A jump rope held stationary by two children, one at each end, hangs in a shape that can be modeled by the equation h=0.01x^2-x+2
6, where h is the height (in inches) above the ground and x is the distance (in inches) along the ground measured from the horizontal position of one end. How close to the ground is the lowest part of the rope? A. 0.5 in. C. 1.25 in. B. 1 in. D. 2 in.
1 answer:
Answer:
B. 1 in.
Step-by-step explanation:
For a quadratic of the form ...
ax^2 +bx +c
The axis of symmetry is found at ...
x = -b/(2a) = -(-1)/(2·0.01) = 50
The value of the function at x=50 is ...
h = (0.01·50 -1)·50 +26 = -25+26
h = 1
The lowest part of the rope is 1 inch above the ground.
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<em>Comment on the solution</em>
It is often easier to evaluate a quadratic or other polynomial if it is written in Horner's form:
h = (ax +b)x +c
If you evaluate a polynomial using a synthetic division tableau, you will find the sequence of arithmetic operations to be identical.
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A graphing calculator can make short work of a problem such as this.
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Answer:
- <u><em>Option b. just below 30%</em></u>
<u><em></em></u>
Explanation:
Please, see attached the <em>histogram that represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. </em>
<em />
The<em> median</em> is the value that separates the lower 50% from the upper 50% of the data.
Since there are 25 business schools, the middle value is the number 13.
The height of each bar is the<em> frequency</em> or number of business school for that acceptace rate:
- The first bar has frequency of 1 school
- The second bar has frequency of 3 schools: cummulative frequency: 1+3=4.
- The third bar has frequency 5 schools: cummulative frequency 4 + 5 = 9.
- The fourth bar has frequency 3 schools: cummulative frequency: 9+3=12.
Then, the 13th value is on the next bar, the fifth bar.
The fifth bar has acceptance rates 25 ≤ rate < 30.
That means that the median acceptance rate is greater than or equal to 25 and less than 30.
Thus, the choice is the option <em>b. just below 30%.</em>
Answer:
176.39 inches or
14.70 feet
Step-by-step explanation:
Consider the right triangle made by Kristen, ground and shadow.
This triangle has one leg as 64 inches.
Next consider the right triangle formed by street light, ground upto shadow tip.
The two triangles have common angle of elevation and also another angle as 90 degrees.
Hence the two triangles would be similar
Also if A is the angle made by hypotenuse of both triangles with the ground we have
This value also equals by bigger triangle as
From these two we get
h = height of street light =