If
is the variable of the horizontal axis, then you can solve for
to get the equation of the line in slope-intercept form in the
plane:
i.e. a line with slope
through the origin, which means it is contained in the first and third quadrants. Since the terminal side of
has a negative sine, the angle must lie in the third quadrant.
Because the slope of the line is
, you can choose any length along the line to make up the hypotenuse of a right triangle with reference angle
. Any such right triangle will have
, regardless of whether the angle is the first or third quadrant. But since
is known to lie in the third quadrant, and so
and
are both negative, you have
It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.
Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.
Now let's analyze the functions from the problem.
Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function <em>f(x)</em> is also increasing.
Use these rules to find whether each function is increasing or decreasing.
Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.
Pythagoras Theorem:
Apply Pythagoras Theorem:
a² + 6² = 11²
a² = 11² - 6²
a²= 85
a = √85
a = 9.22 (nearest hundredth)
Answer: RT = 9.22 cm
Answer:
Step-by-step explanation:
<em>Hey there!</em>
3x * x = 3x^2
3x * 2x = 6x^3
So 3x is a factor of 3x^2 - 6x^3.
<em>Hope this helps :)</em>
45 = (x) + (x + 1) + (x + 2)
45 = 3x + 3
- 3
42 = 3x
/3
14 = x
45 = 14 + (14 + 1) + (14 + 2)
45 = 14 + 15 + 16
The ages of the 3 friends are 14, 15, and 16.
