Answer:
Step-by-step explanation:
Considering the equation
Sin(5x) = ½
5x = arcSin(½)
5x = 30°
Then,
The general formula for sin is
5θ = n180 + (-1)ⁿθ
Dividing throughout by 5
θ = n•36 + (-1)ⁿ30/5
θ = 36n + (-1)ⁿ6
The solution range is
0<θ<2π which means 0<θ<360
First solution
When n = 0
θ = 36n + (-1)ⁿθ
θ = 0×36 + (-1)^0×6
θ = 6°
When n = 1
θ = 36n + (-1)ⁿ6
θ = 36-6
θ = 30°
When n = 2
θ = 36n + (-1)ⁿ6
θ = 36×2 + 6
θ = 78°
When n =3
θ = 36n + (-1)ⁿ6
θ = 36×3 - 6
θ = 102°
When n=4
θ = 36n + (-1)ⁿ6
θ = 36×4 + 6
θ = 150
When n=5
θ = 36n + (-1)ⁿ6
θ = 36×5 - 6
θ = 174°
When n = 6
θ = 36n+ (-1)ⁿ6
θ = 36×6 + 6
θ = 222°
When n = 7
θ = 36n + (-1)ⁿ6
θ = 36×7 - 6
θ = 246°
When n =8
θ = 36n + (-1)ⁿ6
θ = 36×8 + 6
θ = 294°
When n =9
θ = 36n + (-1)ⁿ6
θ = 36×9 - 6
θ = 318°
When n =10
θ = 36n + (-1)ⁿ6
θ = 36×10 + 6
θ = 366°
When n = 10 surpasses the θ range
Thus, the solutions range from n =0 to n=9
Therefore, there are 10 solutions within the interval 0<θ<2π
The total number of individuals surveyed is 280. From the survey results, 65% were satisfied with the park's condition. Given that this satisfied group represents 182 people, we can calculate the overall survey population using this information.
Response:
The equation provided is e=\frac{17}{20}d, where e represents euros and d denotes the equivalent value in U.S. Dollars.
We aim to determine the number of euros for 1 U.S. Dollar.
Substituting d=1 in the above equation
results in
e=\frac{17}{20}(1)
Simplifying gives us
e=\frac{17}{20}
By dividing 17 by 20, we get 0.85.
Thus, 0.85 euros are equivalent to 1 U.S. Dollar.
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Step-by-step explanation:
Response:
The answer to the inquiry is 8 hours.
Step-by-step breakdown:
Information
Ladder length = 200 cm
Distance between rungs = 20 cm
Tide rise rate = 10 cm/h
Fifth rung =?
Procedure
1.- Determine the total height the tide must reach
Height = 20 cm x 4
= 80 cm as the first rung is touching the water.
2.- Calculate the time needed
Rate = distance / time
-Solve for time
Time = distance / rate
-Substitute values
Time = 80 cm / 10 cm/h
-Final outcome
Time = 8 hours.
<span>The volume of a rectangular prism is
V = l · w · h
V = 252 cm3
h = 3 cm
l = 5 + W
Let W = x, therefore l = 5 + x
V = (5 + x) * x * 3 = 252
3x</span><span>^2 + 15x = 252 cm3
</span><span>
This equation models the volume of the tray based on its width, x, in centimeters.</span>
3x^2 + 15x = 252 cm3<span>
</span>
for a width of 7.5 cm
3x^2
+ 15x = 3*(7.5)^2 + 15*7.5 = 281.25 cm3
<span>281.25 > 252 </span><span> </span>
<span>Thus, a width of 7.5 cm is not possible.</span>
