Answer:
1/2x
Step-by-step explanation:
Answer:
Using Green's theorem we have:
int F.dr =
int int d/dx ((y^2-x^2)/(x^2+y^2)^2) - d/dy (2xy/(x^2+y^2)^2) =
(2x^3 - 6xy^2) / (x^2+y^2)^3 - (2x^3 - 6xy^2) / (x^2+y^2)^3 =
0
Therefore:
int F.dr = 0
Step-by-step explanation:
Each pound is 1.75 so if you multiply that by 8 you get $14
Answer is $14
A)
Let x represent the cost of 1 student, and y the cost of 1 teacher.
B)
In the first group, there's 25 students and 2 teachers. Their total cost is $97.50
So 25x + 2y = 97.50
In the second group, there's 32 students and 3 teachers. Their total cost is $127
So 32x + 3y = 127
We get the following system of equations:
25x + 2y = 97.50 (1)
32x + 3y = 127 (2)
C)
25x + 2y = 97.50 (1)
32x + 3y = 127 (2)
In equation (1)
25x + 2y = 97.50
25x + 2y - 2y = 97.50 - 2y
25x = 97.50 - 2y
25x / 25 = 97.50/25 - 2y/25
x = 3.9 - (2/25)y
In equation (2), let's replace x by its algebraic value
32x + 3y = 127
32(-2/25y + 3.9) + 3y = 127
11/25y + 124.8 = 127
11/25y + 124.8 - 124.8 = 127 - 124.8
11/25y = 2.2
(11/25y) / (11/25) = 2.2 / (11/25)
y = 5
x = -2/25y + 3.9
x = -2/25 * 5 + 3.9
x = 3.5
So the cost of each student is $3.5, and the cost of each teacher is $5.
Hope this helps! :)
Hello,
A=(-4,2)
B=(3,-5)
AB≡y-2=(x+4)(-7)/7==>y=-x-2
Slope of the perpendicular: 1
y-2=(x-1)1==>y=x+1 is the equation of the perpendicular.
Intersection: y=x+1 and y=-x-2 ==>(-3/2,-1/2)=Q
|PQ|²=(-1/2-2)²+(1+3/2)²=25/2
|PQ|=5√2/2≈3.5355339059....