Write the equation that represents the graph

The annual net income of a company for the period 2007–2011 could be approximated by P(t) = 1.6t2 − 11t + 44 billion dollars (2

son4ous [18]

Answer:

$P'(t) = 3.2 t -11$

And we can set equal this derivate to 0 in order to find the critical point and we got:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

And we can calculate the second derivate and we got:

$P''(t) = 3.2 >0$

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094

Step-by-step explanation:

For this case we have the following function:

$P(t) = 1.6 t^2 -11t +44$

Where P represent the annual net income for the period 2007-2011 and $2 \leq t \leq 7$

And t represent the time in years since the start of 2005

In order to find the lowet income we need to use the derivate, given by:

$P'(t) = 3.2 t -11$

And we can set equal this derivate to 0 in order to find the critical point and we got:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

And we can calculate the second derivate and we got:

$P''(t) = 3.2 >0$

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094

5 0

3 years ago

A photographer charges $25 to travel to a client's location, plus $55 per hour for her

Sloan [31]

Answer:

8 Hours

Step-by-step explanation:

First, you have to subtract the 25$ because we already know that that is a stable value (meaning it will not change)

Then, you have to divide 440 by 55 to get an answer of 8 hours for the session :D

8 0

3 years ago

Read 2 more answers

which ordered pairs are solutions to the inequality y−4x≥−5? Select each correct answer. (−4, 2) (4, 0) (5, −2) (−2, 1) (1, −1)

sukhopar [10]

This graph should help find the coordinates you need that was made of this inequality!

4 0

3 years ago

Read 2 more answers

find the values of x and y that make these triangles congruent by the hl theorem x=2,y=3 x=-2,y=3x=3,y=2x=4,y=8

AnnyKZ [126]

Answer:

The correct option is x=3 , y=2

Step-by-step explanation:

According to the HL theorem if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle then the triangles are congruent.

By using this theorem we can set up the system of equations as follows:

x=y+1 ...(1)

2x+3= 3y + 3 ..(2)

Now we will plug the value y+1 of equation 1 in equation 2.

2x+3 = 3y+3

2(y+1)+3=3y+3

2y+2+3=3y+3

2y+5=3y+3

Now combine the like terms:

5-3=3y-2y

2=y

y=2

Now plug the value y=2 in equation 1.

x=y+1

x=2+1

x=3

Thus the values of(x.y) are{(2,3)}

Therefore the correct option is x=3 , y=2 .....

3 0

3 years ago

Hillary is planning an expensive surprise party. She is choosing between two venues. The banquet hall at Hotel A will cost $431

In-s [12.5K]

Answer: Hillary would have to invite 15 people before the cost of having the party at Hotel B is less than the cost of having a party at Hotel A

Step-by-step explanation:

Let x represent the number of guests that Hillary would invite.

The banquet hall at Hotel A will cost $431 to rent the room and $38 per guest. This means that the total cost of hosting x guests at hotel A is

38x + 431

The banquet hall at Hotel B will cost $747 to rent the room and $16 per guest. This means that the total cost of hosting x guests at hotel B is

16x + 747

For the cost of having the party at Hotel B to be less than the cost of having a party at Hotel A, it means that

16x + 747 < 38x + 431

747 - 431 < 38x - 16x

316 < 22x

22x > 316

x > 316/22

x > 14.36

6 0

3 years ago