Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.
<u>Answer:</u>
19.5 x 29.25 inches
<u>Step-by-step explanation:</u>
We are given that the top of the table, which we are to build in our factory must of the the dimension 50 cm x 75 cm.
Also, out machine is calibrated in inches. So to find the size of the table in the inches, we need to multiply the given dimensions of the table top with the scale (1 cm = 0.39 inches)
50 cm ---> 50 x 0.39 = 19.5 inches
75 cm ---> 78 x 0.39 = 29.25 inches
Therefore, the dimensions of the table in inches are 19.5 x 29.25 inches.
14 months.
$50 x 14months = $700
Answer:
The radius is always half of the diameter.
Step-by-step explanation:
