Answer: 0, π, 2π
Nevertheless, that is not an option. I see two possibilities: 1) the options are misswirtten, 2) the domain is not well defined.
If the domain were 0 ≤ θ < 2π, then 2π were excluded of the domain ant the answer would be 0, π.
Explanation:
1) The first solution, θ = 0 is trivial:
sin (0) - tan (0) = 0
0 - 0 = 0
2) For other solutions, work the expression:
sin(θ) + tan (-θ) = 0 ← given
sin (θ) - tan(θ) = 0 ← tan (-θ) = tan(θ)
sin(θ) - sin (θ) / cos(θ) = 0 ← tan(θ) = sin(θ) / cos(θ)
sin (θ) [1 - 1/cos(θ)] = 0 ← common factor sin(θ)
⇒ Any of the two factors can be 0
⇒ sin (θ) = 0 or (1 - 1 / cos(θ) = 0,
sin(θ) = 0 ⇒ θ = 0, π, 2π
1 - 1/cos(θ) = 0 ⇒ 1/cos(θ) = 1 ⇒ cos(θ) = 1 ⇒ θ = 0, 2π
⇒ Solutions are 0, π, and 2π
In fact if you test with any of those values the equation is checked. The only way to exclude one of those solutions is changing the domain.
Answer:
$837.5
Step-by-step explanation:
Step one:
given data
He makes a guaranteed salary of $400 per week
Commision on top of his base salary equal to 25% of his total sales for the week
Required
His total salary when he made sales of 25%
Step two
let us solve for 25% of $1750 made
=25/100*$1750
=0.25*$1750
=$437.5
Hence his total payment for the week will be
=$400+$437.5
=$837.5
Also, if the sales is $x his pay would be
let y be his pay
y=0.25x+400
C. 5x - 2y = 16 is your answer
plug in each point into the equation.
(2, -3)
x = 2, y = -3
5(2) - 2(-3) = 16
10 + 6 = 16
16 = 16 (True)
(4,2)
x = 4, y = 2
5(4) - 2(2) = 16
20 - 4 = 16
16 = 16 (True)
hope this helps
Answer:
Shape 1: 25.915
Shape 2: 102.85
Shape 3: 142
Step-by-step explanation:
For shape 1, you have to divide 7.1 to get half the width of the triangle. You get 3.55 from that, and then finding the triangle itself you have to do 7.3*3.55 to get 25.915. For shape 2, you first do the harder parts (the triangles) and since there is two of them we don't need to half the width of each triangle. But first to get the width, we need to do 20-17.4=2.6. But since there are 2 triangles we need to divide that by 2 to get 1.3. Then you multiply that by 5.5 to get the final area of both triangles which is 7.15. Next you simply find the rectangle which is 17.4*5.5=95.7. You add the triangles area to get 102.85. Finally for shape 3 you simply do 7.1*20=142.
