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yKpoI14uk [10]
2 years ago
12

A rectangular plot is enclosed by 200 m of fencing and has an area of A square metres. Show that :

Mathematics
2 answers:
denpristay [2]2 years ago
8 0
Let x be one side and l be the other side of the plot.
Perimeter = 2(x + l)
200 = 2(x + l)
l = 100 - x

Area of this rectangle:
A = (x)(l)
A = x(100 - x)
A = 100x - x²

To find the maximum value of the area, we differentiate with respect to x and equate to 0
dA/dx = 100 - 2x
0 = 100 -2x
x = 50
l = 100 - 50 = 50
This means the area will be maximized when the sides of the rectangle are equal; that is, when it is a square.
Tema [17]2 years ago
5 0
The perimeter of plot is 200 m. Denote sides of plot with x and y.

P=2(x+y)
\\200=2(x+y)
\\100=x+y
\\y=100-x

The area of plot is A=xy

a) A=xy=x(100-x)=100x-x^2

b) The area is maximal for A'=0
A'=(100x-x^2)'=100-2x
100-2x=0
\\100=2x
\\x=50
\\
\\y=100-x
\\y=100-50
\\y=50

The sides of rectangle are x=50 and y=50. Therefore, the area is maximal if the rectangle is a square.
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Rosa has 4 1/2 pounds of pizza dough. She uses 3/4 of a pound for one pizza. How many pizzas could be made from Rosa's dough?
IrinaK [193]
Amount of pizza dough that Rosa has = 4 1/2 pounds
                                                               = 9/2 pounds
Amount of dough required by Rosa to make 1 pizza = 3/4 pounds
Then
The number of pizza that can be made with 9/2 pounds of dough = 1/(3/4) * (9/2)
                                                                                                         = (4/3) * (9/2)
                                                                                                         = 2 * 3
                                                                                                         = 6
So Rosa can make 6 pizzas with the amount of dough she has. I hope the procedure is clear enough for you to understand. Glad to have helped you.



8 0
2 years ago
If we were to make a poset of the form (A, |), where is the symbol for divisibility, which of the following sets A would yield a
Marrrta [24]

Answer:

IV. A+{1, 2, 3, 6, 12}

Step-by-step explanation:

The set of natural numbers form a poset number under relation of > or =. The discrete variables are used to form a poset. The symbols for divisibility in poset form are when an integer is divided by the variable without integer. The correct answer is therefore 4th option.

5 0
2 years ago
A business school professor uses multiple choice tests. Each question on his exams has five possible answers which are assumed t
avanturin [10]

Answer:

a. The null hypothesis for this test is that the observed distribution is the same as uniform distribution

b. The degrees of freedom do you have for this test is 4

c.  The calculated value of the test statistic is 9.250

Step-by-step explanation:

a. According to the given data we can conclude that the null hypothesis for this test is that the observed distribution is the same as uniform distribution.

b. In order to calculate the degrees of freedom do you have for this test we would have to make the following calculation:

degrees of freedom=k-1

degrees of freedom=5-1

degrees of freedom=4

c. In order to calculate the value of the test statistic first we have to calculate the frecuency expected as follows:

expected frecuency=total observed frecuency/total number of category

expected frecuency=1,000/5

expected frecuency=200

Hence, to calculate the value of the test statistic we have to calculate the following formula:

x∧2=∑(fo-fe)∧2/fe

=(185-200)∧2/200+(230-200)∧2/200+(215-200)∧2/200+(180-200)∧2+(190-200)∧2

=9.250

The calculated value of the test statistic is 9.250

7 0
2 years ago
A student received an 82% on an exam. If there were 50 questions on the exam, which ratio would show the number of questions ans
solmaris [256]
Hello!

To solve this we have to find what 82% of 50 is

So we do 50 * 0.82 where 0.82 is 82% as a decimal.

This gives us 41

So the answer is D

Hope this helps!
8 0
2 years ago
Read 2 more answers
Kellianne lined up the interior angles of the triangle along line p below.
Tanzania [10]

Answer:1,4,5,2

Step-by-step explanation:

4 0
2 years ago
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