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katovenus [111]
3 years ago
12

Please help me with the following questions. Thanks in advance!!

Mathematics
2 answers:
puteri [66]3 years ago
7 0

Answer:

Step-by-step explanation:

In choices a and b, the bases are positive numbers greater than 1, and so these are growth functions.  In c and d, the bases are between 0 and 1, and thus these are decay functions.

In the second problem we have 3ln(x + 1).  Rewrite this as ln(x + 1)^3.

We also have 9ln(x - 4).  Rewrite this as ln(x - 4)^9.

Because of the + sign connecting ln(x + 1)^3 and ln(x - 4)^9, these two logs combine to form

ln [ (x + 1)^3 ] * (x - 4)^9 (the log of a product).

Now we have:

ln [ (x + 1)^3 ] * (x - 4)^9  -  4ln(x + 7), or:

       [ (x + 1)^3 ] * (x - 4)^9

ln ------------------------------------

                (x + 7)^9

bonufazy [111]3 years ago
4 0

Answer:

Step-by-step explanation:

Looking at the table

a) f(x) = 0.35(10)^x is a growth function. The rate of change is greater than one.

b) f(x) = 8(3.75)^x is a growth function. The rate of change is greater than one.

c) f(x) = 2.1(0.79)^x is a decay function. The rate of change is lesser than 1

d) f(x) = 4.3(0.28)^x is a decay function. The rate of change is lesser than 1

5) 3ln(x + 1) + 9(ln x - 4) -4ln( x +

7)

Recall

alnb = b^a. Therefore, the expression becomes

ln(x + 1) ^3 + ln(x -4x)^9 - ln(x + 7)^4

= ln [(x+1)^3 × l(x - 4)^9]/(x + 7)^4

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A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time
dimulka [17.4K]

Answer:

1.61.6 248248

Step-by-step explanation:

6 0
2 years ago
Kesha threw her baton up in the air from the marching band platform during practice. The equation h(t) = −16t² + 54t + 40 gives
lapo4ka [179]

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

                           h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

                         h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

                         h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

                        v ( t ) = dh / dt

                        v ( t )= d ( −16t² + 54t + 40 ) / dt

                        v ( t )= -2*(16)*t + 54

                        v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

                        v ( 0 ) = vi = -32*( 0 ) + 54

                        v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

                     h ( t ) = 0

                     0 = −16t² + 54t + 40

                     0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

                     

                    t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t =  \frac{27 + 37}{16} \\\\t = 4

Answer: The time taken for the baton to hit the ground is t = 4 mins

3 0
3 years ago
A number line has marks A question mark, negative 2, B question mark, 0, 1, C-2, 3, D question mark, 5, E 6.
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Answer:

What number is represented by point B = -1  

Which point represents the number 2? = C

3 0
2 years ago
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If 1/3 of a set of numbers is 8 how many numbers are in the total set ?
Eduardwww [97]

Answer:

24

Step-by-step explanation:

1/3 = 8

3/3 = 8*3

7 0
2 years ago
What is this? I need help because I’m very bad at linear functions as you can see
Mademuasel [1]
N has to be negative.
5 0
3 years ago
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