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2 years ago

Find a transformation of sin(x) that gives the following a. b.

Mathematics

1 answer:

riadik2000 [5.3K]2 years ago

4 0

Answer:

a) f(x) = 3sin(2x - π/2) + 1

b) f(x) = 2sin(2x + π) + 2

Step-by-step explanation:

∵ f(x) = Asin(Bx - C) + D

Where ΙAΙ is the the amplitude , 2π/ΙBΙ is the period , -C/B is the horizontal shift and D is the vertical shift

a) The amplitude is 3

The period is π

Shift phase: horizontally π/4 to the right , vertically 1 unit up

b) The amplitude is 2

The period is π

Shift phase: horizontally π/2 to the left , vertically 2 unit up

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2 years ago

The mass of a bacteria culture doubles every four days. If the initial sample is 5mg: a) how much will you have after one week (

maks197457 [2]

Answer:

a) 16.82 mg

b) 24 days

Step-by-step explanation:

Formula for exponential growth is given as:

$A=A_0b^{\frac{t}{c}}$

Where A is the final population

$A_0$ is the initial population

b is the growth factor

c is the time taken for the growth 'b'

t is the amount of time

Here, We are given the following:

$A_0$ = 5 mg

b = 2 (Given because it doubles)

c = 4 days

a) A = ?

Using the formula:

$A=5 \times 2^{\frac{7}{4}}\\\Rightarrow A=5 \times 2^{1.75} \\\Rightarrow A = \bold{16.82\ mg}$

b) Given

A = 320 mg

t = ?

Using the above formula again:

$320 = 5 \times 2^{\frac{t}{4}}\\\Rightarrow \dfrac{320} 5= 2^{\frac{t}{4}}\\\Rightarrow 2^{\frac{t}{4}} = 64\\\Rightarrow 2^{\frac{t}{4}} = 2^6\\\Rightarrow \dfrac{t}{4} = 6\\\Rightarrow t = 6 \times 4\\\Rightarrow \bold{t = 24\ days}$

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3 years ago

What is the volume of this rectangular prisen?<br> Cm<br> 4 cm

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Answer:

64 cm

Step-by-step explanation:

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2 years ago

Alishia rides her bike 45.3 km in 143 minutes. what is her average speed in kilometers per hour?

Nady [450]

Average speed of Alishia is 19 kilometers per hour

Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance. Speed is how fast something is going at a particular moment. Average speed measures the average rate of speed over the extent of a trip

Given :

Distance = 45.3 km

Time taken = 143 minutes = 143/60 =2.384 hours

∴ Average speed = 45.3/2.384 = 19 kilometers per hour

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Learn more about Average speed here :

brainly.com/question/17277454

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1 year ago