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Marta_Voda [28]

1 year ago

12

A new restaurant opens, and on the first night has 100 guests. Each night after that, the number of guests grows by 20 people. W

hat type of sequence does this scenario represent, and why? If the pattern of the sequence continues, how many guests will the restaurant have on its 14th night?

2 answers:

OverLord2011 [107]1 year ago

5 0

Answer:

100, 120, 140, 160, 180, 200,...

pattern : +20

100+20n , where n = 0,1,2,3,...

when n = 14

100 + 20(14) = 380 guests

aliya0001 [1]1 year ago

4 0

What type of sequence does this scenario represent, and why?

✔ arithmetic; the sequence has a common difference

If the pattern of the sequence continues, how many guests will the restaurant have on its 14th night?

✔ 360

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bearhunter [10]

Answer: If I am correct the value of x might be f=0

Step-by-step explanation:

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2 years ago

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

On a coordinate plane, a cube root function goes through (negative 2.5, negative 3.5), crosses the y-axis at (0, negative 3), ha

mart [117]

Answer:

$g(x) = \sqrt[3]{x-1} - 2$

Step-by-step explanation:

We want to find h and k in:

$g(x) = \sqrt[3]{x-h} + k$

At the inflection point, the second derivative is equal to zero, so:

$g'(x) = \frac{1}{3} (x-h)^{\frac{-2}{3}}$

$g''(x) = \frac{1}{3} \frac{-2}{3}(x-h)^{\frac{-5}{3}} = 0$

Then x - h = 0.

Inflection point is located at (1, -2), replacing this x value we get:

1 - h = 0

h = 1

We know that the point (-2.5, -3.5) belongs to the function, so:

$-3.5 = \sqrt[3]{-2.5-1} + k$

k ≈ -2

All data, used or not, are shown in the picture attached.

4 0

2 years ago

On January 4, janelle ruskinoff deposited $2192.06 in a savings account that pays 5.5 percent interest compounded daily. How muc

Andru [333]

Answer:

$7.94

Step-by-step explanation:

We have been given that on January 4, Janelle Ruskinoff deposited $2192.06 in a savings account that pays 5.5 percent interest compounded daily. We are asked to find the amount of interest earned in 24 days.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$ , where,

A = Final amount after t years,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = time in years.

24 days in years would be $\frac{24}{365}$ .

$r=\frac{5.5}{100}=0.055$

Upon substituting our given values in above formula, we will get:

$A=2192.06(1+\frac{0.055}{365})^{365\times\frac{24}{365}}$

$A=2192.06(1+0.0001506849315068)^{24}$

$A=2192.06(1.0001506849315068)^{24}$

$A=2192.06(1.0036227121284570884)$

$A=2200.001202348$

To find amount of interest earned, we will subtract principal amount from final amount as:

$I=A-P$

$I=2200.001202348-2192.06$

$I=7.941202348$

$I\approx 7.94$

Therefore, her money will earn approximately $7.94 in 24 days.

5 0

2 years ago

A bug is moving back and forth on a straight path. The velocity of the bug is given by vt=t2-3t. Find the average acceleration o

g100num [7]

Answer:

2 unit/time²

Step-by-step explanation:

Given the equation:

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V(4) = 4

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Average acceleration = (4 - (-2)) ÷ (4 - 1)

Average acceleration = (4 + 2) / 3

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Average acceleration = 2

3 0

2 years ago