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oee [108]
3 years ago
6

This cube has a volume of 1 cubic millimeter. What is the side length of the cube?

Mathematics
1 answer:
Lynna [10]3 years ago
6 0

Answer:4 millimeters

Step-by-step explanation:

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SEE ATTACHED
fenix001 [56]
To me personally, the first bit f(g(x)) is easy and the domain is tricky. Let's try explain this.

A function takes an input number and returns an output number depending on the function. Look at f(x) = x+3, if we let the input number be 2 then we say that f(2) = 5. We could do f(π) to give us π+3 or even f(x²) to give us x² +3. The trick is to substitute the input into the function equation.

You have been asked to find f(g(x)). You know f(x) = \frac{1+x}{1-x}. Putting numbers in at this point would be easy (try work out f(2), you'll do it really quick) but you have to put in g(x).

f(g(x)) = \frac{1+g(x)}{1-g(x)}
we also know that g(x) = \frac{x}{1-x} so we can say that
f(g(x)) = \frac{1+ \frac{x}{1-x} }{1- \frac{x}{1-x} } and that is f(g(x)) but the question requires that we simplify it so
\frac{1+ \frac{x}{1-x} }{1- \frac{x}{1-x} }  =  \frac{ \frac{1-x}{1-x} +  \frac{x}{1-x} }{ \frac{1-x}{1-x} - \frac{x}{1-x} } =  \frac{ \frac{1}{1-x} }{ \frac{1-2x}{1-x} } =  \frac{1}{1-2x}

f(g(x)) = \frac{1}{1-2x}

Now for the tricky bit (for me, at least). The domain is the full set of values that you can 'put in to' the function and still get a real value out. So how do we work out what numbers 'break' the function? I like to use the fact that DIVIDING BY ZERO IS IMPOSSIBLE. What value of x can we put into the function to make it so the function is being divided by 0? i.e. 1-2x = 0 solve that and you have a value of x that isn't part of the domain.

This means the domain is all real numbers EXCEPT the solution to that equation. (Because if we put that value into f(g(x)) it's impossible to get a value out.)

[I know this was a lot to read, if you have any questions or don't get anything feel free to message me or leave a comment.]

5 0
3 years ago
A juggler perform in a telant contest. He is given 10 marks by each of the 4 judges. What’s his total score?
Mars2501 [29]

Answer:

40

Step-by-step explanation:

The answer is 40. There are 4 judges, and each gave him a 10. This can be shown by an equation.

1. 4 * 10 = total score

2. 40 = total score.

Hope this helps! (Please consider giving brainliest)

6 0
3 years ago
Read 2 more answers
What is the equation for the translation of X^2+y^2=9 four units to the right and three units down
icang [17]
We know that
X²+y²=9 -------> X²+y²=3²
is the equation of a circle with center (0,0) and radius r=3 units
so
<span>the translation of four units to the right and three units down is equals to move the center (0,0)--------> (0+4,0-3)------> (4.-3)

the new center of the circle is (4,-3)
the new equation is
(x-4)</span>²+(y+3)²=3²

see the attached figure

4 0
3 years ago
Find an equation of the tangent line to the curve at the given point. y = x + tan(x) at (pi, pi)
S_A_V [24]
<span>Differentiating :

y' = 1 + sec^2(x),
</span><span>
cosπ=−1</span><span>

plug in pi = -1 ,for x:

1 + sec^2(pi) = 1 +  (-1)^2 
                      = 2</span>
8 0
3 years ago
Factor out the GCF:<br> 16n^2 + 10n
zimovet [89]

Answer:

2n(8n + 5)

Step-by-step explanation:

you need to see what you can take out of both the numbers.

ex they both have an 'n' and they both are divisible by 2

3 0
2 years ago
Read 2 more answers
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