Answer:
a. A(x) = (1/2)x(9 -x^2)
b. x > 0 . . . or . . . 0 < x < 3 (see below)
c. A(2) = 5
d. x = √3; A(√3) = 3√3
Step-by-step explanation:
a. The area is computed in the usual way, as half the product of the base and height of the triangle. Here, the base is x, and the height is y, so the area is ...
A(x) = (1/2)(x)(y)
A(x) = (1/2)(x)(9-x^2)
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b. The problem statement defines two of the triangle vertices only for x > 0. However, we note that for x > 3, the y-coordinate of one of the vertices is negative. Straightforward application of the area formula in Part A will result in negative areas for x > 3, so a reasonable domain might be (0, 3).
On the other hand, the geometrical concept of a line segment and of a triangle does not admit negative line lengths. Hence the area for a triangle with its vertex below the x-axis (green in the figure) will also be considered to be positive. In that event, the domain of A(x) = (1/2)(x)|9 -x^2| will be (0, ∞).
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c. A(2) = (1/2)(2)(9 -2^2) = 5
The area is 5 when x=2.
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d. On the interval (0, 3), the value of x that maximizes area is x=√3. If we consider the domain to be all positive real numbers, then there is no maximum area (blue dashed curve on the graph).
If you would like to solve the inequality x - 8 > -3, you can do this using the following steps:
<span>x - 8 > -3
</span>x > -3 + 8
x > 5
The correct result would be x > 5.
38 weeks times 7 pieces of homework equals 266 pieces per student in a school year
38 × 7 = 266
The correct statements about the box plots are:
the median of nadia’s data is equal to the median of ben’s data.
nadia had the highest score on a test.
<h3>Which statements are true?</h3>
A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
The ends of the whiskers represents the minimum score and the maximum score. The maximum score of Nadia is 99 while that of Ben is 98.
The median is the line at the center of the box. Both lines are on the same number.
Please find attached the complete question. To learn more about box plots, please check: brainly.com/question/27215146
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Answer:
132 people bought balcony seats and 450 people bought ground seats.
Step-by-step explanation:
We want to solve the system of equations:
We can solve this by using substitution. From the second equation, we can subtract <em>b</em> from both sides:
In the first equation, we can divide both sides by five:
Substitute:
Distribute:
Simplify:
Solve for <em>b: </em>
<em />
<em />
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Using the modified equation again, substitute:
Evaluate:
Therefore, 132 people bought balcony seats and 450 people bought ground seats.
