Answer:
<u>The correct answer is A. 1/8</u>
Step-by-step explanation:
<u>Let's solve (1/3 * 9/16) / 1 1/2 = x</u>
(1/3 * 9/16) / 1 1/2 = x
9/48 / 1 1/2 = 9/48 * 2/3 = 18/144
18/144, we can simplify dividing by 18 at the numerator and the denominator, this way:
x = 18 ÷ 18/ 144 * 18 = 1/8
<u>The correct answer is A. 1/8</u>
Answer:
d> -3/16
Step-by-step explanation:
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.
Multiply the denominator by 4
Complementary angles = 90
x+y =90
y=x+24
substitute this in to the equation
x+x+24=90
2x+24=90
subtract 24 from each side
2x = 66
divide by 2
x=33
y = 33+24
y=57
Answer: 33, 57
