The perimeter of a rectangle Is 108 centimeters. If the length of the rectangle is five times the width, what are the dimensions of the rectangle?

Answer:

The correct answer is $800.

Step-by-step explanation:

Let the length and width of the field be equal to l meters and b meters respectively and l > b.

Area of the field is given by l × b = 400 square meters.

The river is supposed to be along the longest side so that the price of fencing the other three sides is minimum. Thus the total perimeter of the fence is b+ b+ l = 2b+l.

Total cost for fencing the other sides of the field = $ 10 × (2b + l)

The wall is supposed to be perpendicular to the river and thus the length of the wall is b meters.

Total cost for the wall is $ 20 × b

Therefore, the total price for making the field is given by

C = 10 × (2b + l) + 20 × b

⇒ C = 40b + 10l

⇒ C = + 10l

To minimize the cost we differentiate the cost with respect to l and equate it to zero.

= 0 = - + 10

⇒ = 1600

⇒ l = 40 ; [ negative sign neglected as length cannot be negative ]

⇒ b = 10

The second order derivative of C is positive giving the minimum value of the cost.

Thus the minimum cost required to make the field is given by $800.

Final answer:

To find the lowest possible cost to build the field, we need to determine the dimensions that will yield the minimum perimeter and then calculate the total cost of building the field. By differentiating the cost equation and solving for x, we can find the dimensions that minimize the cost.

Explanation:

To find the lowest possible cost to build the field, we need to determine the dimensions that will yield the minimum perimeter. Since the area of the field is 400 square meters and it will be divided into two equal halves by a brick wall, each half will have an area of 200 square meters. Let's say the length of the field is x meters. Then the width of each half will be 200/x meters.

The perimeter of the field is the sum of the lengths of the three sides:

Perimeter = 2x + 200/x + 200/x

Now, we can define the total cost to build the field as:

Total Cost = Cost of wall + Cost of fence

Cost of wall = 2x * $20 (since there are two halves)

Cost of fence = (2x + 200/x + 200/x) * $10 (since there is a fence on three sides)

Therefore, the total cost is: Total Cost = 2x * $20 + (2x + 200/x + 200/x) * $10.

To minimize the cost, we can differentiate the total cost with respect to x and set it equal to zero:

d(Total Cost)/dx = 0

Simplifying this equation will give us the value of x that minimizes the cost. We can solve this equation to find the minimum cost to build the field.

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Answer: Miguel forgot to create the title.

Step-by-step explanation:

Miguel made the histogram originally histogram to show the ages of all the participants that took part in a fundraiser.

The intervals of histogram are present on the given histogram. 1-10, 11-20, 21-30, 31-40, 41-50.

Same as the frequency for each interval. One notable omission from the histogram which is missing is the title, this implies that Miguel forgot to create the title.

Answer:

C: Miguel forgot to create the title.

Step-by-step explanation:

edg2020

(there is also no title in the picture:))

Answer:

He climed 3 steps before he started counting the steps.

Step-by-step explanation:

pls mark me as a branliest

Answer:

The answer is he climbed 44 steps. Hope this helped :D

Step-by-step explanation:

Answer:

i dont do taxes

Step-by-step explanation:

The equivalent ratios of the cups of sugar to cups of flour are shown in table B.

What are ratios and proportions?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that for a recipe, Paul uses 3 cups of sugar for every 4 cups of flour. Check the table number B for the ratios of the cups of sugar to cups of flour,

Cups of sugar   Cups of flour      ratio

3                              4                     3 / 4 = 0.75

6                              8                     6 / 8 = 0.75

9                             12                   9 / 12 = 0.75

12                            16                   12 / 16 = 0.75

Hence, the table which shows the equivalent ratio is B

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Answer:

B

Step-by-step explanation:

In the chart for b it shows the use of 3 cups of sugar per 4 cups of flour which is what the question wants you to find.

Answer:

1/16

Step-by-step explanation:

To have one real solution, the discriminant must be 0.

b² − 4ac = 0

1² − 4a(4) = 0

1 − 16a = 0

a = 1/16