(5,5), (-5,5) is a function. To be a function x
cannot be repeated.
It would be on a positive incline and pass through the points (0,-5), (1, -2), and (4,3)
Given:
Area = 18
Length = 8
Width = ?
Area = length * width
(Substitute the values)
18 = 6 * width
Width = 18 / 6
Width = 3mm
Therefore, width of the rectangle is 3mm
To check if the answer is correct
Area = length * width
Area = 6 * 3
Area = 18 mm2
Answer:
72.578 to the nearest thousandth.
Step-by-step explanation:
g(x)=3x^3 + 3x^2 - 30x + 24
Find the derivative:
g'(x) = 9x^2 + 6x - 30.
This equals zero for values of turning points:
9x^2 + 6x -30 = 0
3(3x^2 + 2x - 10) = 0
x = [-(2) +/- √(2^2 - 4*3*-10)] / 2*3
x = (-2 +/- √124) / 6
x = (-2 + 11.136)/6, (-2 - 11.136)/6
x = 1.523, -2.189.
To check which value of x gives a maximum value for f(x) use the second derivative test:
g"(x) = 18x + 6
when x = -2.189 g"(x) = 18(-2.189) + 2 which is negative so this value gives a local maximum.
Local maximum value for f(x)
= 3(-2.189)^3 + 3(-2.189)^2 - 30(-2.189) + 24
= 72.578 answer.
