Here's a hint: count all the numbers that are not peachy then subtract from all the 2 digit numbers.
Isolate the log on one side to get \(\log_{36}{x} = -\frac{1}{2}.\)
From there, we get \(x^{-\frac{1}{2}} = 36.\)
Hope this helps.
I will keep that in mind, thank you!
3. f(x) has degree 4 and g(x) has degree 4. Because b is a constant, the maximum degree of \(f(x) + b\cdot g(x)\) can only be 4.
4. f(x) has degree 4 and g(x) has degree 4. By multiplying, you are adding the degrees, so the degree of f(x) * g(x) is 8.
1. \((x-3)(2x^2 + 5x - 7) = (2x^3 + 5x^2 - 7x) -(6x^2 - 15x + 21)\)
\(\boxed{2x^3 - x^2 + 8x - 21}\)
2. \((-3z^2 - 7z + 4)(6z^2 - z + 6) = -18z^4 - 39z^3 + 13z^2 -\boxed{ 46z} + 24\)
The coefficient of z is -46.
\(\frac{\sqrt{72}}{\sqrt{10}} = \frac{\sqrt{2} \sqrt{36}}{\sqrt{2} \sqrt{5}} = \frac{6}{\sqrt{5}}\)
\(\frac{6}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \boxed{\frac{6\sqrt{5}}{5}}\)
Complete the square: \(f(x) = x^2 - 5x + c = (x - \frac{5}{2})^2 + (c - \frac{25}{4})\)
So, \(c - \frac{25}{4} = 1\) which makes the minimum value of c equal to 29/4.
Let \(\frac{1}{x} = a\) and \(\frac{1}{y} = b..\)
We can rewrite the system like so:
a + b = 3
a - b = 7
Adding, we get a = 5 and b = -2, which means that x = 1/5 and y = -1/2.
x + y = -3/10
This means that the integer closest to y rounded down is 42.
\(\boxed{y \in [42, 43)}\)
11^(8^5) = 11^(2^15)
2^15 = 32768, so we are finding the number of digits of 11^(32768) in base 11. The answer is simply 32768.
