All categories

3 years ago

Suppose you have 40 meters of fencing what is the greatest rectangular area that you can enclose

1 answer:

8 0

It'd help if you could sketch this situation. Note that the area of a rectangle is equal to the product of its width and length: A = L W.

Consider the perimeter of this rectangular area. It's P = 2 L + 2 W. Note that P = 40 meters in this problem.

Thus, if we choose to use W as our independent variable, then P = 40 meters = 2 L + 2 W. Let's express L in terms of W. Divide both sides of the following equation by 2: 40 = 2 L + 2 W. We get 20 = L + W. Thus, L = 20 - w.

Then the area of the rectangle is A = ( 20 - W)*W.

Multiply this out. Your result will be a quadratic equation. Graph this quadratic equation (in other words, graph the function that represents the area of the rectangle). For which W value is the area at its maximum?

Alternatively, find the vertex of this graph: remember that the x- (or W-) coordinate of the vertex is given by

W = -b/(2a), where a is the coefficient of W^2 an b is the coefficient of W in your quadratic equation.

Finally, substitute this value of W into your quadratic equation, to calculate the maximum area.

You might be interested in

Enter the missing values in the area model to find –3(5.5n - 1) 5.5n -1 -3 According to the model above, -3(5.5n - 1)

Elena-2011 [213]

Answer:

“Information science is the science and practice dealing with the effective collection, storage, retrieval, and use of information. It is concerned with recordable information and knowledge, and the technologies and related services that facilitate their management and use.

Step-by-step explanation:

3 0

2 years ago

Please answer I’ll rate brainlyest

12345 [234]

Answer:

$5P3*6C4=60*15=900$

Step-by-step explanation:

$5P3$ refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;

$5P3=\frac{5!}{(5-3)!}$

The factorial of an integer n is evaluated as;

$n!=n*(n-1)*(n-2)*(n-3).......3*2*1$

Using this concept, the above expression can now be simplified as follows;

$5P3=\frac{5!}{2!}=\frac{5*4*3*2!}{2!}=5*4*3=60$

Therefore, the permutations of 5 items taken 3 at a time is 60.

The next expression, $6C4$ refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;

$6C4=\frac{6!}{4!(6-4)!}=\frac{6!}{4!*2!}=\frac{6*5*4!}{4!*2*1}=\frac{6*5}{2*1}=15$

Therefore, the combinations of 6 items taken 4 at a time is 15.

The final step is to evaluate the product;

$5P3*6C4=60*15=900$

3 0

3 years ago

Can you help me find the perimeter

stiv31 [10]

Answer:

The formula for the perimeter of a rectangle is P = (2*width) + (2*height)

this is basically saying, since opposite sides are equal in a rectangle,

Perimeter = 5 + 5 + 6 + 6, so P = 22ft

Step-by-step explanation:

6 0

3 years ago

To create an entry code, you must first choose 2 letters and then 2 single digit numbers. How many entry codes can you create?

ivann1987 [24]

Answer:

55600

Step-by-step explanation:

First times the number of possibilities of the amount of letters it could be so 26X26 as it is a non consecutive possibility that means both letters have the possibility to be the same. Then take the product of 26X26 and multiply it by the possibilities of the first number which is 10 then repeat that by again multiplying the product by 10 to represent the number of possibilities for the second number

3 0

3 years ago

Sterling has prepared the following two-column proof below. He is given that ZON 2 XLNO and he is trying to prove that OL 2 ON.

xeze [42]

What grade is this? can you maybe break it down

6 0

2 years ago