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3 years ago

(30 points) HELP PLEASEAlso include how you did it please. I need to know how to solve this.

Mathematics

1 answer:

Doss [256]3 years ago

5 0

Let $a_n$ be the amount of money he has in the account at the end of the $n$ th month.

So at the end of the first month (assuming he doesn't make a withdrawal then) he would have

$a_1=450$ .

Halfway through the next month, he withdraws 1/3 of the account. The account doesn't earn interest, so only his withdrawals affect the amount of money in the bank. So at the end of the second month, he would have

$a_2=\dfrac13(\text{current amount})=\dfrac13\times450$
$a_2=\dfrac13a_1$

At the end of the third, $a_3=\dfrac13(\text{new current amount})=\dfrac13a_2$

And so on. So the recursive rule is

$a_n=\dfrac13a_{n-1}$

starting with $a_1=450$ .

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Domain and range of -3x^2+16x+3

Zarrin [17]

Answer:

＜=16

Step-by-step explanation:

3 0

3 years ago

The number of internet users in mexico between 2004 and 2008 can be modeled as u(t) = 8.02(1.17t) million users where t is the n

maxonik [38]

Answer:

a) 1.479 Million

b) 36.9%

c) 13.668%

Step-by-step explanation:

The complete question is attached in the image below.

The number of internet users in Mexico between 2004 and 2008 is modelled by the following equation:

$u(t)=8.02(1.17)^{t}$

Where, u(t) is in millions and t is the number of years since 2004.

Part a) Rate of change of internet users between 2004 and 2006

The rate of change of a function is defined as:

$\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$

We have to find the rate of change between 2004 and 2006. For 2004 t = 0, and for 2006, t = 2. So the rate of change for the given function will be:

$\frac{u(2)-u(0)}{2-0}\\\\ =\frac{8.02(1.17)^{2}-8.02(1.17)^{0}}{2}\\\\ =1.479$

Thus, the average rate of change in number of internet users in Mexico from between 2004 and 2006 was 1.479 million.

Part b) Percentage change of internet users between 2004 and 2006

The formula to calculate the percentage change is:

$\frac{\text{New value - Original Value}}{\text{Original Value}} \times 100\%$

Here, New value means the users in 2006 and original value means the users in 2004.

Using the values in this formula, we get:

$\frac{8.02(1.17)^{2}-8.02(1.17)^0}{8.02(1.17)^{0}} \times 100\%\\\\ =36.89\%$

Thus, the percentage change in the number of internet users between 2004 and 2006 was 36.89%

Part c) Percentage of internet users in 2008

For 2008, t would be equal to 4.

So, the number of internet users in Mexico in 2008 would be = $8.02(1.17)^{4}=15.02857542$ million = 15,028,575 (rounded to nearest integer)

Total population of Mexico in 2008 = 109,955,400

We have to calculate what percentage of Mexico population was Internet users in 2008. The formula for this would be:

$\frac{\text{Concerned Value}}{\text{Total Value}} \times 100\%$

Here, concerned value is the number of internet users and total value is the total population. Using the values in this formula we get:

$\frac{15028575}{109955400} \times 100\%\\\\=13.668\%$

Thus, 13.668% of the population was internet users in 2008 in Mexico.

5 0

3 years ago

The kerwoods went out to eat at Chili's if there's a bill if they're bill was 58.16 they get in they gave their serve a 15% tip

cestrela7 [59]

8.724 15% of 58.16 is 8.724$

5 0

3 years ago

Read 2 more answers

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(e^x) is rotated about the x-ax

charle [14.2K]

First, it would be good to know that the area bounded by the curve and the x-axis is convergent to begin with.

$\displaystyle\int_{-\infty}^{\ln\pi}\sin(e^x)\,\mathrm dx$

Let $u=e^x$ , so that $\mathrm dx=\dfrac{\mathrm du}u$ , and the integral is equivalent to

$\displaystyle\int_{u=0}^{u=\pi}\frac{\sin u}u\,\mathrm du$

The integrand is continuous everywhere except $u=0$ , but that's okay because we have $\lim\limits_{u\to0^+}\frac{\sin u}u=1$ . This means the integral is convergent - great! (Moreover, there's a special function designed to handle this sort of integral, aptly named the "sine integral function".)

Now, to compute the volume. Via the disk method, we have a volume given by the integral

$\displaystyle\pi\int_{-\infty}^{\ln\pi}\sin^2(e^x)\,\mathrm dx$

By the same substitution as before, we can write this as

$\displaystyle\pi\int_0^\pi\frac{\sin^2u}u\,\mathrm du$

The half-angle identity for sine allows us to rewrite as

$\displaystyle\pi\int_0^\pi\frac{1-\cos2u}{2u}\,\mathrm du$

and replacing $v=2u$ , $\dfrac{\mathrm dv}2=\mathrm du$ , we have

$\displaystyle\frac\pi2\int_0^{2\pi}\frac{1-\cos v}v\,\mathrm dv$

Like the previous, this require a special function in order to express it in a closed form. You would find that its value is

$\dfrac\pi2(\gamma-\mbox{Ci}(2\pi)+\ln(2\pi))$

where $\gamma$ is the Euler-Mascheroni constant and $\mbox{Ci}$ denotes the cosine integral function.

5 0

4 years ago

Name:

Effectus [21]

Answer:

8421

Step-by-step explanation:

8050 < abcd < 8500

We must have a = 8, so the number is 8bcd.

The value of a is 20 times the value of b, or a= 2b.

a = 8, so b = 4.

The value of b is 20 times the value of c, or b = 2c.

b = 4, so c = 2.

The value of c is 20 times the value of d, or c = 2d.

c = 2, so d = 1.

The secret number is 8421.

8 0

3 years ago