In a 45 - 45 - 90 right triangle, the hypotenuse is √2 · legs = hypotenuse, so legs= and to rationalize the denominator all we have to do is multiply the numerator and denominator by √2.
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How many different 4 digit numbers can be formed using only digits 1,2,3 and 4 given that they contain each of these digits as m
1 answer:
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Answer:
19/13 ft/s ≈ 1.4615 ft/s
Step-by-step explanation:
It may be convenient to choose the time reference as the instant where we want to compute dh/dt. That is, we want to find h'(0).
If w represents the height of the ladder on the wall, we can write two relations: one for w, and one for h, the height of the firefighter.
w² + x² = 13² . . . . . . where x=5+3t is the distance of the foot of the ladder from the wall
h = w·(4 +2t)/13 . . . . where 4+2t is the length along the ladder that the firefighter has climbed
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Differentiating with respect to time, we get ...
2ww' +2xx' = 0
w' = (-x/w)x' = -3x/w . . . . . solving for w'
and ...
h' = w'(4 +2t)/13 +w(2/13) . . . . . . . using the product rule
h' = (-3x/w)(4 +2t)/13 + w(2/13) . . . . filling in w'
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At t=0, x=5, w=12. and we have ...
h' = (-3·5/12)(4/13) +(12·2)/13 = 19/13 ≈ 1.4615
dh/dt = 19/13 ft/s ≈ 1.4615 ft/s at the given instant
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The attachment shows a solution using a graphing calculator. It gives the same result.
