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Yuliya22 [10]
3 years ago
12

Two trucks started toward each other at the same time from towns 500 km apart. One truck traveled at a rate of 65 km per hour wh

ile the other traveled at 60 km per hour. After how many hours did they meet?
If x represents the number of hours, which of the following equations could be used to solve the problem?
Mathematics
1 answer:
vredina [299]3 years ago
7 0
They will meet in 4 hours.
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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
What is 19% of 72? I NEED TO KNOW HOW YOU GOT THE ANSWER TO!!
irinina [24]
First you must multiply the number by the percent. (19*27= 513)
Then you divide the answer by 100, or move decimal two places to the left. (513/100= 5.13)
Then round to the nearest whole number (5.13 is approximately 5)
Therefore 19%of 27 = 5
:)
4 0
3 years ago
Round to the nearest dime: $3.489
mr_godi [17]
3.49 is the anwser you need
5 0
3 years ago
A company that manufactures cell phones has been given a quarterly operating budget of $1,176,912.42. The company's quarterly op
amm1812

Answer:

maximum is 16,853 cell phones

≤  18.853

Step-by-step explanation:

1,176,912.42.   per quarter budget

247,638.00    per quarter fixed cost

We subtract then divide the amount cost of phones and ensure its less or rounded down.

1,176,912.42 -247,638 = 929274.42

929274.42 / 55.14 = 16853

16,852 < m ≤ 16,853

6 0
3 years ago
Use the distributive property to simplify the expression.<br> 4 (1/4a + b - 6)
nadya68 [22]

Answer:

a+4b-24

Step-by-step explanation:

4 0
2 years ago
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