Answer:
y = -3
Step-by-step explanation:
Each side of an equilateral triangle will have a length that is 1/3 the perimeter. This triangle has sides of length 21/3 = 7, so ...
y + 10 = 7
y = 7 - 10
y = -3
This is consistent with the other given side measure ...
y^2 -2 = (-3)^2 -2 = 9 -2 = 7
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.
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.
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.
#SPJ3
The function is a line. As such, its domain and range is the whole real number set , and it has no horizontal nor vertical asymptotes.
Moreover, there's no constant term, so it's x and y intercept is the origin (0,0).
Answer:
(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.
Step-by-step explanation:
The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.
If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.
So the initial weight would occur at (0, 79.5) which is the positive y-intercept.
And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.
Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.
Cheers.
Answer:
Answer attached
Step-by-step explanation: