If I have ten apples and 9 of games how would it take to have 9 apple
1 answer:
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First we need to find the slope of line k. Using the slope formula, we fill in accordingly: 
. The slope is -3/2. The slope of a line that is perpendicular to line k will have the opposite sign (so, positive) and will be the reciprocal of the line k's slope (so, 2/3). You could also say, more "mathematically legal", that the product of the slopes of perpendicular lines is -1, but it's easier to just say that they are opposite reciprocals. The slope you're looking for is 2/3. Choice 3 above.
For each curve, plug in the given point and check if the equality holds. For example:
(I) (2, 3) does lie on since 2^2 + 2*3 - 3^2 = 4 + 6 - 9 = 1.
For part (a), compute the derivative , and evaluate it for the given point
. This is the slope of the tangent line at the point. For example:
(I) The derivative is
so the slope of the tangent at (2, 3) is
and its equation is then
For part (b), recall that normal lines are perpendicular to tangent lines, so their slopes are negative reciprocals of the slopes of the tangents, . For example:
(I) The tangent has slope 7/4, so the normal has slope -4/7. Then the normal line has equation