The Range of a function is the set of all values that that function can take.
Given the sine function f(x)=sinx,
This function is the function which calculates the sine of the values of x.
According to the definition of the sine of an angle x in the unit circle,

,
so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.
This means that the values that the sine function takes are any values between -1 and 1, inclusive.
This determines the Range of the sine function.
So the Range of the sine function is [-1, 1]
Answer:
![h = \sqrt[3]{\frac{49V}{4}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%7D%7B4%7D%7D)
Step-by-step explanation:
Represent the volume of the box with V and the dimensions with l, b and h.
The volume (V) is:

Make h the subject of the formula

The surface area (S) of the aquarium is:

Where lb represents the area of the base (i.e. slate):
The cost (C) of the surface area is:



Substitute
for h in the above equation



Differentiate with respect to l and with respect to b


To solve for b and l, we equate both equations and set l to b (to minimize the cost)


By comparison:

becomes

Cross Multiply

Solve for l

![l = \sqrt[3]{\frac{2V}{7}}](https://tex.z-dn.net/?f=l%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D)
Recall that: 
![b = \sqrt[3]{\frac{2V}{7}}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D)
Also recall that:

![h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7BV%7D%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D%2A%5Csqrt%5B3%5D%7B%5Cfrac%7B2V%7D%7B7%7D%7D%7D)
![h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7BV%7D%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B4V%5E2%7D%7B49%7D%7D%7D)
Apply law of indices
![h = \sqrt[3]{\frac{49V^3}{4V^2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%5E3%7D%7B4V%5E2%7D%7D)
![h = \sqrt[3]{\frac{49V}{4}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%7D%7B4%7D%7D)
The dimension that minimizes the cost of material of the aquarium is:
![h = \sqrt[3]{\frac{49V}{4}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B49V%7D%7B4%7D%7D)
Answer:
After 2.9 years the town's tax status will change
The towns tax status change within the next 3 years
Step-by-step explanation:
The question below is
Will the towns tax status change within the next 3 years ?
Let
y -----> the population of a small town
t ----> the number of years
we have a exponential function of the form

where
a is the initial value
b is the base
In this problem


substitute

Remember that
The town's tax status will change once the population is below 6,000 people
so
The inequality that represent this situation is
Solve for t

Apply log both sides


Multiply by -1 both sides


so
After 2.9 years the town's tax status will change
therefore
The answer is
Yes, the towns tax status change within the next 3 years
Answer:
40,999
Step-by-step explanation:
95,234-35,295= 59,939 and then 59,939-19,240= 40,999
The answer is -500, hope this helped