Given that the integral is given as , Hence, we are required to find the area under the graph where t is between 0 and 12. The correct answer is 2 (Option A) See the explanation below.
<h3>What is an integral?</h3>
An integral is a function of which a given function is the derivative, that is, when differentiated, it returns that function, and it can express the area under the curve of a graph of the function.
Hence the areas under the graph for the above function are given as:
12 + 6 + 2 + (-2) + (-16)
= 20-18
= 2
Notice that the following figures were arrived at by dividing the areas under the graph into common geometric shapes and deriving their area.
For example, the first three positive values were derived by dividing the positive part of the graph into two triangles and a rectangle.
The length of the rectangle is 6 while its height is 2
Area of a rectangle is L x W
= 6 * 2
= 12
It is to be noted that the areas under the curve are negative hence the negative results. See the attached image.
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First half is negative and second is positive
Answer:
The share price increased by $40
Step-by-step explanation:
<u><em>In the first year: (t = 1)</em></u>
=> V =
=>
=>
=> V = $ 24.95
<em><u>In the 3rd Year: (t = 3)</u></em>
=>
=>
=>
=> V = 2.95 + 62
=> V = $64.95
<u><em>The Share Price increased by:</em></u>
=> $64.95-$24.95
=> $40
The share price increased by $40
Answer:
The distance between 4 and 7 is : 3
Answer:
y = 1/2sin(x) - 2
Step-by-step explanation:
Since 2 is subtracted from the end of the function, the graph will be shifted down 2 units. The parent function y = sin(x) goes through the origin, (0, 0); this means the y-intercept of this graph will be at (0, -2).
Additionally, since the function has been stretched horizontally, we know it has been multiplied by a fraction. This means it must be y = 1/2sin(x) - 2.