Answer:
e^(ln x) is just plain x
Step-by-step explanation:
The functions f(x) = e^x and g(x) = ln x are inverses of one another. In other words, one "undoes" the other.
Thus, as the rule goes, e^(ln x) is just plain x.
Here, e^(ln x) = 4 simplifies to x = 4.
We will use demonstration of recurrences<span>1) for n=1, 10= 5*1(1+1)=5*2=10, it is just
2) assume that the equation </span>10 + 30 + 60 + ... + 10n = 5n(n + 1) is true, <span>for all positive integers n>=1
</span>3) let's show that the equation<span> is also true for n+1, n>=1
</span><span>10 + 30 + 60 + ... + 10(n+1) = 5(n+1)(n + 2)
</span>let be N=n+1, N is integer because of n+1, so we have
<span>10 + 30 + 60 + ... + 10N = 5N(N+1), it is true according 2)
</span>so the equation<span> is also true for n+1,
</span>finally, 10 + 30 + 60 + ... + 10n = 5n(n + 1) is always true for all positive integers n.
<span>
</span>
Answer:
6
Step-by-step explanation:
We have two fractions and are asked to find the answer if they both are divided.
3/5 and 1/10.
When we divide fractions, we need to follow KCF
KEEP - Keep the fractions
CHANGE - Change the division sign to a multiplication sign
FLIP - Flip the second fraction
Follow :
KEEP :
3/5 / 1/10
CHANGE :
3/5 * 1/10
FLIP :
3/5 * 10/1
Now we need to multiply, which is simple because it's multiplying across :
30/5
Simplify by dividing the numerator and denominator by 5 :
Divide the numerator by denominator :
