Explanation: The sum<span> of the measure of the </span>internal<span> angles of any triangle is 180o . In a right angled triangle, one angle will be 90o . Since we know the measure of one of the other acute (less than 90o ) angles, we subtract the </span>sum<span> of the two known angles from 180 to calculate the measure of the other acute angle.</span>
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

If I understand the problem correctly
The blank on the left would be 14
and the blank on the top would be 350
104.818891427
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