Given that a ball is thrown into the air and its height in feet after t seconds is given by y = 45t - 15t², the instantaneous velocity when t=4 is -75ft/s.
<h3>What is the instantaneous velocity when t=4?</h3>
Given that;
- Initial velocity = 45ft/s
- Height in feet after t seconds is given by y = 45t - 15t²
- Instantaneous velocity = ?
First, we determine the derivative of y = 45t - 15t²
y' = (1)45 - (2)15t
y' = 45 - 30t
We substitute in t = 4
y' = 45 - 30t
y' = 45 - 30(4)
y' = 45 - 120
y' = -75ft/s
Given that a ball is thrown into the air and its height in feet after t seconds is given by y = 45t - 15t², the instantaneous velocity when t=4 is -75ft/s.
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Answer:
f(-9) = 184
Explanation:
f(x)=3x²+5x-14
f(-9)= 3(-9)² +5(-9)-14 Order of Operations : Exponents
= 3(81)+5(-9)-14
= 243+5(-9)-14
= 243-45-14
= 198-14
f(-9)= 184
Hope this helps :)
Answer: The terrestrial planets, Mars, Earth, Venus, and Mercury all have relatively high densities and low gas content, e.g., they are small and rocky. The Jovian (or giant planets), Jupiter, Saturn, Uranus, and Neptune, are very large and have rather low densities, e.g., they are gaseous.
Explanation:
:)
Answer:
Explanation:
This is a Law of Momentum Conservbation problem, where the total energy of the system cannot increase or decrease, only change form. The total energy equation for this situation is
TE = PE + KE where TE is total energy, PE is potential energy, and KE is kinetic energy. We begin by realizing that the go-kart is motionless at the top of a hill. If the kart isn't moving, then it has no KE, but if it is up off the ground and has the potential to fall to a point lower than it is curremtly, it has potential energy. That means that the total energy available to this go-kart is found in its potential energy and will not change throughout the trip's entirety. Thus,
TE = PE + 0 and
TE = (50.0)(9.8)(10.0) so
TE = 4900 J and since that's the total energy available throughout the trip, and we are looking to find the height of the next hill where this is both potential and kinetic energy, then
4900 = PE + KE and
4900 = (50.0)(9.8)(h) + and
4900 = 490h + 25.0 and
4875 = 490h so
h = 9.9 m (I kinda ignored the rules for significant digits at the end, which goes against every teacher's bone in my body, but nonetheless, there's your answer!)