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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<h2>Answer</h2>
0.43
<h2>Explanation</h2>Remember that
Since the problem is telling us "Among tenth graders", we must focus on the 10th graders row only. From the row, we can infer that the frequency is the number of 10th graders who prefer going to sporting events, so . Now, the sum of all frequencies will be the sum of all the 10th graders, so
. Let's replace the values:
And rounded to the nearest hundredth:
Answer:
, ∠C ≅∠Z
, ∠A≅∠X
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
In this problem
The corresponding sides are
BA and YX
BC and YZ
AC and XZ
The corresponding angles are
∠A and ∠X
∠B and ∠Y
∠C and ∠Z
so
and
∠A≅∠X
∠B≅∠Y
∠C ≅∠Z
therefore
, ∠C ≅∠Z
, ∠A≅∠X