A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second. The quadratic function h(t)=-16t^2+35t+5 represents the height of the balloon, h, in feet t seconds after it is thrown. Determine when the balloon is more than 10 feet above the ground. Round your answer to the nearest thousandth.

t>2.034s and t>0.154s

Step-by-step explanation:

Given the quadratic function h(t)=-16t^2+35t+5 which represents the height of the balloon, h, in feet t seconds after it is thrown.

To determine when the balloon is more than 10feet above the ground, we will substitute h = 10 into the expression to have;

h(t)=-16t^2+35t+5

-16t^2+35t+5>10

-16t^2+35t+5-10>0

16t^2-35t+5>0

Find t;

t > 35±√35²-4(16)(5)/2(16)

t>35±√1225-320/32

t>35±√905/32

t>35±30.08/32

t > 35+30.08/32 and t > 35-30.08/32

t>65.08/32 and t>4.92/32

t>2.034s and t>0.154s

Hence the balloon is more than 10feet above the ground at when t>2.034s and t>0.154s

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)