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)
Answer:
Step-by-step explanation:
The area of the circle is 
The area of the triangle is 
Hence, the probability of a randomly selected point within the circle falls in the red shaded area is 
I do not have your choices but all the statements that I can think of is the following: A point in the x,y form has two dimensions, a plane has a definite beginning and end, the line has one dimension or length, and finally a point consists of an infinite set of the lines <span />
Answer:
Range is number of copies produced and set of values is; 1 ≤ N ≤ 200
Domain; Cost of publishing book in dollars; set of values are; $710 ≤ N ≤ $2700
Step-by-step explanation:
Range is a set of all the possible output values in a function while domain is the set of all possible input values.
Now, the function is given as;
C = 10N + 700
Where;
C is the cost of publishing the book in dollars
N is the number of copies of books produced
Thus, the domain will be a set of N values while Range will be a set of C values.
We are told that the first printing can produce up to 200 copies of the book.
That means a maximum of 200 books and a minimum of 1.
Thus;
Range is; 1 ≤ N ≤ 200
Maximum possible cost of the 200 books is;
C = 10(200) + 700
C = $2700
Minimum cost which will be for 1 book will be;
C = 10(1) + 700
C = $710
Thus,domain is;
$710 ≤ N ≤ $2700
Answer:
Step-by-step explanation:The new line will be parallel to the line represented by y =2x +2
The equation y = 2x + 2 is written in slope- intercept form (i.e. y=mx + b) where m represents the slope. So the slope of this line is 2. A line parallel to y = 2x + 2 will have the same slope. This means the slope of the new line will also be 2.
To determine the equation of the new line, we can use the given point to find the y intercept of the new line:
y = 2x + b
Use x = -1 and y =3 to find b (or the y intercept ) of the new line:
3 = 2 * (-1) + b
3= -2 + b
b=5
Therefore, the equation of the line passing thru (-1,3) with the same slope as that of y = 2x + 2 will be:
y = 2x + 5
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