15 points please help thank you
1 answer:
Answer:
1.8
Step-by-step explanation:
The point of intersection of the left-side function with the right-side function is the value of x where the two functions evaluate to the same quantity. That value of x is near 1.785, as indicated on the attached graph. Rounded to the nearest tenth, the value of x is 1.8.
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<em>Refinement of the graphical solution</em>
An iteration method called Newton's Method can be used to refine the estimate to the limit of accuracy of the calculator. For that, it is convenient to define a function such as the one you get when you subtract the right side from the left side. Newton's Method is good at finding the zero(s) of such a function.
The function defined as g(x) in the attachment is the iterator for Newton's Method. It gives the next "guess" based on the guess you give it as an argument. When there is no change, the guess is as accurate as the calculator can provide. Here, that refined estimate of x is x ≈ 1.78522264685.
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Answer <u>(assuming it is allowed to be in point-slope format)</u>:
Step-by-step explanation:
1) First, determine the slope. We know it has to be perpendicular to the given equation, . That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since
is in place of the m in the equation, that must be the slope of the given line.
Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be .
2) Now, use the point-slope formula, to write the new equation with the given information. Substitute
,
, and
for real values.
The represents the slope, so substitute
in its place. The
and
represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for
and 4 for
. This gives the following equation and answer:
Answer:
The number of edge stones needed has a constant rate of change, but the number of stones for the center does not.
Step-by-step explanation:
The complete question is shown in the picture attached below.
Two functions E(x) and C(x) are given in the table along with some of the function values. We have to identify if any of these functions show constant rate of change or not.
By constant rate of change we mean that the slope is constant or in other words, a linear relationship is shown by the function. For a Linear function, the first differences of the function values are same.
By first differences we mean the difference between two consecutive output values. We can see that difference between consecutive input values is constant i.e. 1. If the difference between consecutive output values of any of the functions is same, then that function will be a Linear Function and, therefore, the rate of change for that function will be constant.
Lets analyze E(x) first. The output values are:
34, 52, 70 and 88
The difference between consecutive output values is:
18, 18 and 18
Since, this difference is constant, we can conclude that E(x) is a Linear function with a constant rate of change.
Now lets analyze C(x). The output values are:
62, 133, 260 and 435
The difference between consecutive output values is:
71, 127 and 175
Since, the differences are not constant, C(x) is not a Linear Function and , therefore, the rate of change of C(x) is not constant.
Conclusion:
The number of edge stones which is represented by E(x) has a constant rate of change, but the number of stones for center which is represented by C(x) does not have constant rate of change. This makes the first option our correct answer.
