Given:
t A = 2.4 h
t B = 4 h
v A = 22 + v B
Solution:
Distance A and distance B is the same, distance could be defined using formula d = v × t
d A = d B
(v A × t A) = (v B × t B)
plug in the numbers
v A × 2.4 = v B × 4
(22 + vB) × 2.4 = 4 vB
remove the parenthesis using distributive property
(22 × 2.4) + (2.4 × vB) = 4vB
52.8 + 2.4vB = 4vB
add like terms
52.8 = 4vB - 2.4vB
52.8 = 1.6vB
52.8/1.6 = vB
vB = 33
the speed of car B is 33 mph
vA = 22 + vB
vA = 22 + 33
vA = 55
the speed of car A is 55 mph
2sinxcosx - sin(2x)cos(2x) = 0
<span>Part I </span>
<span>The double angle identity for sine states that sin(2x) = 2sinxcosx </span>
<span>Thus we get: </span>
<span>sin(2x) - sin(2x)cos(2x) = 0 </span>
<span>Part II </span>
<span>sin(2x)(1 - cos(2x)) = 0 </span>
<span>Part III </span>
<span>Either sin(2x) = 0 or </span>
<span>1 - cos(2x) = 0 </span>
<span>=> cos(2x) = 1 </span>
<span>For sin(2x) = 0, this is true for </span>
<span>2x = n(pi) where n = 0, 1, 2, .... </span>
<span>x = n(pi/2) </span>
<span>For cos(2x) = 1, this is true for </span>
<span>2x = n(pi) where n = 0, 2, 4, .... </span>
<span>x = n(pi/2)
</span>
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