(repost) Please help! It involves inequalities! Also please include a number line.
1 answer:
Answer:
-5 ≤ x
Step-by-step explanation:
2(x -3) -5x ≤ 9 . . . . . given
2x -6 -5x ≤ 9 . . . . . . eliminate parentheses
-3x -6 ≤ 9 . . . . . . . . combine like terms
-6 ≤ 9 +3x . . . . . . . add 3x
-15 ≤ 3x . . . . . . . . subtract 9
-5 ≤ x . . . . . . . . . divide by 3
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The point x=-5 is included in the solution set, so there is a sold dot at that point. The rest of the solution set is values of x that are greater than that value, so the number line is shaded to the right of that point. Your number line should show an arrow at the right end of the graph to indicate it extends that direction indefinitely. (My graphing program doesn't draw arrows easily.)
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<em>Additional comment</em>
Perhaps the most straightforward way to solve this would have been to add 6 instead of 3x. That would give ...
-3x ≤ 15
Then dividing by -3 would give x. That operation would reverse the inequality symbol (because the divisor is negative). Then you would have ...
x ≥ -5
Either way works. We judge it to be less confusing when we don't have to change the direction of the inequality symbol.
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Answer:
Step-by-step explanation:
The velocity of an object moving on a line is given by the function:
And we want to determine the velocity of the object when its acceleration is 3.
So, we will need to determine our acceleration function. Remember that acceleration is simply the derivative of speed. Therefore, our acceleration function a(t) will be:
Differentiate. We will use the chain rule on the second part. Hence, our acceleration function is:
We want to find the velocity when the acceleration is 3.
So, let’s set a(t) equal to 3 and determine at what time t our function equals 3. Hence:
Divide both sides by 3:
Take the inverse cosine of both sides.
Remember that cosine is 1 for every 2π. Hence:
Where n is an integer.
Divide both sides by 3. Therefore, our solutions are:
However, our domain was π/2≤x≤π.
Hence, we can test values of n such that it is within our domain.
Testing for n=0, 1, and 2, we see that:
However, the only solution that is within our domain is the second solution.
Hence, the acceleration is 3 when the t is 2π/3.
Therefore, our velocity at that time t is: