Answer:
Step-by-step explanation:
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways
Answer:
a) ![f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000](https://tex.z-dn.net/?f=f%28t%29%3D0.001155%5B%5Cfrac%7B2%7D%7B3%7Dt%28t-1980%29%5E%7B3%2F2%7D-%5Cfrac%7B4%7D%7B15%7D%28t-1980%29%5E%7B5%2F2%7D%5D%2B264%2C034%2C000)
b) f(t=2015) = 264,034,317.7
Step-by-step explanation:
The rate of change in the number of hospital outpatient visits, in millions, is given by:
a) To find the function f(t) you integrate f(t):
![\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdf%28t%29%7D%7Bdt%7Ddt%3Df%28t%29%3D%5Cint%20%5B0.001155t%28t-1980%29%5E%7B0.5%7D%5Ddt)
To solve the integral you use:
Next, you replace in the integral:
Then, the function f(t) is:
![f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'](https://tex.z-dn.net/?f=f%28t%29%3D0.001155%5B%5Cfrac%7B2%7D%7B3%7Dt%28t-1980%29%5E%7B3%2F2%7D-%5Cfrac%7B4%7D%7B15%7D%28t-1980%29%5E%7B5%2F2%7D%5D%2BC%27)
The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient visits.
Hence C' = 264,034,000
The function is:
b) For t = 2015 you have:
![f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7](https://tex.z-dn.net/?f=f%28t%3D2015%29%3D0.001155%5B%5Cfrac%7B2%7D%7B3%7D%282015%29%282015-1980%29%5E%7B1%2F2%7D-%5Cfrac%7B4%7D%7B15%7D%282015-1980%29%5E%7B5%2F2%7D%5D%2B264%2C034%2C000%5C%5C%5C%5Cf%28t%3D2015%29%3D264%2C034%2C317.7)
The answer is -5. Just plug in -5 to check and x will equal 3.
Answer: 85 degrees
Step-by-step explanation:
When a triangle is a 45-45-90 triangle, the following rules apply:
-the 2 legs are equal lengths
- the length of the hypotenuse is: the square root of 2 x the length of a leg.
- the length of the leg is: hypotenuse divided by the square root of 2.
if the hypotenuse is 10, then 10 divided by the square root of 2 is how you find the leg.
the square root of 2 is <span>1.41421356237.
10 divided by </span>1.41421356237 is <span>7.07106781188, which can be rounded to about 7.1. The length of one leg is about 7.1 units!</span>
