How many fixed points are there for the function f(x)=x^4

On the first january 2014 carol invested some money in a bank account the account payes 2.5% compound interest per year on 1st j

Sladkaya [172]

Answer:

$23,360

Step-by-step explanation:

Calculation to determine how much carol originally invested in the account

First step is to divide £23517.60 by 1.025

= (23,517.60)/(1+.025)

= (23,517.60)/1.025

=$22,944

Second step is to add back the $1,000 withdrew

=$22,944+$1,000

=$23,944

Now let calculate how much carol originally invested in the account

$23,944=1.025P

Divide both side by 1.025

P=$23,944/1.025

P=$23,360

Therefore the amount that carol originally invested in the account is $23,360

4 0

2 years ago

A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to th

solmaris [256]

Answer:

Total number of riders that ride on carpool daily = 2000

Total Cost of one way ticket = $ 5.00

Total Amount earned if 2000 passengers rides daily on carpool = 2000 × 5

= $10,000

If fare increases by $ 1.00

New fare = $5 + $1

= $6

Number of passengers riding on carpool = 2,000 - 100 = 1,900

If 1,900 passengers rides on carpool daily , total amount earned ,if cost of each ticket is $ 6 = 1900 × $6 = $11400

As we have to find the inequality which represents the values of x that would allow the carpool service to have revenue of at least $12,000.

For $ 1 increase in fare = (2,000 - 1 × 100) passengers

For $ x increase in fare, number of passengers = 2,000 - 100·x

= (2,000 - 100·x) passengers

New fare = 5 + x

New Fare × Final Number of passengers ≥ 12,000

(5+x)·(2,000 - 100 x) ≥ 12,000

5 (2,000 - 100 x) + x(2,000 - 100 x) ≥ 12,000

10,000 - 500 x + 2,000 x - 100 x² ≥ 12,000

100 - 5 x + 20 x - x² ≥ 120

- x² + 15 x +100 - 120 ≥ 0

-x² + 15 x -20 ≥ 0

x² - 15 x + 20 ≤ 0

⇒ x = 1.495

x ≥ $ 1.495, that is if we increase the fare by this amount or more than this the revenue will be at least 12,000 or more .

Also, f'(x) = 0 gives x = 7.5

⇒ The price of a one-way ticket that will maximize revenue is $7.50

7 0

2 years ago

The picture below shows a right-triangle-shaped charging stand for a gaming system: The side face of a charging stand is a right

mamaluj [8]

Answer:

AB = 8/ cos 60

Step-by-step explanation:

We want to find the hypotenuse AB

Since we have a right triangle

cos theta = adj/ hyp

cos 60 = 8/ AB

AB cos 60 = 8

AB = 8/ cos 60

3 0

2 years ago

HELP PLS>>> The vector (3, - 7) ) is rotated by an angle of (3pi)/4 radians and then reflected across the y-axis. If th

horsena [70]

Answer:

$a \approx -2.826$ , $b \approx 7.072$

Step-by-step explanation:

First, the vector must be transformed into its polar form:

$r = \sqrt{3^{2}+ (-7)^{2}}$

$r \approx 7.616$

$\theta \approx 2\pi - \tan^{-1}\left(\frac{7}{3} \right)$

$\theta \approx 1.629\pi$

Let assume that vector is rotated counterclockwise. The new angle is:

$\theta' = \theta + \frac{3\pi}{4}$

$\theta' = 2.379\pi$

Which is coterminal with $\theta'' = 0.379\pi$ . The reflection across y-axis is:

$\theta''' = \pi - \theta''$

$\theta''' = 0.621\pi$

The equivalent vector in rectangular coordinates is:

$a = 7.616\cdot \cos 0.621\pi$

$a \approx -2.826$

$b = 7.616\cdot \sin 0.621\pi$

$b \approx 7.072$

7 0

2 years ago

A vertical pole, 40 feet tall, casts a shadow onto the ground. If the angle of elevation from the tip of the shadow on the groun

aksik [14]

Answer:

Lenght of a shadow is 96.6

Step-by-step explanation:

you may use right angle triangle to find distance if you know angle of elevation.

(a) adjacent (b) hypotenuse

(c) Opposite

we know that:

adjacent (a)=40

opposite (b)=?

tan ∅= opposite/adjacent

tan 67°=opposite/40

2.4142 * 40 = adjacent

adjacent =96.6

3 0

2 years ago