To find the height equation for the soccer ball's trajectory, we start with the acceleration due to gravity of g=9.81 m/s². Converting this gives us approximately 32.18 ft/s², rounded to 32 ft/s². The height formula is h = -g/2 * t² + vt + h0. Setting t=0 and h=0, we deduce that h0=0. Thus h=-16t² + vt applies. Given that the ball reaches 50 ft in 2.5 s, it reaches 25 ft in 1.25 s. Now, using 25=-16(1.25)² + v(1.25), we find velocity v=50/1.25, which simplifies to 40. Therefore, the height equation is h = -16t² + 40t.
one must evaluate 12 minus 5B9 as the base and remember to include the integer
Answer:
-1
Step-by-step explanation:
The roots of the polynomial are -2 and 3. According to the zero product property:
Given that the last term in the cubic equation is -6, it indicates that a must equal 1 as the product of -2 and 3 already results in -6. This can be verified by expanding the three factors:
Thus, following the zero product property, the final value is -1.
Hope this clarifies!
a) The original rectangle has dimensions of length = 5 and width = 4. b) The new rectangle has dimensions of length = 15 and width = 8. Step-by-step explanation: The formula for the perimeter of a rectangle is 2(l+w). For the original rectangle, this results in 18 = 2(l+w), which simplifies to 18 = 2l + 2w. The new rectangle's perimeter is expressed as 46 = 2(3l + 2w), which leads to 46 = 6l + 4w. By solving these equations, the original lengths can be derived as 5 inches for the length and 4 inches for the width.
