Mrs.Peterson dropped a ball from the top of a tower. At the same time, her son, Drake, launches a rocket from a different level
2 answers:
9514 1404 393
Answer:
- two solutions: t = -4, t = 4
- t = -4 is not reasonable
- 4 seconds
Step-by-step explanation:
A graphing calculator shows the two solutions to be ...
(t, h) = (-4, 18) and (4, 2)
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The two heights will be equal when ...
p(t) = b(t)
-2t +10 = -t^2 -2t +26
t^2 -16 = 0 . . . . subtract the right side expression
(t -4)(t +4) = 0 . . . factor the difference of squares
t = 4 or -4 . . . . values of t that make the factors zero
At these times, the heights will be ...
p(t) = -2{4, -4} +10 = {-8, 8} +10 = {2, 18}
The solutions are ...
(t, height) = (-4, 18) and (4, 2).
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We generally discount solutions for negative time, because we start counting time when the objects are launched. t = -4 is an extraneous solution.
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The rocket and ball reach the same height after 4 seconds.
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Answer: First option
Step-by-step explanation:
By definition, the horizontal shift depends on the value of <em>h </em>and the vertical shift depends on the value of <em>k</em><u>.</u>
indicates that the function if shifted to the right <em>h </em> units.
indicates that the function if shifted to the left <em>h </em> units.
indicates that the function if shifted down <em>k </em> units.
indicates that the function if shifted up <em>k </em> units.
Then:
If <em>h </em>is positive, the graph will shift to the right.
If <em>k </em>is negative, the graph will shift down.
As you can see in the graph, the function is shifted 4 units to the right and 2 units down. Therefore g(x) has the form:
Where:
Step-by-step explanation:
2(x-3)=5(x-3)+10
=> 2x - 6 = 5x - 15 + 10
=> -6 + 15 -10 = 5x - 2x
=> 5x -2x = 15 - 6 - 10
=> 3x = 15 - 16
=> 3x = -1