Assignment:
Q1. Diameter of a circle. If the diameter of a circle is 1.3 x10^-12 meters, then what is its radius?
Q2. 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.
Q3. 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?
Q4. 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.
Q5. Selling shirts. If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000 - 100p shirts at a tournament.
Q6. 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.
Q7. 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%.
Q8. 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.
Provide complete and step by step solution for the question and show calculations and use formulas.