Answer:
x = 500 yd
y = 250 yd
A(max) = 125000 yd²
Step-by-step explanation:
Let´s call x the side parallel to the stream ( only one side to be fenced )
y the other side of the rectangular area
Then the perimeter of the rectangle is p = 2*x + 2* y ( but only 1 x will be fenced)
p = x + 2*y
1000 = x + 2 * y ⇒ y = (1000 - x )/ 2
And A(r) = x * y
Are as fuction of x
A(x) = x * ( 1000 - x ) / 2
A(x) = 1000*x / 2 - x² / 2
A´(x) = 500 - 2*x/2
A´(x) = 0 500 - x = 0
x = 500 yd
To find out if this value will bring function A to a maximum value we get the second derivative
C´´(x) = -1 C´´(x) < 0 then efectevly we got a maximum at x = 500
The side y = ( 1000 - x ) / 2
y = 500/ 2
y = 250 yd
A(max) = 250 * 500
A(max) = 125000 yd²
Answer:
B
Step-by-step explanation:
The chances of the first student walking to school is 7/30.
Without replacement, there are 29 students left. Hence the chance of the second student walking to school is 6/29 of the original 7/30 chance.
Answer:
102 an hour
Step-by-step explanation:
all you do is add all of them together
Answer:
This case has NO solutions.
Step-by-step explanation:
Notice that you are in a case of an obtuse triangle (one of its angles is larger than 90 degrees), the side opposite to the obtuse triangle is shorter than the side adjacent to the angle, so no actual triangle can be formed.
This can be found by simply trying to apply the Law of Sines to solve for the value of angle "B" opposite to side "b":
As shown above, we get an impossible mathematical condition (also call an absurd), since the sine of an angle cannot give a value larger than 1 (one).
Therefore, there is no angle we can find to build a triangle with the given data.
Answer:
m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.
Step-by-step explanation:
Given,
Total cost of maths book and novel = $54
Let,
Cost of maths book = m
Cost of novel = n
According to given statement;
m+n=54 Eqn 1
the price of the math textbook, m, is $8 more than 3 times the price of the novel
m = 3n+8 Eqn 2
m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.
Step-by-step explanation:
