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sasho [114]
2 years ago
15

Help me please it’s due today

Mathematics
1 answer:
Zolol [24]2 years ago
5 0

Answer:

49 ft  

Step-by-step explanation:

h(t) = 56t - 16t²

This is the equation of a parabola.

We must solve the equation to find the time (t) when the ball reaches its maximum height (h).  

The coefficient of t² is negative, so the parabola opens downward, and the vertex is a maximum.

One way to solve this problem is to convert the equation to the vertex form.

We do that by completing the square.

Calculation:

h = -16t² + 56t  

Divide both sides by -16 to make the coefficient of  t² equal to 1.

(-1/16)h = t² - ⁷/₂t

Square half the coefficient of t

(-7/4)² = 49/16

Add and subtract it on the right-hand side

(-1/16)h = t² - ⁷/₂t  + 49/16 - 49/16  

Write the first three terms as the square of a binomial

(-1/16)h = (t - ⁷/₄)² - 49/16

Multiply both sides by -16

h = -16(t - ⁷/₄)² + 49

You have converted your equation to  the vertex form of a parabola:

y = a(t - h)² + k = 0,

where (h, k) is the vertex.

h = ⁷/₄ and k = 49, so the vertex is at (⁷/₄, 49).

The time to reach maximum height is ⁷/₄ s = 1.75 s.

The graph below shows that the ball reaches a maximum height of 49 ft after 1.75 s.

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I think of a number, add 3 to it and multiply the result by 7.
Alla [95]

Answer:

7(x + 3)

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3 years ago
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6 0
3 years ago
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Aleksandr [31]

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Step-by-step explanation:

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3 0
2 years ago
Read 2 more answers
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
jekas [21]

Using the normal distribution, it is found that 1851 people would have an IQ less than 115.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

\mu = 100, \sigma = 15

The proportion of IQ scores less than 115 is the <u>p-value of Z when X = 115</u>, hence:

Z = \frac{X - \mu}{\sigma}

Z = \frac{115 - 100}{15}

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Z = 1 has a p-value of 0.8413.

Out of 2200 people:

0.8413 x 2200 = 1851.

More can be learned about the normal distribution at brainly.com/question/27643290

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5 0
1 year ago
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