Which is equivalent to 3log(x) + 4log(y)? A) log(12xy) B) log(x3 y4) C) log( 3x 4y ) D) log( x3 y4 )
1 answer:
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Answer:
x ≈ 8.99
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.
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<h3>setup</h3>The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(angle of elevation) = (tower height)/(length of shadow)
Solving for the length of shadow, we have ...
length of shadow = (tower height)/tan(angle of elevation)
The difference in shadow lengths is 2x for the two different angles, so we have ...
2x = 24.57/tan(30°) -24.57/tan(45°)
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<h3>solution</h3>Dividing by 2 and factoring out the tower height, we have ...
x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)
x ≈ 8.993244
The value of x is about 8.99.
Now... both are traveling in opposite direction
after some time "t", they cover altogether a distance of 65 miles
let's say, the one at 12mph cover a distance of "d",
thus
the other biker, cover the difference of that and 65, or 65-d
whatever "d" is
now, the time for both, is the exact same time,
since by the time they've covered 65 miles, let's say is
11:30am, is the same 11:30am for the first biker as well
as the second biker
now... do you see the substitution there?
so.. do that, and solve for "t"
after some time "t", they cover altogether a distance of 65 miles
let's say, the one at 12mph cover a distance of "d",
thus
the other biker, cover the difference of that and 65, or 65-d
whatever "d" is
now, the time for both, is the exact same time,
since by the time they've covered 65 miles, let's say is
11:30am, is the same 11:30am for the first biker as well
as the second biker
now... do you see the substitution there?
so.. do that, and solve for "t"