The ratio would be 75:45 so there would be 75 waters and 45 sodas
restrict the domains of quadratic functions and absolute value functions, because these functions are
functions. For instance, the quadratic function f(x) = x^2 pairs both −2 and 2 with 4, and the absolute value function f(x) = |x| pairs both −2 and 2 with 2.
Linear functions (excluding constant functions) and exponential functions are
functions, so their domains
to be restricted.
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An absolute value function, without domain restriction, has an inverse that is NOT a function.
In order to guarantee that the inverse must also be a function, we need to restrict the domain of the absolute value function to make it a one-to-one function.
Recall that
sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1
for all <em>θ</em>, and given that cos(<em>θ</em>) < 0, we find that
cos(<em>θ</em>) = -√(1 - sin²(<em>θ</em>)) = -√(1 - (2/5)²) = -√(21)/5
Now,
csc(<em>θ</em>) = 1/sin(<em>θ</em>) = 1/(2/5) = 5/2
and
cot(<em>θ</em>) = cos(<em>θ</em>)/sin(<em>θ</em>) = (-√(21)/5)/(2/5) = -√(21)/2
Answer:
Equation: P = P0(1.04)^n
Population at 12 years: 4323
Step-by-step explanation:
The population starts at 2700 and increases by 4% per year. In equation form this can be written as:
P = P0(1.04)^n
Where P is the final population, P0 is the initial population, and n is the number of years.
Subbing in 2700 for P0 and 12 for n we get:
P = 2700(1.04)^12
P = 4323