PLEASE HELP. D: !!!!
1 answer:
Answer:
- 52 seconds
- 7093 feet
Step-by-step explanation:
This is the kind of problem that is most easily solved graphically, because the solution point coordinates give both the time and the altitude.
The attached graph shows the planes both arrive at the altitude of 7093 feet after 52 seconds.
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The equations for altitude in feet (y) as a function of time in seconds (x) are ...
y = 3687 +65.5x . . . . . plane A
y = 5000 +40.25x . . . plane B
Subtracting the second equation from the first gives . . .
0 = -1313 +25.25x
x = 1313/25.25 = 52 . . . . . . . add 1313 and divide by the x-coefficient
y = 3687 +65.5(52) = 3687 +3406 = 7093
After 52 seconds both planes have an altitude of 7093 feet.
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Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
