Answer:
Step-by-step explanation:
<u>Let the cost of daylilies = d and ivy = i, then we have below equations:</u>
- d + 12i = 114
- 10d + 10i = 150
<u>Simplify the second equation:</u>
<u>Subtract the second equation from the first:</u>
- d - d + 12i - i = 114 - 15
- 11i = 99
- i = 9, ivy costs $9
<u>Now find d:</u>
- d = 15 - 9 = 6, daylilies cost $6
The height of the <em>water</em> depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.
<h3>How to derive equations for periodical changes in time</h3>
According to the two cases described in the statement, we have clear example of <em>sinusoidal</em> model for the height as a function of time. In this case, we can make use of the following equation:
h = a + A · sin (2π · t/T + B) (1)
Where:
- a - Initial position, in meters.
- A - Amplitude, in meters.
- t - Time, in hours or seconds.
- T - Period, in hours or seconds.
- B - Phase, in radians.
Now we proceed to derive the equations for each case:
Water depth (u = 20 m, l = 8 m, a = 14 m, T = 12 h):
A = (20 m - 8 m)/2
A = 6 m
a = 14 m
Phase
20 = 14 + 6 · sin B
6 = 6 · sin B
sin B = 1
B = π/2
h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.
Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):
A = (40 m - 2 m)/2
A = 19 m
a = 21 m
Phase
2 = 21 + 19 · sin B
- 19 = 19 · sin B
sin B = - 1
B = - π/2
h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.
Lastly, we proceed to graph each case in the figures attached below.
To learn more on sinusoidal models: brainly.com/question/12060967
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The last one is the right answer
<em>1.6/3 = 16/30 = 8/15 </em>
<em> Volume Ratio: 512:27
∙•❁I hope this helps!❁•∙ </em>
Answer:
531.73
Step-by-step explanation: