Given:
To find:
The function .
Solution:
we have,
Put g(x)=y.
Interchange x and y.
Isolate y.
Substitute .
Therefore, the correct option is (3).
Mary’s dog weighs 185 pounds. Her dog needs to lose between 9 and 15 pounds. Between what two percentages, rounded to the neares
1 answer:
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First, let's use the given information to determine the function's amplitude, midline, and period.
Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.
Finally, we should determine the parameters of the function's formula by considering all the above.
Determining the amplitude, midline, and period
The midline intersection is at y=5 so this is the midline.
The maximum point is 1 unit above the midline, so the amplitude is 1.
The maximum point is π units to the right of the midline intersection, so the period is 4 * π.
Determining the type of function to use
Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function.
This means there's no horizontal shift, so the function is of the form -
a sin(bx)+d
Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.
The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1.
The midline is y=5, so d=5.
The period is 4π so b = 2π / 4π = 1/2 simplified.
= Solution
Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.
Finally, we should determine the parameters of the function's formula by considering all the above.
Determining the amplitude, midline, and period
The midline intersection is at y=5 so this is the midline.
The maximum point is 1 unit above the midline, so the amplitude is 1.
The maximum point is π units to the right of the midline intersection, so the period is 4 * π.
Determining the type of function to use
Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function.
This means there's no horizontal shift, so the function is of the form -
a sin(bx)+d
Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.
The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1.
The midline is y=5, so d=5.
The period is 4π so b = 2π / 4π = 1/2 simplified.
Answer:
Step-by-step explanation:
To make "n" the subject of the formula, rearrange the formula so it begins with " n = "
To isolate the variable "n", you need to inverse the other terms on that side of the equation where "n" really is.
=> m = 5n - 21
- <em>there's</em><em> </em><em>a</em><em> </em><em>"</em><em>-21</em><em>"</em><em> </em><em>next</em><em> </em><em>to</em><em> </em><em>"</em><em>5n</em><em>"</em><em>,</em><em> </em><em>inverse</em><em> </em><em>of</em><em> </em><em>subtraction</em><em> </em><em>is</em><em> </em><em>addition</em><em>,</em><em> </em><em>so</em><em> </em><em>add</em><em> </em><em>21</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>equation</em><em>.</em><em> </em>
=> m + 21 = 5n <u>-</u> <u>21</u> + <u>21</u>
=> m+ 21 = 5n
- <em>There's</em><em> </em><em>also</em><em> </em><em>a</em><em> </em><em>5</em><em> </em><em>attached</em><em> </em><em>to</em><em> </em><em>n</em><em>,</em><em> </em><em>that</em><em> </em><em>means</em><em> </em><em>the</em><em> </em><em>multiplication</em><em> </em><em>of</em><em> </em><em>n</em><em> </em><em>with</em><em> </em><em>5</em><em>,</em><em> </em><em>the</em><em> </em><em>inverse</em><em> </em><em>of</em><em> </em><em>multiplication</em><em> </em><em>is</em><em> </em><em>division</em><em>,</em><em> </em><em>so</em><em> </em><em>dividing</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>equation</em><em> </em><em>by</em><em> </em><em>5</em>
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