If it takes 5 hours to drive 62 miles how fast are you going

Two hot air balloons are traveling

xxMikexx [17]

Answer:

Traveling to where?

Step-by-step explanation:

3 0

3 years ago

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P and q are two arithmetic sequences. The first four terms of sequence P are 2,6,10,14. The nth term of sequence Q is 145-3n. Th

Tomtit [17]

Answer:

r = 21

Step-by-step explanation:

nth of sequence P :

$T_{n} = 4n -2$

$r^{th} term$ : $4r-2=145-3r\\4r+3r=145+2\\7r=147\\r=21$

5 0

1 year ago

<img src="https://tex.z-dn.net/?f=%5Csf%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Ccfrac%7B%5Csqrt%7Bx-1%7D-2x%20%7D%7Bx-7%7D" id=

BARSIC [14]

<h3>Answer: -2</h3>

======================================================

Work Shown:

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}\left(\sqrt{x-1}-2x\right) }{ \frac{1}{x}\left(x-7\right) }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}*\sqrt{x-1}-\frac{1}{x}*2x }{ \frac{1}{x}*x-\frac{1}{x}*7 }\\\\\\$

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}}*\sqrt{x-1}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}*(x-1)}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x}-\frac{1}{x^2}}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \frac{ \sqrt{0-0}-2 }{ 1-0 }\\\\\\\displaystyle L = \frac{-2}{1}\\\\\\\displaystyle L = -2\\\\\\$

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Explanation:

In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.

I'm using the rule that

$\displaystyle \lim_{x\to\infty} \frac{1}{x^k} = 0\\\\\\$

where k is some positive real number constant.

Using that rule will simplify the expression greatly to leave us with -2/1 or simply -2 as the answer.

In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.

This effectively means,

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 } = \lim_{x\to\infty} \frac{ -2x }{ x} = -2\\\\\\$

I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.

5 0

3 years ago

Which table does not represent a proportional relationship?

bogdanovich [222]

Answer:

A does not have any proportional relationship.

Step-by-step explanation:

All of the other tables have obvious relationships, leaving A to be the answer.

3 0

2 years ago

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In the year 2002, the world population was estimated at 6 billion people. Based on research from the World Bank, about 20% lived

olga_2 [115]

In the given question all the information's are provided based on which the answer to the question can be easily deduced. It is already given that the population of the world in the year 2002 was estimated to about 6 billion. Among them 20% of the people lived on an an income of less that $1 per day.Firstly let us convert 6 billion from words to numbers.
6 billion = 6000000000
Now
Number of people earning less that $1 per day = (20/100) * 6000000000
= 6000000000/5
= 1200000000
So the number of people earning less than $1 per day is 1200000000

8 0

3 years ago