MTH 209 3 questions.
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1.Diagonal brace. The width of a rectangular gate is 2 meters
(m) larger than its height. The diagonal brace measures
square root 6 m. Find the width and height.
2.Foul ball. Suppose Charlie O'Brian of the Braves hits a
baseball straight upward at 150 ft/sec from a height of 5 ft.
a) Use the formula to determine how long it takes the ball
to return to the earth.
b) Use a graph to estimate the maximum
height reached by the ball.
3. Sharing cost. The members of a flying club plan to share
equally the cost of a $200,000 airplane. The members
want to find five more people to join the club so that the
cost per person will decrease by $2000. How many members
are currently in the club?
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Solution Summary
The solution helps go through algebra problems with regards to diagonal braces, foul balls and sharing costs.
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1. Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures square root 6 m. Find the width and height.
Answer...
Let the height be "x" meters
Then the width is "x+2" meters
Draw the diagonal = sqrt(6) meters
EQUATION:
Use Pythagoras to solve for "x":
x^2 + (x+2)^2 = [sqrt(6)]^2
2x^2 + 4x + 4 = 6
2x^2 + 4x -2 = 0
x^2 + 2x -1 = 0
Use the Quadratic Formula:
x = [-2 +- sqrt(4 -4*1*-1)]/2
x = [-2 +- sqrt(8)]/2
Positive solution:
x = [-2 + 2sqrt(2)]/2
x = [-1 + ...
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