Answer:
log(2)
Step-by-step explanation:
In order to combine log(10) and log(5), you need to look at the sign that's combining them. In this example, it is a subtraction sign. When two logs are being subtracting from each other, it's the same as dividing the two. You would rewrite it like this:
log(10/5)
You would then solve 10/5, and get 2. You would rewrite the log as:
log(2)
There are two of them.
I don't know a mechanical way to 'solve' for them.
One can be found by trial and error:
x=0 . . . . . 2^0 = 1 . . . . . 4(0) = 0 . . . . . no, that doesn't work
x=1 . . . . . 2^1 = 2 . . . . . 4(1) = 4 . . . . . no, that doesn't work
x=2 . . . . . 2^2 = 4 . . . . . 4(2) = 8 . . . . . no, that doesn't work
x=3 . . . . . 2^3 = 8 . . . . . 4(3) = 12 . . . . no, that doesn't work
<em>x=4</em> . . . . . 2^4 = <em><u>16</u></em> . . . . 4(4) = <em><u>16</u></em> . . . . Yes ! That works ! yay !
For the other one, I constructed tables of values for 2^x and (4x)
in a spread sheet, then graphed them, and looked for the point
where the graphs of the two expressions cross.
The point is near, but not exactly, <em>x = 0.30990693...
</em>If there's a way to find an analytical expression for the value, it must involve
some esoteric kind of math operations that I didn't learn in high school or
engineering school, and which has thus far eluded me during my lengthy
residency in the college of hard knocks.<em> </em> If anybody out there has it, I'm
waiting with all ears.<em>
</em>
Answer:
3,451 cm³
Step-by-step explanation:
The ball is a sphere.
Formula for finding the volume of a sphere = ⁴/3*πr³
Volume of the 3 balls = 3(⁴/3*πr³)
Where,
radius (r) = ½ of diameter = ½(13) = 6.5 cm
Plug in the values into the formula:
Volume of the 3 balls = 3(⁴/3*π*6.5³)
= 4*π*274.625
= 3,451.03953 ≈ 3,451 cm³
Answer:
No.
If y is greater than 3, it is not a solution to the system of inequalities. (7,5) has a y value of 5, therefore it is is not a solution.
