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.
Answer:
7.1 (7.06 rounded to the tenth)
Step-by-step explanation:
The formula for Area of a Circle is: π·r²
R = Radius
π = pi, or 3.14
As long as you know the formula, this is easy!
In class, you may have already been told that the radius is <em>half </em>of the diameter.
1. Half of 3 ft is 1.5 ft.
2. Plug 1.5 in for r, in your calculator
3. Do the calculation, and you should come out to get 7.06858347058
4. Round it!
Finding area for a circle is satisfying, isn't it? xD
Answer:
6.5 hours
Step-by-step explanation:
First try to find the rate he can paint per hour
375 ÷ 3 = 125 ft^2 per hour
Then try to find how long it should take it for him to paint 812.5 sq ft
812.5 ÷ 125 = 6.5 hours
Answer:
2.5 yards
Step-by-step explanation:
75÷30=2.5 yards
Hope this helps!
