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2 years ago

What is the sum of the geometric sequence -4,24,-144, ... if there are 7 terms?

1 answer:

const2013 [10]2 years ago

4 0

$S_7=-4+24-144+864-5184+31104-186624$
$S_7=-4(1-6+36-216+1296-7776+46656)$
$(-6)S_7=-4(-6+36-216+1296-7776+46656-279936)$
$S_7-(-6)S_7=-4(1+279936)$
$S_7=-\dfrac47\times279937=-159964$

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the school newspaper has a circulation of 500 and sells for $.035 a copy. the students decide to raise the price to increase the

Alik [6]

Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

$.35+.05x$

Let y be the newspaper they sell, then the income will be

$y(.35+.05x)$

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

$y=500-20x$

Plugging the value of y in the first expression we have that the income will be

$\begin{gathered} f(x)=(500-20x)(.35+\text{0}.5x)=175+25x-7x-x^2 \\ =-x^2+18x+175 \end{gathered}$

Then the income is given by the function

$f(x)=-x^2+18x+175$

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

$\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}$

no we equate the derivative to zero and solve for x.

$\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}$

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

$\begin{gathered} \frac{d^2f}{dx^2}=\frac{d}{dx}(\frac{df}{dx}) \\ =\frac{d}{dx}(-2x+18) \\ =-2 \end{gathered}$

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

Therefore the price to maximize the income is $0.35+$0.45=$0.80.

4 0

10 months ago

The sales tax in the city of Taxemalot is 8.1%. What is the growth factor for any item purchased at your local Tarmart? a.8.1 c.

Rama09 [41]

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7 0

3 years ago

Please please help. Marking Brilliant for the correct answer

NISA [10]

Answer:

x = 19

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(x-7+4) * 4 = 8^2

(x-3)*4 = 64

Divide each side by 4

x-3 =16

Add 3 to each side

x-3+3 = 16+3

x = 19

5 0

2 years ago

A class votes for their class President Kennedy receives 21 votes which is 6% of the vote what is the total number of students w

Katarina [22]

Answer:

Step-by-step explanation:

literally says it in the text ight

6 0

2 years ago

Read 2 more answers

A runner increased her distance from 9 miles to 12.5 miles a week. Find the percent increase in mileage.

kondor19780726 [428]

Answer:

39 percent is increase in mileage.

Thus, the correct option is B. 39%.

Step-by-step explanation:

Given:

A runner increased her distance from 9 miles to 12.5 miles a week.

Now, to find percent increase in mileage.

Previous mileage = 9 miles.

Present mileage = 12.5 miles.

Mileage increase = 12.5 - 9 = 3.5 miles.

Now, to get the percent increase in mileage:

$\frac{Mileage\ increased}{previous\ mileage} \times 100$

$=\frac{3.5}{9} \times 100$

$=\frac{350}{9}$

$=38.88\%.$

Approximately the percent increase = 39%.

Therefore, 39% is increase in mileage.

Thus, the correct option is B. 39%.

4 0

2 years ago