Answer:
Geometry help?????????????????????
1 answer:
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Answer:
<em>2,136,605</em>
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Step-by-step explanation:
To estimate growth, we use the formula shown below:
Where
F is the future amount (we want to find for Jan 2024)
P is the present amount (present population of 1,988,817)
r is the rate of growth (0.9% means 0.009)
t is the time in years (from Jan 2016 to Jan 2024 is 8 years, t = 8)
<em>Let's put these into the formula and figure out F:</em>
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<em>Rounding we get the population in Jan 2024 to be </em><em>2,136,605</em>
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