sketch a graph and write an equation for a sinusoidal function that has a period of 12 seconds, a maximim height of 8ft and a mi
nimim height of -4 ft. At a time t=0, the function's height is at its highest point.
1 answer:
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The amplitude of the function is half the difference between the maximum and minimum:
A = (8 -(-4))/2 = 6
The multiplier of t is (2π)/period, so is ...
B = (2π)/12 = π/6
The vertical offset is the average of the minimum and the maximum:
D = (8 +(-4))/2 = 2
The peak is at t=0, so the cosine function is the appropriate choice.
__
Then the function is ...
f(t) = Acos(Bt) +D
f(t) = 6cos(πt/6) +2
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Answer:
The area of the shape is .
Step-by-step explanation:
The shape in the graph is a composite figure is made up of several simple geometric figures such as triangles, and rectangles.
Area is the space inside of a two-dimensional shape. We can also think of area as the amount of space a shape covers.
To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together.
First separate the composite shape into three simpler shapes, in this case two rectangles and a triangle. Then find the area of each figure.
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
The area of the first rectangle is
The area of the second rectangle is
The area of a triangle is given by the formula where <em>b</em> is the base and <em>h</em> is the height of the triangle.
The area of the triangle is
Finally, add the areas of the simpler figures together to find the total area of the composite figure.