Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
The trick here is to not use sin and cos at all.
The -13/15 is the x coordinate of a line from the origin to the unit circle (the line with angle theta). That happens to be the cos(theta).
The y coordinate is the sin(theta).
You can draw this as a triangle where x^2 + y^2 = 1.
So y = √(1 - (13/15)^2) ≈ 0.49889. But your exact answer should be:
Answer:
17.3
Step-by-step explanation:
a² = b² + c² - 2bc cos A
t² = 11² + 14² - 2(11)(14) cos 87
t² = 121 + 196 - 308 (.052336)
t² = 300.88
t = 17.3
Y^9-y^3 can also be written as y^9-y^3=x
so it is also equivalent to x+y^3=y^9
and x-y^9=-y^3