Answer:
x= .75
Step-by-step explanation:
hope this helps (:
Answer:
B. y = -0.58x^2 -0.43x +15.75
Step-by-step explanation:
The data has a shape roughly that of a parabola opening downward. So, you'll be looking for a 2nd-degree equation with a negative coefficient of x^2. There is only one of those, and its y-intercept (15.75) is in about the right place.
The second choice is appropriate.
_____
The other choices are ...
A. a parabola opening upward
C. an exponential function decaying toward zero on the right and tending toward infinity on the left
D. a line with negative slope (This might be a good linear regression model, but the 2nd-degree model is a better fit.)
Total volume = Volume of Sphere + Volume of Cylinder
16 = (4/3)πr³ + πr²h
Express h in terms of r:
πr²h = 16 - (4/3)πr³
h = 16/πr² - (4/3)r
Next, let's solve for surface area:
Total Surface Area = SA of sphere + SA of cylinder
A = 4πr² + 2πrh
Substitute the expression for h:
A = 4πr² + 2πr[16/πr² - (4/3)r]
A = 4πr² + 32/r - (8/3)πr²
Find the derivative of A with respect to r and equate to zero.
dA/dr = 8πr - 32r⁻² - (16/3)πr = 0
Solve for r:
[(8/3)πr - 32/r² = 0]*r²
(8/3)πr³ - 32 = 0
r³ = 32*3/8π = 12/π
r = ∛(12/π)
<em>r = 1.56 inches</em>
this is the answer I came up with hopes this helps