Answer:
The value of Ф is 3π/2
Step-by-step explanation:
* Lets revise the angle Ф in the four quadrant
∵ r = √(x² + y²) ⇒ square the two sides
∴ x² + y² = r²
∵ r = 1
∴ x² + y² = 1
∵ cos² Ф + sin² Ф = 1
∵ x is the adjacent side to Ф and y is the opposite side to Ф
∴ x = cos Ф and y = sin Ф
- At point (1 , 0)
∵ x = 1 , y = 0
∴ cos Ф = 1 and sin Ф = 0
∵ The positive part of x-axis represents the angle 0 and 2π
∴ cos 0 and 2π are 1 and sin 0 and 2π are 0
- At point (0 , 1)
∵ x = 0 , y = 1
∴ cos Ф = 0 and sin Ф = 1
∵ The positive part of y-axis represent the angle π/2
∴ cos π/2 is 0 and sin π/2 is 1
- At point (-1 , 0)
∵ x = -1 , y = 0
∴ cos Ф = -1 and sin Ф = 0
∵ The negative part of x-axis represents the angle π
∴ cos π is -1 and sin π is 0
- At point (0 , -1)
∵ x = 0 , y = -1
∴ cos Ф = 0 and sin Ф = -1
∵ The negative part of y-axis represent the angle 3π/2
∴ cos 3π/2 is 0 and sin 3π/2 is 1
* For the value of Ф = 3π/2 is sin Ф = -1
Answer:
they each hike 2 miles
Step-by-step explanation:
Jeff: 15=1/2
*4 *4
60 min=2 miles
Lisa: 10=1/3
*6 *6
60 = 2
Answer:
Ok, we have a system of equations:
6*x + 3*y = 6*x*y
2*x + 4*y = 5*x*y
First, we want to isolate one of the variables,
As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:
(6*x + 3*y)/(2*x + 4*y) = 6/5
now we isolate one off the variables:
6*x + 3*y = (6/5)*(2*x + 4*y) = (12/5)*x + (24/5)*y
x*(6 - 12/5) = y*(24/5 - 3)
x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y
Now we can replace it in the first equation:
6*x + 3*y = 6*x*y
6*(0.5*y) + 3*y = 6*(0.5*y)*y
3*y + 3*y = 3*y^2
3*y^2 - 6*y = 0
Now we can find the solutions of that quadratic equation as:

So we have two solutions
y = 0
y = 2.
Suppose that we select the solution y = 0
Then, using one of the equations we can find the value of x:
2*x + 4*0 = 5*x*0
2*x = 0
x = 0
(0, 0) is a solution
if we select the other solution, y = 2.
2*x + 4*2 = 5*x*2
2*x + 8 = 10*x
8 = (10 - 2)*x = 8x
x = 1.
(1, 2) is other solution
Answer:
mmm but picture of the triangle
Step-by-step explanation: