Here you go, good luck
Let f(x) = x2 - 16 and g(x) = x + 4. Find (f = g)(x).
2 answers:
Answer:
,
Step-by-step explanation:
Given,
Find,
÷
1. Approach
The easiest way to solve the problem is to set up the problem as a fraction. Then factor both the numerator (value on top of the fraction bar), and the denominator (value under the fraction bar). After doing so, simplify the fraction. Remember to take note of the value eliminated from the denominator, for this value will serve as the domain of the expression.
2. Divide the two functions
The two given functions are the following:
Set up the division problem,
Substitute,
Factor,
Simplify,
3. Find the domain of the expression
The value that was removed from the denominator is the following:
Set this equal to zero and solve,
This expression is true as long as ().
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Answer: Approximately 9.43 meters
The more accurate version is 9.4339811320566 but that's not exact.
This is exact magnitude is sqrt(89)
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Explanation:
Let's draw an xy grid for this. Place the starting point at (0,0) which I'll call point A. Now let's say the mouse goes east 15 meters. That would move it to (15,0) which is marked as point B. Refer to the diagram below.
From point B, we move to C which is at (15,8). So the mouse has gone 8 meters north. It might help to turn the page so that the east direction is facing completely north, and then look to the left and you'll see "north". In other words, each 90 degree left turn is a 90 degree counterclockwise turn.
After doing another 90 degree counterclockwise turn, the mouse will move 10 meters westward. It moves from C(15,8) to D(5,8). Point D is the final position of the mouse.
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A(0,0) was the initial position and D(5,8) is the final position
The vector v is
v = <5,8>
This is because we basically are saying "the mouse ultimately moved 5 meters east and 8 meters north" when going from start to finish. We're ignoring the intermediate stops along the way.
------------------------
Recall that for any vector of the form
v = <a,b>
the magnitude of that vector is
|v| = sqrt(a^2+b^2)
this is the length of the vector based on the pythagorean theorem.
Applying this formula gets us
|v| = sqrt(5^2+8^2)
|v| = sqrt(89)
|v| = 9.43398 approximate
This represents the straight line distance from start to finish, where we ignore any intermediate stops. So this isn't the distance the mouse travels (since it goes from A to B, to C to D). Instead, it's the distance it would travel if it wanted to take the shortest path from A to D.
