. A field will be made in the shape of a rectangle with an area of 400 square meters. One side of the field is along a river and a fence will be built along the other three sides. A brick wall perpendicular to the river will be built to divide the field into two equal halves. the wall costs $20 per meter and the fence costs $10 per meter to build. what is the lowest possible cost to build such a field?
Answers
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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Answers
Answer:
True
Step-by-step explanation:
A number and its reciprocal have the same sign.
The cosecant is the reciprocal of the sine.
Therefore, the cosecant has the same sign as the sine.
Final answer:
The signs of the cosecant function will change in each quadrant, making the statement false.
Explanation:
The statement is false. The cosecant function, csc(x), is defined as the reciprocal of the sine function, so csc(x) = 1/sin(x). Since the sine function changes sign between the different quadrants, the cosecant function will also change sign in each quadrant. In the 1st and 3rd quadrants, both the sine and cosecant functions have positive values. In the 2nd and 4th quadrants, both functions have negative values.
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+ 34x+ 30) = (2x+4)
Answers
Answer:
2 = 0
This equation has no solution.
Step-by-step explanation:
A a non-zero constant never equals zero
find f(10)
Answers
10= x2 - 7x -13
10= -5x -13
-10 -10
5x = -23
Answer is X = -23/5 or -4.6
Final answer:
To find f(10) for the function f(x) = x² - 7x - 13, you replace x with 10. The result is 17.
Explanation:
The function provided is f(x) = x² - 7x - 13. To find f (10), you would need to substitute x in the function with 10. Therefore, f (10) = 10² - 7*10 - 13 which equals 100 - 70 - 13 = 17.
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B. Bonnie can spend $10 on a shirt, $20 on 2 shirts, and $20 on 3 shirts.
C. Maria can spend $15 on 1 shirt, $15 on 2 shirts, or $30 on 3 shirts.
D. Natalie can spend $15 on 1 shirt, $30 on 2 shirts, or $45 on 3 shirts.
Answers
The equation is y = 15x , where y is the total cost of the shirt and x is the number of shirts
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the total cost of the shirt be represented as y
Let the number of shirts be represented as x
Now , the cost of 1 shirt = $ 15
The cost of 2 shirts = $ 30
And , the cost of 3 shirts = $ 45
So , the equation will be y = 15x , where x is the number of shirts
Hence , the equation is y = 15x , where y is the total cost of the shirt
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Answer:
D.
Step-by-step explanation:
the simplest form of this equation would be that (x) is the number of shirts and 15 would be your (y). (1)15=15, (2)15=30 and so on.
b. Find P(X ≤ 2).
c. Find P(X > 3).
d. Find μX.
e. Find σX
Answers
Answer:
a) X 1 2 3 4 5
P(X) 0.7 0.15 0.10 0.03 0.02
b)
c)
d)
e)
Step-by-step explanation:
Part a
From the information given we define the probability distribution like this:
X 1 2 3 4 5
P(X) 0.7 0.15 0.10 0.03 0.02
And we see that the sum of the probabilities is 1 so then we have a probability distribution
Part b
We want to find this probability:
Part c
We want to find this probability
And for this case we can use the complement rule and we got:
Part d
We can find the expected value with this formula:
Part e
For this case we need to find first the second moment given by:
And we can find the variance with the following formula:
And we can find the deviation taking the square root of the variance:
Answers
C = 9b + 3k.