write the integer that represents a depth of 128 feet below sea level. then write the opposite of that integer.
1 answer:
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Answer:
a) see the plots below
b) f(x) is exponential; g(x) is linear (see below for explanation)
c) the function values are never equal
Step-by-step explanation:
a) a graph of the two function values is attached
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b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).
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c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.
In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.
Answer:
33 square units
Step-by-step explanation:
Assuming that each line on this grid increases by a value of one, the area of the polygon can be determined by breaking it down into a large rectangle and two smaller triangles.
<h3>Area of the rectangle</h3>The area of a rectangle is simply , where b represents the base and h represents the height.
Counting the size of each side, we can determine that they are 6 units for the base and 4 units for the height.
Substituting in the values, we get:
The area of the rectangle is 24 square units
<h3>Area of the triangles</h3>The area of a triangle is simply .
The base of each triangle is 3, and the height of each triangle is also 3.
Substituting in the values, we get:
The area of each triangle is 4.5 square units
<h3>Area of the polygon</h3>To get the area of the polygon, we simply add up the area of the rectangle and both triangles
The total area of the polygon is 33 square units.