Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
The equation would be 4x+5y=6.33 and 3x+3y=4.11
so from their you would do the calculations and get 0.52 and 0.85
To make sure the caluclations aare right you just hae to put in the numbers for the x and y
4(0.52)+5(0.85)=6.33
So 1 donutis $).52
1 large coffee is $0.85
The actual block is 1800 feet long and 1260 feet wide. We know that 1 foot is equivalent to 12 inches.
Luke is now using the Feet scale measurement.
Solving for the area in square inches is shown below:
Area = L * W
Area = (1800 feet *12 inches/1 foot) * (1260 feet *12 inches/1 foot)
Area = 326.592 x10^6 inches²
Answer: See explanation
Step-by-step explanation:
Point slope form: y - y₁ = m (x - x₁)
y₁ = 6
x₁ = -7
y - 6 = -1 (x - [-7])
y - 6 = -1 (x + 7)
y - 6 = -1x - 7
Add 6 to both sides
y = -1x - 1 <em>or </em>y = -x -1
Slope intercept form: y = mx + b
m = -1
b = 6
y = -1x + 6 <em>or </em>y = -x + 6
Standard form: Ax + By = C
Change slope intercept form into _x + _y = c
Slope intercept form: y = -x + 6
Standard form:
y = -x + 6
Add x to both sides
x + y = 6 <em>or </em>-x - y = -6
Hope I helped!
