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).
Answer:
you cant connect it
Step-by-step explanation:
If you observe the graph, the graph is touching the x-axis at the point x=-1 and is turning away.
This means, the graph as an even multiplicity at x=-1. So the two roots of the given polynomial are x = -1 and x = -1. Thus, the two factors of the polynomial are (x+1) and (x+1)
Product of the factors is equal to the polynomial. So the given polynomial will be (x+1)(x+1).
Therefore, the answer to this question is option C
If the woman's shed is used as one side of the garden, she will only have to use her fencing for 3 sides of the shape. So, if you divide 96 by 3, each side should be 32 yards. Then, to find the area, multiply 32 (one side) by 32 (another side) to equal 1,024 yards².
Sounds like it will be big enough for whatever she wants!
Hope this helps :)
Answer:
A) $42.674
B) $524,387
Step-by-step explanation: