Answer:
84 in²
Step-by-step explanation:
The side lengths of the triangle are 3 consecutive integers whose sum (the perimeter) is 42. The average of those integers, 42/3 = 14, is the middle of the three, so they are 13, 14, 15. We're told the perimeter is in inches, so all of these dimensions are inches.
These are the last three of 4 consecutive integers, so the first, the height of the triangle, is 12. The base of the triangle is the 3rd of the four integers, so is 14. Then the area is ...
A = (1/2)bh = (1/2)(14)(12) = 84 . . . . . square inches.
Answer:
55
Step-by-step explanation:
By the factor theorem, if x + 3 is a factor of f(x) = -3x^3 + 6x^2 + 6x + 9, then f(-3) = 0
f(-3) = -3(-3)^3 + 6(-3)^2 + 6(-3) + 9 = -3(-27) + 6(9) - 18 + 9 = 81 + 54 - 9 = 126.
Therefore, x + 3 is not a factor of the given function
Part (b)
We use the result of part (a) and plug in (x,y) = (0,0). This is directly from the initial condition y(0) = 0.
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This means,
is the solution with the initial condition y(0) = 0.
