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Aleksandr [31]
2 years ago
11

What is the remainder

Mathematics
1 answer:
prisoha [69]2 years ago
4 0
The answer is 7, hope this helps!! just plug in 2 for the x and type the answer in :)
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Someone please help me will give BRAILIEST!!!!
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That is dependent because it is changing.independent stays the same
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3 years ago
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For the function g(x)=3-8(1/4)^2-x
Reika [66]

Using function concepts, it is found that:

  • a) The y-intercept is y = 2.5.
  • b) The horizontal asymptote is x = 3.
  • c) The function is decreasing.
  • d) The domain is (-\infty,\infty) and the range is (-\infty,3).
  • e) The graph is given at the end of the answer.

------------------------------------

The given function is:

g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}

------------------------------------

Question a:

The y-intercept is g(0), thus:

g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5

The y-intercept is y = 2.5.

------------------------------------

Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3

--------------------------------------------------

\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty

Thus, the horizontal asymptote is x = 3.

--------------------------------------------------

Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

--------------------------------------------------

Question d:

  • Exponential function has no restrictions in the domain, so it is all real values, that is (-\infty,\infty).
  • From the limits in item c, the range is: (-\infty,3)

--------------------------------------------------

The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631

8 0
2 years ago
I need help with INTERIM CHECKPOINT problems
GenaCL600 [577]
67 ones more than others

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In 1987​, 522 comma 000 people worked in the air transportation industry. In 2003​, the number was 480 comma 000. ​(a) Find a li
umka2103 [35]

Answer:

the linear equation is :

y= -2625x+5737875

and 440000 employees will be in year 2271

Step-by-step explanation:

in order to find the linerar equation let us first convert the given data into (x,y ) co-ordinates i.e

x1= 1987 y1= 522,000  

and

 

x2= 2003, y2 = 480000

according to two point form:

y-y1 = (y2-y1) \frac{x-x1}{x2-x1}

In this example we have x1=1987 , y1=522000 , x2=2003 and y2=480000. So,

y - 522000 = \frac{480000-522000}{2003-1987}  (x-1987)\\y- 522000 = -2625(x-1987)\\y- 522000= -2625x+5215875\\\\y= -2625x+5737875

now to find the year when there will be 440000 employs working , we simply put y= 440000 in the above derived equation

440000= -2625x+ 5737875\\\\2526x = 5737875 -440000\\2526x =  5736555\\x= \frac{5736555}{2526} \\x= 2271

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Answer:

26

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