Word problems on linear and quadratic equations

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114. Diameter of a circle. If the diameter of a circle is
1.3 x10^-12 meters, then what is its radius?

94. Perimeter of a rectangle. The width of a rectangular playground
is 2x x- 5 feet, and the length is 3x + 9 feet. Write a
polynomial P(x) that represents the perimeter and then
evaluate this perimeter polynomial if x is 4 feet.

98. Height difference. A red ball and a green ball are
simultaneously tossed into the air. The red ball is given an
initial velocity of 96 feet per second, and its height t seconds
after it is tossed is -16t^2 + 96t feet. The green ball
is given an initial velocity of 80 feet per second, and its
height t seconds after it is tossed is -16t^2 + 80t feet.
a) Find a polynomial D(t) that represents the difference in
the heights of the two balls.
b) How much higher is the red ball 2 seconds after the
balls are tossed?
c) In reality, when does the difference in the heights stop
increasing?

79. Area. A roof truss is in the shape of a triangle with height
of x feet and a base of 2x +1 feet. Write a polynomial A(x)
that represents the area of the triangle.

86. Selling shirts. If a vendor charges p dollars each for
rugby shirts, then he expects to sell 2000 - 100p shirts at
a tournament.

98. Area of a parallelogram. Find a trinomial A(x) that represents
the area of a parallelogram whose base is 3x + 2
meters and whose height is 2x + 3 meters.

96. Compounded semiannually. P dollars is invested at annual
interest rate r for 1 year. If the interest is compounded
semiannually, then the polynomial P (1+r/2)^2

represents the
value of the investment after 1 year. Rewrite this expression
without parentheses. Evaluate the polynomial if
P = $200 and r = 10%.

88. Perimeter of a rectangle. The perimeter of a rectangular
backyard is 6x + 6 yards. If the width is x yards, find a
binomial that represents the length.