Tutor profile: Mihir B.
Subject: SAT II Mathematics Level 1
The volume of a rectangular solid is equal to 1000 m³. What is the volume of the solid if its length, width and height are increased by 50%
Let V be the volume, L be the length, W be the width and H be the height of the solid thus V = L x W x H = 1000 m³ If length is increased by 50% new length will equal L + 50%L = L + 0.5L = 1.5L Similarly the new W and H would be 1.5W and 1.5H respectively Now the new volume would be V = 1.5L x 1.5W x 1.5H = (1.5)³ x L x W x H = 3.375 x 1000 = 3,375 m³
Find tan Θ if sin Θ = 24/25 and Θ is in Quadrant II
cos²Θ = 1 - sin²Θ so cos²Θ = 1 - (24/25)² = 1 - (576/625) = 49/625 Since Θ is in quadrant II, cos Θ will be negative Thus cos Θ = -7/25 tan Θ = sin Θ / cos Θ = (24/25) / (-7/25) = -24/7
Find the slope of the line perpendicular to y = 5x - 9
The slope intercept form is y = mx + b where m is the slope of the line and b is the intercept on the y-axis So the slope of the given line is 5 If two lines are perpendicular, the product of their slopes equals -1 Thus is the slope of the given line is 5 and lets assume the slope of the perpendicular like is m, then m x 5 = -1 Thus m = (-1/5)
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