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John made $200 this month mowing lawns.
2 answers:
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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
Using the Empirical Rule, it is found that:
- a) Approximately 99.7% of the amounts are between $35.26 and $51.88.
- b) Approximately 95% of the amounts are between $38.03 and $49.11.
- c) Approximately 68% of the amounts fall between $40.73 and $46.27.
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The Empirical Rule states that, in a <em>bell-shaped </em>distribution:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
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Item a:
Within <em>3 standard deviations of the mean</em>, thus, approximately 99.7%.
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Item b:
Within 2<em> standard deviations of the mean</em>, thus, approximately 95%.
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Item c:
- 68% is within 1 standard deviation of the mean, so:
Approximately 68% of the amounts fall between $40.73 and $46.27.
A similar problem is given at brainly.com/question/15967965