Answer:
- The graph that represents a reflection of f(x) across the x-axis is the blue line on the picture attached.
Explanation:
The function f(x) is:
Which is an exponential function with these features:
- y-intercept: f(0) = 6(0.5)⁰ = 6(1) = 6
- multiplicative rate of change: 0.5 (the base of the exponential term), which means that it is a decaying function (decreasing)
- Horizontal asympote: y = 0 (this is the limit of f(x) when x approaches +∞.
The reflection of f(x) across the x-axis is a function g(x) such that g(x) = - f(x).
Thus, the reflection of f(x) across the x-axis is:
The features of that function are:
- Limit when x approaches - ∞: -∞ (thus the function starts in the third quadrant).
- y-intercerpt: g(0) = -6 (0.5)⁰ = -6(1)= - 6.
- Horizontal asympote: y = 0 (this is the limit of f(x) when x approaches +∞.
- Note that the function never touches the x-axis, thus the function increases from -∞, crosses the y-axis at (0, -6) and continous growing approaching the x-axis but never touchs it. So, this is an increasing frunction, that starts at the third quadrant and ends in the fourth quadrant.
With those descriptions, you can sketch the graph, which you can see in the figure attached. There you have the function f(x) (the red increasing line) and its reflection across the x-axis (the blue increasing line).
Based on dimensional analysis and unit conversion theory we conclude that an area of 359 square inches is equivalent to an area of 2.5 square feet.
<h3>How to apply dimensional analysis in unit conversion</h3>
In this question we need to convert a magnitude in a given unit to an <em>equivalent</em> magnitude with another unit. According to dimensional analysis, <em>unit</em> conversions are represented by the following expression:
y = A · x (1)
Where:
- x - Original magnitude, in square inches.
- y - Resulting magnitude, in square feet.
- A - Conversion factor, in square feet per square inch.
Dimensionally speaking, area is equal to the product of length and length:
[Area] = [Length] × [Length]
And a feet is equivalent to 12 inches. Now we proceed to convert the magnitude to square feet:
x = 359 in² × (1 ft/12 in) × (1 ft/12 in)
x = 359 in² × (1 ft²/144 in²)
x = 2.5 ft²
Based on dimensional analysis and unit conversion theory we conclude that an area of 359 square inches is equivalent to an area of 2.5 square feet.
To learn more on unit conversions: brainly.com/question/11795061
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Answer:
the answer is solved in the image below.
Step-by-step explanation:
Cassie has a serious talk with her father because he tells her that because she is a young African american she must basically be a slave for someone that is white.
Answer:
Step-by-step explanation:
<h2>This account can be modeled using the compound interest formula.</h2><h2>the compound interest formula is expressed as</h2>
Where
A =final amount = y
P=initial principal balance
= $300
r=interest rate = 16%= 0.16
t=number of time periods elapsed= x
Hence the equation to model his account balance/ final amount A (y) after time (x) years is
