5. Positive
6. Negative
7. Negative
8. Positive
9. No correlation
10. Positive
11. No correlation
12. Positive
Answer:
a) 240°
b) 30°
c) 225°
Step-by-step explanation:
To solve these equations you have to use the inverse of the given trigonometric functions. The inverse of <em>sin</em> is <em>arcsin</em>, and the inverse of <em>tan </em>is <em>arctan. </em>Instead of giving an angle, what is its sine?, the question is: given a sine, what is the angle?.
a)
sin(θ) = -√3/2
θ = arcsin(-√3/2)
θ = -60°
Given the periodicity of sine function, sin(-60°) is equivalent to sin(240°) (-60+180) and sin(300°) (-60+360).
b)
tan(θ) = 1/√3
θ = arctan(1/√3)
θ = 30°
c)
csc means cosecant, by definition:
csc(θ) = 1/sin(θ)
csc(θ) = -√2
1/sin(θ) = -√2
sin(θ) = -1/√2
θ = arcsin(-1/√2)
θ = -45° or 360-45 = 315° or 180+45 = 225°
Answer:
y=2
Step-by-step explanation:
9(y-2)-8y=-16
9y-18-8y=-16
9y-8y=-16+18
y=2
Hope this helps!
Answer:
The sidewalk is 2 feet wide
Step-by-step explanation:
The area of the sidewalk is given as 80 square feet
The length and width of pool
including side walks will be;
10 + 2x and 6 + 2x
To get the area of the side walk
That will be area of total minus area of the pool
That will be ;
(10 + 2x)(6 + 2x) - 10(6) = 80
60 + 12x + 20x + 4x^2 - 60 = 80
4x^2 + 32x -80 = 0
x^2 + 8x -20
x^2 + 10x - 2x - 20 = 0
x(x + 10) -2(x + 10) = 0
(x-2)(x + 10) = 0
x = 2 or -10
since width cannot be negative;
The sidewalk is 2 feet wide
