long is the wire in millimeters?
Answer:
The length of the wire in millimeters is 9 × 10² mm.
Step-by-step explanation:
1 meter is equal to 1000 millimeters. This is the ratio that we use to convert a length in meters to one in millimeters. A scientist is working with 0.9 m of gold wire. We will use a conversion fraction to express this number in millimeters.
0.9 m × (1000 mm/ 1 m) = 900 mm = 9 × 10² mm (we round off to 1 significant figure)
The length of the wire in millimeters is 9 × 10² mm.
This problem involves empirical probability. The table shows the breakdown of 97 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is in the Army.
The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is [tex]\( \frac{6}{97} \)[/tex], which is approximately 0.0619 or 6.19%.
To find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force, we need to divide the number of women in the Air Force by the total number of single parents in the military.
1. First, find the number of women in the Air Force from the table. This is given as 6 thousand.
2. Next, find the total number of single parents in the military. This is given as 97 thousand.
3. Finally, divide the number of women in the Air Force by the total number of single parents in the military and express the result as a fraction or decimal to represent the probability.
So, the probability P can be calculated as:
[tex]\[ P = \frac{{\text{Number of women in the Air Force}}}{{\text{Total number of single parents}}} \][/tex]
Substituting the values:
[tex]\[ P = \frac{6}{97} \][/tex]
[tex]\[ P ≈ 0.0619 \][/tex]
Therefore, the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is approximately 0.0619 or 6.19%.
Complete question:
This problem involves empirical probability. The table shows the breakdown of 97 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force.
Army Navy Marine Corps Air Force Total
Male 27 26 4 14 71
Female 11 8 1 6 26
Total 38 34 5 20 97
The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is?
A rectangle has a length of 32 yards less than 3 times its width. If the area of the rectangle is 748 square yards, find the length of the rectangle.
The length of the rectangle will be 34 yards.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The two-dimensional space occupied by the rectangle is called the area of the rectangle.
Given that A rectangle has a length of 32 yards less than 3 times its width. If the area of the rectangle is 748 square yards. The length and the width will be calculated by forming an expression.
Area = L x W
Area = W ( 3W - 32 )
748 = 3W² - 32W
3W² -32W -748 = 0
W = 22 and W = -11
The width will be 22 yards put W in the expression of L to get L.
L= ( 3W - 32 )
L = ( 3 x 22 - 32 ) = 34 yards
Therefore, the length of the rectangle will be 34 yards.
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Solve in terms of x and Y
A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving?
I'm pretty sure its D.