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3 years ago

Which expression is not equivalent to the other expressions?

1 answer:

4 0

-6(2x - 4) = -6*(2x) -6*(-4) = -12x + 24

-(12x - 6) + 18 = -12x + 6 + 18 = -12x + 24

-3(4x - 3) + 15 = -3*(4x) -3*(-3) + 15 = -12x + 9 + 24 = -12x + 24

-4(3x + 6) = -4*(3x) -4*(6) = -12x -24

All the expressions gave the same answer as -12x + 24, except for the last expression.

So, -4(3x + 6) is not equivalent to the others.

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In 2012, the population of a city was 6.27 million. The exponential growth rate was 1.47% per year.

Tcecarenko [31]

Answer:

a) $a(t)= 6.27e^{0.0147*t}$

b) 6.84 million

c) 2028.52

d) 47 years

Step-by-step explanation:

a)Here we know standard exponential growth rate is

$a(t)= ae^{k*t}$

In this put t=0 and a(t)=6.27 million

thus we get a = 6.27 million

now $\frac{da}{dt}=a(t)k$

this is equal to(in 2012)= $\frac{1.47}{100}*=0.0147$

b)Put t = 6

we get

$a(t)= 6.27e^{0.0147*6}$

=6.84 million

c) $8 = 6.27e^{0.0147*t}$

take log both sides

we get 16.52 years

d) $2*6.27=6.27e^{0.0147*t}$

take log both sides we get 47 years to get double the current population.

3 0

3 years ago

Answer the question with explanation;

PSYCHO15rus [73]

Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

$\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0$

Therefore, by the series divergence test, the series $\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}$ diverges.

EDIT: To VectorFundament120, if $(x_n)_{n\in\mathbb N}$ is a sequence, both $\lim x_n$ and $\lim_{n\to\infty}x_n$ are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.

7 0

3 years ago

Read 2 more answers

PLEASE PLEASE PLEASE HELP I WILL GIVE BRAINLIEST

Marat540 [252]

Answer:

y > 6x -100

Step-by-step explanation:

the slope intercept equation of the line is

y=mx+b

m is the slope = (y2-y1) / (x2-x1) so between the y-intercept (0,-100) and the given point (25, 50) we have m= -100-50/0-25 = -150/-25 = 6

y= 6x -100

now we have to figure the inequqlity part so take point (0, 0) that belongs to the solution and substitute in the equation

0 = 6*0 -100

0 = -100 for the equation to be true we have to make it 0 > -100, we also need to make it NOT greater or equal then because the line is doted not solid so the inequality is

y > 6x -100

4 0

3 years ago

Read 2 more answers

0.2.0.4, 0.6, 0.8, 1....<br> Arithmetic or geometric

Basile [38]

Arithmetic sequences have a common difference between consecutive terms.

Geometric sequences have a common ratio between consecutive terms.

Let's compute the differences and ratios between consecutive terms:

Differences:

$0.4-0.2 = 0.2,\quad 0.6-0.4=0.2,\quad 0.8-0.6=0.2,\quad 1-0.8=0.2$

Ratios:

$\dfrac{0.4}{0.2}=2,\quad \dfrac{0.6}{0.4} = 1.5,\quad \dfrac{0.8}{0.6} = 1.33\ldots, \quad\dfrac{1}{0.8}=1.25$

So, as you can see, the differences between consecutive terms are constant, whereas ratios vary.

So, this is an arithmetic sequence.

3 0

3 years ago

adrian began riding his scooter at 7:00am. He stopped riding it at 8:10am. How long did adrian ride his scooter for?

Alenkinab [10]

Answer:

Adrian rode his scooter for a total of 70 minutes, or an hour and ten minutes.

Step-by-step explanation:

There are 60 minutes in an hour, so if Adrian started riding his scooter at 7:00AM, to get to 8:10AM he needs to add 70. Again, since there are 60 minutes in an hour, 70 minutes converts to one hour and 10 minutes. Adrian rode his scooter for 70 minutes, or an hour and ten minutes.

7:00 + :70 = 8:10

8 0

3 years ago