Answer:
f(x) = -5.1x² +14.6x +3
Step-by-step explanation:
The three given points are obviously not on a line, but can be modeled exactly by a 2nd degree polynomial. (The degree is 1 less than the number of points.) I find it convenient to let a graphing calculator's quadratic regression function tell me the coefficients.
<em>Solving by hand</em>
Since the "y-intercept" is 3, the equation can be written
... f(x) = ax² +bx + 3
Filling in the given numbers, we have 2 equations in the 2 unknowns, <em>a</em> and <em>b</em>.
... f(1) = 12.5 = a·1² +b·1 +3
... f(2) = 11.8 = a·2² +b·2 +3
Simplifying these gives ...
Subtracting the first equation from the second gives ...
... (2a +b) -(a +b) = (4.4) -(9.5)
... a = -5.1
The first equation tells us
... b = 9.5 -a = 9.5 +5.1
... b = 14.6
The equation is f(x) = -5.1x² +14.6x +3.
Answer:
x²+y²+4x-21=0
Step-by-step explanation:
(x-h)²+(y-k)²=r²
(x--2)²+(y-0)²=(5)²
(x+2)²+y²=25
x²+4x+4+y²=25
x²+y²+4x-21=0
Answer:
2141.76 cubic inches
Step-by-step explanation:
Given that it measures 8.8 inches across a properly inflated basketball i.e. the diameter of each basketball is 8.8 inches.
So, the radius of the spherical ball is inches.
Now, a spherical solid has a volume given by .
Hence, volume of air in side each basketball is = cubic inches.
Therefore, the total volume of air inside six balls will be = 6 × 356.96 = 2141.76 cubic inches. (Answer)