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pogonyaev
3 years ago
5

The height h of a thrown object as a function of horizontal distance d that it has traveled is a quadratic function. An object i

s thrown from ground​ level, 57 m away from the base of a tower 17 m high and just barely clears the top of the tower. It then lands 57 m away on the other side. Find​ h(d), the quadratic function that represents this.

Mathematics
1 answer:
omeli [17]3 years ago
5 0

Answer:

  h(d) = (17/3249)(-d² +114d)

Step-by-step explanation:

For this purpose, it is convenient to translate and scale a quadratic parent function so it has the desired characteristics. We can start with the function ...

  f(x) = 1 -x² . . . . . . . has zeros at x = ±1 and a vertex at (0, 1)

We want to horizontally expand this function by a factor of 57, so we can replace x by x/57. We want to vertically scale it by a factor of 17, so the vertex is at (0, 17). Finally, we want to translate the function 57 m to the right, which requires replacing x with x-57. After these transformations, we have ...

  f(x) = 17(1 -((x-57)/57)²) = (17/3249)(-x²+114x)

Using the appropriate function name and variable, we have ...

  h(d) = (17/3249)(-d² +114d)

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The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket (Bureau of Transportation St
saveliy_v [14]

Answer:

a)0.067

b)0.111

c)0.612

d)$687.28

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $385

Standard Deviation, σ = $110

We are given that the distribution of domestic airfares is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(domestic airfare is $550 or more)

P(x > 550)

P( x > 550) = P( z > \displaystyle\frac{550 - 385}{110}) = P(z > 1.5)

= 1 - P(z \leq 1.5)

Calculation the value from standard normal z table, we have,  

P(x > 550) = 1 - 0.933 = 0.067= 6.7\%

b) P(domestic airfare is $250 or less)

P(x \leq 250) = P(z \leq \displaystyle\frac{250-385}{110}) = P(z \leq -1.22)

Calculating the value from the standard normal table we have,

P( x \leq 250) = 0.111 = 11.1\%

c))P(domestic airfare is between $300 and $500)

P(300 \leq x \leq 500) = P(\displaystyle\frac{300 - 385}{110} \leq z \leq \displaystyle\frac{500-385}{110}) = P(-0.77 \leq z \leq 1.04)\\\\= P(z \leq 1.04) - P(z < -0.77)\\= 0.851 - 0.239 = 0.612 = 61.2\%

P(300 \leq x \leq 500) = 61.2\%

d) P(X=x) = 0.03

We have to find the value of x such that the probability is 0.03.

P(X > x)

P( X > x) = P( z > \displaystyle\frac{x - 385}{110})=0.03

= 1 -P( z \leq \displaystyle\frac{x - 385}{110})=0.03

=P( z \leq \displaystyle\frac{x - 385}{110})=0.997

Calculation the value from standard normal z table, we have,  

\displaystyle\frac{x - 385}{110} = 2.748\\x = 687.28

Hence, the domestic fares must be $687.28 or greater for them to lie in the highest 3%.

7 0
3 years ago
The length of a rectangle is 3 more than the width. If the perimeter of the rectangle is 16 units, find the
pentagon [3]
L = 3x width
2L + 2W = 16 units
2(3W) + 2W = 16 units
8W = 16 units
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7 0
2 years ago
30 points!
slamgirl [31]

Answer:

Hello, Your answer is 1.02$

Step-by-step explanation:

First of all, let's calculate the total amount payed by Veena for her meal:  t =9.25$ + 4.35$ =13.6$ The tax was 7.5%, which corresponds to a fraction of 7.5% =7.5/100 therefore, the amount of tax payed by Veena for her meal is   tax = 7.5/100 . t = 7.5/100 (13.6$) =1.02$<em> Hope This Helps!</em>

8 0
3 years ago
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Given: 2/3 every 30 seconds

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Therefore, 1/3 of the length every 15 seconds.

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3 years ago
What is the approximate solution to this equation?
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The answer is B because 5^3 is 125 so the approximate answer is 124.75
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