Answer:
a. 8.4 ft³
b. 4.44 ft × 2.44 ft × 0.78 ft
Step-by-step explanation:
a. <em>Maximum volume
</em>
We are creating a box with dimensions
l = 6 – 2x
w = 4 – 2x
h = x
V = lwh = x(6 – 2x)(4 – 2x)
We must determine the value of x that makes V a maximum.
One way is to plot the function V = x(6 – 2x)(4 – 2x).
The maximum appears to be at about (0.78, 8.4).
Thus, the maximum volume is 8.4 ft³.
b.<em> Dimensions
</em>
l = 6 – 2 × 0.78 = 6 – 1.56 = 4.44 ft
w = 4 – 2 × 0.78 = 4 – 1.56 = 2.44 ft
h = 0.78 ft
The box with maximum volume has dimensions 4.44 ft × 2.44 ft × 0.78 ft.
The following equation represents the function g in function notation,
g(x) = 3x - 14 [Option (A)]
Definition of a Function
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.
Given equation is,
y -3x = -14
⇒ y = -14 + 3x
or y = 3x - 14
Here, y stands for or represents the function g(x) which is a function of independent variable x.
Thus, the correct function notation is as follows,
g(x) = 3x - 14
Learn more about a function here:
brainly.com/question/12431044
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Answer:
6
Step-by-step explanation:
Slope intercept form is y=mx+b, with m being the slope and be being the y intercept, so when you look for what b is in the equation for y=-3x+6 then 6 is b.
