All categories

3 years ago

What is the amplitude, period, and phase shift of f(x) = −4 sin(2x + π) − 5?

Mathematics

1 answer:

Nostrana [21]3 years ago

4 0

Answer:

Amplitude = -4; period = π; phase shift: x = π/2

Step-by-step explanation:

* Lets revise the trigonometry translation

- If the equation is y = A sin (B(x + C)) + D

* A is the amplitude

- The amplitude is the height from highest to lowest points and

divide the answer by 2

* The period is 2π/B

- The period is the distance from one peak to the next peak

* C is the horizontal shift (phase shift)

- The horizontal shift is how far the function is shifted to left

(C is positive) or to right (C is negative) from the original position.

* D is the vertical shift

- The vertical shift is how far the function is shifted vertically up

(D is positive) or down (D is negative) from the original position.

* Now lets solve the problem

∵ f(x) = A sin (B(x + C)) + D

∵ f(x) = -4 sin (2x + π) - 5 ⇒ take 2 from the bract (2x + π) common factor

∴ f(x) = -4 sin 2(x + π/2) - 5

∴ A = 4 , B = 2 , C = π/2 , D = -5

∵ A is the amplitude

∴ The amplitude is -4

∵ The period is 2π/B

∴ The period = 2π/2 = π

∵ C is the horizontal shift (phase shift)

∴ The phase shift π/2 (to the left)

* Amplitude = -4; period = π; phase shift: x = π/2

You might be interested in

Calculate a and b if

const2013 [10]

Notice that

$7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}$

$12=2^2\times3$ , so

$\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}$

Then taking the positive square root gives

$\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}$

so $\boxed{a=2}$ and $\boxed{b=1006}$ .

4 0

2 years ago

Solve for the value of k.

OLEGan [10]

Answer:

The value of K is 5

Step-by-step explanation:

I reversed it.

The tiny squares means 90⁰, so 90+49=139

All of these angles add up to 180⁰

So 180-139=41

The k equation equals 41⁰, so reverse it to find answer

41-1=40

40÷8=5

7 0

2 years ago

Read 2 more answers

Thank you so much, my friend

ss7ja [257]

Answer:

Step-by-step explanation:

This is quite a doozy, my friend. We will set up a d = rt table, fill it in...and pray.

The table will look like this before we even fill anything in:

d = r * t

SUV

sedan

Ok now we start to pick apart the problem. Motion problems are the hardest of all story problems ever. This is because there are about 100 ways a motion problem can be presented. So far what we KNOW for an indisputable fact is that the distance from Georgetown to Greenville is 120 km. So we fill that in, making the table:

d = r * t

SUV 120

sedan 120

The next part is derived from the sentence "After an hour, the SUV was 24 km ahead of the sedan." This tells us the rate of the SUV in terms of the sedan. If the SUV is 24 km ahead of the sedan in 1 hour, that tells us that the rate of the sedan is r and the rate of the SUV is r + 24 km/hr. BUT we have other times in this problem, one of them being 25 minutes. We have a problem here because the times either have to be in hours or minutes, but not both. So we will change that rate to km/min. Doing that:

24 $\frac{km}{hr}$ × $\frac{1hr}{60min}=.4\frac{km}{min}$ So now we can fill in the rates in the table:

d = r * t

SUV 120 = r + .4

sedan 120 = r

They left at the same time, so now the table looks like this:

d = r * t

SUV 120 = r + .4 * t

sedan 120 = r * t

We will put in the time difference of 25 minutes in just a sec.

If d = rt, then the equation for each row is as follows:

SUV: 120 = (r + .4)t

sedan: 120 = rt

Since the times are the same (because they left at the same time, we will set the equations each equal to t. The distances are the same, too, I know that, but if we set the distances equal to each other and then solve the equations for a variable, the distances cancel each other out, leaving us with nowhere to go. Trust me, I tried that first! Didn't work.

Solving the first equation for time:

sedan: $\frac{120}{r}=t$ That's the easy one. Now the SUV. This is where that time difference of 25 minutes comes in from the last sentence. Let's think about what that sentence means in terms of the times of each of these vehicles. If the sedan arrived 25 minutes after the SUV, then the sedan was driving 25 minutes longer; conversely, if the sedan arrived 25 minutes after the SUV, then the SUV was driving 25 minutes less than the sedan. The latter explanation is the one I used in the equation. Again, if the SUV was driving 25 minutes less than the sedan, and the equations are solved for time, then the equation for the SUV in terms of time is

$\frac{120}{r+.4}=t-25$ and we solve that for t:

$\frac{120}{r+.4}+25=t$

Again, going off the fact that times they both leave are the same, we set the equations equal to one another and solve for r:

$\frac{120}{r+.4}+25=\frac{120}{r}$

I began by first multiplying everything through by (r + .4) to get rid of it in the denominator. Doing that:

$[r+.4](\frac{120}{r+.4}) +[r+.4](25)=[r+.4](\frac{120}{r})$ which simplifies very nicely to

$120+25(r+.4)=\frac{120}{r}(r+.4)$ So maybe it's not so nice. Let's keep going:

$120+25r+10=\frac{120r}{r}+\frac{48}{r}$ and keep going some more:

$130+25r=120+\frac{48}{r}$ and now we multiply everything through by r to get rid of THAT denominator:

$r(130)+r(25r)=r(120)+r(\frac{48}{r})$ giving us:

$130r+25r^2=120r+48$ Now we have a second degree polynomial we have to solve by factoring. Get everything on one side and factor using the quadratic formula.

$25r^2+10r-48=0$

That factors to

r = 1.2 and r = -1.6 and both of those rates are in km/minute. First of all, we cannot have a negative rate (this is not physics where we are dealing with velocity which CAN be negative) so we throw out the -1.6 and convert the rate of 1.2 km/minute back to km/hr:

$1.2\frac{km}{min}$ × $\frac{60min}{1hr}$ and we get

r = 72 km/h, choice B.

Wow...what a pain THAT was, right?!

5 0

3 years ago

X² = 35<br> show your work

crimeas [40]

Answer:

x=±√35

Step-by-step explanation:

Take the square root of both sides of the equation to eliminate the exponent on the left side.

x=±√35

The complete solution is the result of both the positive and negative portions of the solution.

4 0

3 years ago

FREE BRAINLIEST!! ill also answer questions that you have posted if you answer correctly!!!! (22pts)

GenaCL600 [577]

Answeri think its b lmk if im right or wrong :)

Step-by-step explanation:

8 0

3 years ago