Answer: x is doubled.
Step-by-step explanation:
A proportional relationship between x and y is written as:
y = k*x
where k is called the constant of proportionality.
In this case, we know that we have a proportional relationship between z and x^3
Then:
z = k*x^3
What will happen to x when z is 8 times greater?
Let's rewrite this equation for two new quantities, z' and x'
z' = k*(x')^3
Now we need to replace z' by 8*z, then:
8*z = k*(x')^3
We want to find a relationship between x' and x.
And by the first relationship, we know that:
z = k*x^3
Then we can replace this in the equation "8*z = k*(x')^3" to get:
8*(k*x^3) = k*(x')^3
8*k*x^3 = k*(x')^3
Now we can divide both sides by k, so we get:
8*x^3 = (x')^3
Now we can apply the cubic root to both sides, to get:
∛(8*x^3) = ∛(x')^3
∛(8)*x = x'
2*x = x'
Then when we increase the value of z 8 times, the value of x will be doubled.
Answer:
Positive
Step-by-step explanation:
The product of two negative numbers has a positive sign, whereas the product of a positive and a negative number is negative.
Since -35 and -625 are both negative, they would have a positive sign for their product.
Hope this helps.
I'm sorry but I'm not into square roots yet :(
Looks like the given limit is

With some simple algebra, we can rewrite

then distribute the limit over the product,

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.
For the second limit, recall the definition of the constant, <em>e</em> :

To make our limit resemble this one more closely, make a substitution; replace 9/(<em>n</em> - 9) with 1/<em>m</em>, so that

From the relation 9<em>m</em> = <em>n</em> - 9, we see that <em>m</em> also approaches infinity as <em>n</em> approaches infinity. So, the second limit is rewritten as

Now we apply some more properties of multiplication and limits:

So, the overall limit is indeed 0:
