Jumping spiders can commonly be found in homes and barns throughout the United States. A jumping spider's jump can be modeled by the equation h = 33.3t - 16t2, where t represents the time in seconds and h is the height in feet.
When is the spider's height at zero feet?
0 = t(33.3-16t)
so height=0 at t=0 (duh)
and at t = 33.3/16, or 2.08 sec
Thanks for the help I appericate it very much!!!!
To find the time when the spider's height is at zero feet, we need to solve the equation h = 0.
Hence, 33.3t - 16t^2 = 0.
To solve this quadratic equation, we can set it equal to zero and factor it or use the quadratic formula.
In this case, let's use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / 2a.
For the equation 33.3t - 16t^2 = 0, a = -16, b = 33.3, and c = 0.
Plugging these values into the quadratic formula gives us: t = (-33.3 ± √(33.3^2 - 4(-16)(0))) / 2(-16).
Simplifying further, t = (-33.3 ± √(1108.89)) / -32.
Calculating the square root, we get t ≈ (-33.3 ± 33.29) / -32.
This gives us two possible solutions: t ≈ -0.02 and t ≈ 2.02.
Given that time cannot be negative in this context, the jumping spider's height is zero feet around t ≈ 2.02 seconds.
To find the time when the spider's height is zero feet, we need to solve the equation h = 33.3t - 16t^2 for t when h = 0.
The equation becomes:
0 = 33.3t - 16t^2
Now let's solve this quadratic equation by factoring or using the quadratic formula.
We can factor out a common term:
0 = t(33.3 - 16t)
Since the product of two factors is zero, either t = 0 or 33.3 - 16t = 0.
For t = 0, the spider's height is zero at the beginning, which makes sense.
Now let's solve 33.3 - 16t = 0 for t:
16t = 33.3
t = 33.3 / 16
t ≈ 2.077
Therefore, the spider's height is zero at t = 0 seconds and t ≈ 2.077 seconds.