One of the following expressions is equivalent to 8x^2-10x+3. Which expression is it?
1 answer:
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Answer:
The rocket will reach its maximum height after 6.13 seconds
Step-by-step explanation:
To find the time of the maximum height of the rocket differentiate the equation of the height with respect to the time and then equate the differentiation by 0 to find the time of the maximum height
∵ y is the height of the rocket after launch, x seconds
∵ y = -16x² + 196x + 126
- Differentiate y with respect to x
∴ y' = -16(2)x + 196
∴ y' = -32x + 196
- Equate y' by 0
∴ 0 = -32x + 196
- Add 32x to both sides
∴ 32x = 196
- Divide both sides by 32
∴ x = 6.125 seconds
- Round it to the nearest hundredth
∴ x = 6.13 seconds
∴ The rocket will reach its maximum height after 6.13 seconds
There is another solution you can find the vertex point (h , k) of the graph of the quadratic equation y = ax² + bx + c, where h = and k is the value of y at x = h and k is the maximum/minimum value
∵ a = -16 , b = 196
∴
∴ h = 6.125
∵ h is the value of x at the maximum height
∴ x = 6.125 seconds
- Round it to the nearest hundredth
∴ x = 6.13 seconds
Answer:
the initial value -- f(0) -- results in a value of 1.5
Step-by-step explanation:
f(0) = ·
(any value raised to the power of zero equals one)
f(0) = · 1
f(0) = 3/2 or 1.5
Soccer ball reaches its highest position when its equation turns from positive slope to zero and then negative. Mathematically it is where the derivative of the its function equals to zero. so:
d(-3x^2 + 6x + 3) / dx = -6x + 6
-6x + 6 = 0 -> x = 1 ->
it seems Paige's ball reaches higher than Viaola's with only 6 meters height.