MATHEMATICS COLLEGE

Population the populations P (in thousands) of Las Vegas Nevada from 1960 through 2009 can be modeled by p = 70.751e 0.0451t, where t is the time in years,with t = 0 corresponding to 1960.(a) Find the populations in 1960,1970,1980,1990,2000,and 2009.
(b) Explain why the change in population from 1960to 1970 is not the same as the change in population from 1980 to 1990.
(c) Use the model to estimate the population in 2020.

Answers

Answer 1

Answer:

Answer:

the answer is below

Step-by-step explanation:

The model is:

$p=70751e^(0.0451t)$ where t is the time in years.

when t=0 (year 1960) $p=70751e^(0.0451*0)=70751$

when t=10 (year 1970) $p=70751e^(0.0451*10)=111071$

when t=20 (year 1980) $p=70751e^(0.0451*20)=174368$

when t=30 (year 1990) $p=70751e^(0.0451*30)=273737$

when t=40 (year 2000) $p=70751e^(0.0451*40)=429734$

when t=49 (year 2009) $p=70751e^(0.0451*49)=644882$

The change in population from 1960to 1970 is 111071-70751 =40320

The change in population from 1980 to 1990 is 273737-174368=99369

The change from 1960to 1970 is not the same as the change from 1980 to 1990 because the model function is not linear, it is exponential. Therefore, the rate of the change is not constant.

The population in 2020 using the model can be estimated as

when t=60 (year 2020) $p=70751e^(0.0451*60)=1059091$

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An attacker at the base of a castle wall 4 m high throws a rock straight up with speed 7.5 m/s from a height of 1.5 mabove the ground.
(a) Will the rock exceed the top of the wall?
(b) If so, what is its speed when it reaches the top of the wall?
Page 4 of 7
4
(c) If we don’t want the stone to exceed the top of the wall (we want the top of the wall to be the maximum height)
what the initial speed that the stone must have?

Answers

Answer:

a) Yes, b) $v\approx 2.686\,(m)/(s)$ , c) $v_(o) \approx 7.002\,(m)/(s)$

Step-by-step explanation:

a) The maximum height reached by the rock is:

$\Delta y = (\left(0\,(m)/(s) \right)^(2)-\left(7.5\,(m)/(s) \right)^(2))/(2\cdot \left(-9.807\,(m)/(s^(2)) \right))$

$\Delta y = 2.868\,m$

$y = 1.5\,m + 2.868\,m$

$y = 4.368\,m$

Yes, the rock will exceed the top of the wall.

b) The speed when the rock reaches the top of the wall:

$v = \sqrt{\left(7.5\,(m)/(s) \right)^(2)+2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m)}$

$v\approx 2.686\,(m)/(s)$

c) The initial speed required so that stone does not exceed the top of the wall is:

$v_(o) = \sqrt{\left(0\,(m)/(s) \right)^(2)-2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m) }$

$v_(o) \approx 7.002\,(m)/(s)$

What point represents the coordinate of point (4, 17) after a reflection about the x-axis

Answers

Answer:

Step-by-step explanation: do you have a graph?

Which of the following correctly describes the graph of this function?

Answers

Answer: The graph of the function is symmetric about the y-axis.

Explanation:

Symmetric about the y-axis means that the graph can be reflected over, in this case the y-axis, without altering it. Your function is able to do this! I’ve attached a picture of the function so that you can visualize what I wrote.

HELP ME I WILL GIVE BRAINLIEST California has a population of approximately 4 × 10^7 people and South Dakota has a population of approximately 8 × 10^5 people.

Answers

The population in California is 50 times greater than the population in South Dakota.

The number of times the population in California is higher than that in South Dakota

To find out how many times greater the population in California is than in South Dakota, you can divide the population of California by the population of South Dakota:

Population of California = 4 * 10⁷

Population of South Dakota = 8 * 10⁵

Population ratio = (Population of California) / (Population of South Dakota)

Population ratio = (4 * 10⁷) / (8 * 10⁵)

Population ratio = 50

Therefore the population in California is 50 times greater than the population in South Dakota.

Learn more on calculating ratio here brainly.com/question/2328454

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Question

California Has A Populatio Of Approximately 4*10^(7)People And South Dakota Has Populatio Of Approximately 8*10^(5) People. How Many Times Greater Is The Population In California Than In South Dakota

california has a populatio of approximately 4*10^(7)people and south dakota has populatio of approximately 8*10^(5) people. how many times greater is the population in california than in south dakota

Answer:

40000000 800000

Step-by-step explanation:

whats the question here?

How many meters are in 100 millimeters? 1
10
0.1
100

Answers

Answer:

0.1

Step-by-step explanation:

divide the length value by 1000

“In which quadrant would you find point P if the coordinates of P are (–5, ...”Assuming that P is not on an axis, what are the possible answers to this question?
quadrant I or quadrant II
quadrant II or quadrant III
quadrant II or quadrant IV
quadrant III or quadrant IV

Answers

Answer:

quadrant II or quadrant III

Step-by-step explanation:

Quadrants are numbered I to IV in the counterclockwise direction, starting with upper right. Quadrants II and III are to the left of the y-axis, where x-coordinates are negative.

Answer:

B - quadrant ll or quadrant lll

Step-by-step explanation:

Got it right on edge

Also I ain’t never seen two pretty best friends

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