You are going to solve this in such a quick, slick way
that you will blink and not believe it. Fasten your seat belt.
Here are the tools you'll need:
-- Volume of a cylinder = (pi) (radius)² (height)
-- Volume of a sphere = (4/3) (pi) (radius)³
Now ... the question says that your cylinder and your sphere
have the same volume. Fine ! So you can immediately write
an equation saying that their volumes are equal.
(pi) (radius)² (height) = (4/3) (pi) (radius)³
Divide each side by pi: (radius)² (height) = (4/3) (radius)³
Divide each side by (radius)² (height) = (4/3) (radius)
Fill in the given height: (6 cm) = (4/3) (radius)
Multiply each side by 3/4 : (6 cm) x (3/4) = radius
I'm pretty sure that you can take over now and find the radius.
The answer is A.
The way you know this is by graphing the first function.
The second function is in a different format, so you just have to isolate Y.
-1/3x + y = -1
y= 1/3x -1 OR y= -1 + 1/3x
both of the functions have the same slope, but different y-intercepts. therefore, they'll never touch. making them infinite solutions.
it's also A because both of the slopes are positive, the slopes in graph D are negative.
So, the answer is A.
Hope this helps! xx
<h3>
Answer: 2</h3>
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Explanation:
The function f(x) = -4x+1 is the same as y = -4x+1 where y = f(x)
Compare this to y = mx+b and we see the slope here is m = -4
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Now let's find the slope of g(x)
use the slope formula with any two rows you want. I'll pick on the last two rows.
m = (y2-y1)/(x2-x1)
m = (21-9)/(3-1)
m = 12/2
m = 6 is the slope of g(x)
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From here, we add the two slope values
(slope of f)+(slope of g) = -4+6 = 2
