Answer:
Step-by-step explanation:
Going side to side(horizontal) is always length and going up and down (vertical) width
When y varies inversely as x ⇒ y*x=k
y=27 and x=40 ⇒27*40=1080=k
y*10=1080
y=1080:10
y=108
The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
<h3>How to derive a sinusoidal expression</h3>
In this problem we need to find a <em>sinusoidal</em> expression that models the curve seen in the picture. The most typical <em>sinusoidal</em> model is described below:
f(x) = a · sin (b · x + c) + d (1)
Where:
- a - Amplitude
- b - Angular frequency
- c - Angular phase
- d - Vertical midpoint
Now we proceed to find the value of each variable:
Amplitude
a = - 2 - (-6.5)
a = 4.5
Angular frequency
b = 2π / T, where T is the period.
0.25 · T = 4 - 3
T = 4
b = 2π / 4
b = π / 2
Midpoint
d = - 6.5
Angular phase
- 2 = 4.5 · sin (π · 4/2 + c) - 6.5
4.5 = 4.5 · sin (π · 4/2 + c)
1 = sin (2π + c)
π = 2π + c
c = - π
The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
To learn more on trigonometric functions: brainly.com/question/15706158
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The expression representing the volume of the prism is given as:
Volume=[base area]*[height]
base area is the area of the pentagon;
The area of pentagon is given by:
Area of pentagon=a^2ntan(180/n)
a=apothem length
n=number of sides
Area=2.8^2*5tan(180/5)
Area=28.48=28.5 cm^2
Therefore the expression for the volume of the prism with height,h, will be:
volume=28.5h cm^3
