Write an equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9.
x =-.20752
step-by-step explanation:
4^(x+2)=12
4^(x+2)=12
take the log base 4 on each side
log 4 (4^(x+2) = log 4(12)
we know log b(a^y) = y log b (a)
(x+2) log 4(4) = log 4 (12)
x+2 = log 4 (12)
we know logb c = loga c/loga b
we want to convert to base 10 so a = 10
by default, we do not write the 10 c = 4 and b = 10
log4 10 = log 12/log 4
log4 10 = log 12/ log 4
x+2 = log 12/ log 4
subtract 2 from each side
x +2 -2 = log 12/ log 4 -2
x = 1.79248125 -2
x =-.20752
7.9m and 4.3°
step-by-step explanation:
let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ
for 3.5 south, y = -3.5
for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30
for 15 west, x = -15
total x = 8.2 * cos 30 – 15 ≈ -7.9
total y = -3.5 + 8.2 * sin 30 = 0.6
magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5
the magnitude is approximately 7.9 m
tan θ = y/x = 0.6/-7.9
the angle is approximately 4.3˚ north of west
5: 20
step-by-step explanation:
step-by-step explanation:
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