All categories

3 years ago

Find the range of y= 3/2 cos 4x-1

Mathematics

2 answers:

hoa [83]3 years ago

6 0

Answer:

The range of y is $[-\dfrac{5}{2},\dfrac{1}{2}]$

Step-by-step explanation:

Given: $y=\dfrac{3}{2}\cos (4x) -1$

It is cosine function of trigonometry.

We need to find the range of given function. The value of y shows range of function.

y is depends on cosine function.

As we know cosine max/min value is fixed.

y is max when cosine max.

y is min when cosine is min.

Maximum value of cosine = 1

$y_{max}=\dfrac{3}{2}(1) -1=\dfrac{1}{2}$

Minimum value of cosine = -1

$y_{min}=\dfrac{3}{2}(-1) -1=-\dfrac{5}{2}$

Range of y: [min,max]

Range: $[-\dfrac{5}{2},\dfrac{1}{2}]$

Hence, The range of y is $[-\dfrac{5}{2},\dfrac{1}{2}]$

Furkat [3]3 years ago

5 0

I have attached how to work through this problem. I hope this helps

You might be interested in

What is the total surface area

AlekseyPX

The Total Surface Area Would Be A number

7 0

3 years ago

Linda bought $87.95 worth of merchandise at an electronics store. She

forsale [732]

Answer: She paid $66.33

Step-by-step explanation:

The overall amount that you paid for the video game was 87.95. She got 27.79 back as a refund. So you subtract what she paid from her refund. 87.95-27.79 = 60.16. She also had to pay a fine for the video game. So you add the fine to the amount. 60.16+6.17 = 66.33.

Overall, she paid 66.33.

6 0

2 years ago

Read 2 more answers

College LEVEL can you help me? :S

Yanka [14]

Although the formula looks involved, the key here is looking to see where the information goes.

We are given all the pieces but need to convert mph to ft/s to use the formula. Let's do it with 1 mph so that we have a ratio to use. We and solve a unit conversion problem.

$\frac{1mile}{hour} * \frac{hour}{60 minutes} * \frac{minute}{60 seconds} * \frac{5280 feet}{mile} = \frac{5280}{60*60} = \frac{5280}{3600} = 1.46666$

That ratio tells us that 1 mph is 1.466666 ft/s. Now we solve two proportions.

1 mph / 1.466666 feet per second = 60 mph / x feet per second.

1x = (60)(1.466666)

So x = 88 feet per second.

Next, We repeat for 24 mph.

1 mph / 1.46666 feet per second = 24 mph / x feet per second.

1x = (1.4666666)(24)

x = 35.2 feet per second

Now we have the found appropriate V₁ and V₂. V₁ > V₂, so V₁ is 88 ft/s and V₂ is 35.2 ft/s. The problem tells us θ = 2.3 degrees, K₁ = .4 and K₂ = .06. The rest of the problem is calculator work. Start by substituting our degree measure of 2.3 degrees and the given values in the problem for V₁, V₂, K₁, and K₂

$D = \frac{1.05[(88)^{2}-(35.2)^{2}]}{64.4(.4+.06 + (sin 2.3))}$