Use the half angle identity, tan157.5=(1-cos315)/sin315
cos315=cos(-45)=√2/2, sin315=-√2/2
tan157.5=(1-√2/2)/(-√2/2)=(2-√2)/(-√2)=(2√2-2)/(-2)=1-√2
e is irrational; that is, that it cannot be expressed as the quotient of two integers a/b because e is 2.71828.....and on and on for ∞
Answer:
Adding 6 translates the graph up 6 units.
The leading coefficient, 3, stretches the graph vertically.
Red: 3x^3+6
Blue:x^3
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
I hope this good enough:
Answer:
≈ 1.32471795725...
Explanation:
If x is one less than its cube, then
x = x³ - 1,
x³ - x - 1 = 0
so f(x) = ? would be an appropriate (continuous) function to apply the Intermedate Value Theorem on some appropriate interval to see if it takes on the value 0 in that interval.
f(x) = x³ - x - 1
For large x the left hand side is positive, for x = 0 it is negative. The root can be calculated exactly, it is given by:
![\sqrt[3]{\frac{1}{2} + \sqrt{\frac{1}{4} - \frac{1}{27} } } + \sqrt[3]{\frac{1}{2} - \sqrt{\frac{1}{4} - \frac{1}{27} } }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%20-%20%5Cfrac%7B1%7D%7B27%7D%20%7D%20%20%7D%20%2B%20%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%20-%20%5Cfrac%7B1%7D%7B27%7D%20%7D%20%20%7D)
≈ 1.32471795725...