Solve the Problem $( a , b )$ And $( c , d )$

question 147

Multiple Choice

Solve the problem.
-Let $( a , b )$ and $( c , d )$ be two points in the first quadrant, and let $\theta$ be the angle between the line segment connecting $( a , b )$ with the origin and the line segment connecting $( c , d )$ with the origin. It can be shown that
$\cos \theta = \frac { a c + b d } { \sqrt { \left( a ^ { 2 } + b ^ { 2 } \right) \left( c ^ { 2 } + d ^ { 2 } \right) } }$
Find $\theta$ if $a = 7 , b = 5 , c = 2$ , and $d = 8$ . Give your answer in degrees rounded to the nearest hundredth.

• A) \(111.50 ^ { \circ }\)
• B) \(40.43 ^ { \circ }\)
• C) \(55.68 ^ { \circ }\)
• D) \(78.62 ^ { \circ }\)

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Definitions:

Midpoint Formula

A mathematical equation used to find the exact center point between two points on a line segment by averaging the x-coordinates and y-coordinates.

Price Elasticity

The measure of how much the quantity demanded of a good responds to a change in the price of that good.

Midpoint Formula

A method for calculating the elasticity of demand or supply by using the average percentage change in both quantity and price.

Price Elasticity

This measures how sensitive the quantity demanded of a good or service is to a change in its price.