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cupoosta [38]
2 years ago
7

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

Mathematics
1 answer:
motikmotik2 years ago
5 0

Answer:

B. -2\frac{1}{2} \leq y \leq \frac{1}{2}

Step-by-step explanation:


The given trigonometric function is

f(x)=\frac{3}{2}cos4x-1.


The amplitude of this function is \frac{3}{2}, so under normal circumstances the range is supposed to be

-\frac{3}{2} \leq y \leq \frac{3}{2}

But the -1 is a downward vertical shift.

Therefore the normal boundaries  of the range will shift down one unit to give the range of the transformed function.


We subtract 1 from the lower boundary to get -\frac{3}{2}-1=-2\frac{1}{2}


We also subtract 1 from the upper boundary to get -frac{3}{2}-1=\frac{1}{2}


Hence the range is


-2\frac{1}{2} \leq y \leq \frac{1}{2}

Also see graph

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An airplane flies due north from ikeja airport for 500km.It then flies on a bearing of 060 from a further distance of 300km befo
Nata [24]

Answer:

482 km

63.94 degrees

Step-by-step explanation:

to solve this question we will use the cosine rule. For starters, draw your diagram. From point A, up north is 500km and 060 from there, another 300. If you join the point from the road junction back to the starting point, yoou have a triangle.

Cosine rule states that

C = \sqrt{A^{2} + B^{2} -2AB   cos(c)  }

where both A and B are the given distances, 500 and 300 respectively, C is the 3rd distance we're looking for and c is the given angle, 060

solving now, we have

C = \sqrt{500^{2} + 300^{2} -2 * 500 * 300 cos(60)  }

C = \sqrt{250000 + 90000 - [215000   cos(60)  }]

C = \sqrt{340000 - [215000 * 0.5  }]

C = \sqrt{340000 - [107500  }]

C =\sqrt{232500}

C = 482 km

The bearing can be gotten by using the Sine Rule.

\frac{sina}{A} = \frac{sinc}{C}

sina/500 = sin60/482

482 sina = 500 sin60

sina = \frac{500 sin60}{482}

sina = 0.8983

a = sin^-1(0.8983)

a = 63.94 degrees

6 0
2 years ago
Put the following in order for the most area in the tails of the distribution. ​(a) Standard Normal Distribution ​(b) Student's​
tensa zangetsu [6.8K]

Answer:

(b) (c) (a)

Step-by-step explanation:

Standard Normal distribution has a higher peak in the center, with more area in this región, hence it has less area in its tails.

Student's​ t-Distribution has a shape similar to the Standard Normal Distribution, with the difference that the shape depends on the degree of freedom. When the degree of freedom is smaller the distribution becomes flatter, so it has more area in its tails.

Student's​ t-Distributionwith 1515 degrees of freedom has mores area in the tails than the Student's​ t-Distribution with 2020 degrees of freedom and the latter has more area than Standard Normal Distribution

5 0
3 years ago
Please help me solve this by substitution: <br> y=x+2<br> 3x+3y=6
VikaD [51]

Answer:

x = 0, y = 2

Step-by-step explanation:

  1. solve the equation for x

3x + 3(x + 2) = 6

2. Substitute the given value of x into the simplest equation y= x + 2

y = 0 + 2

3. Solve the equation for y

y= 2

4. The possible solution of the system is the ordered pair ( x, y)

( x, y) = ( 0, 2)

3 0
3 years ago
Find a negative integer M so that the equation (x-12)(x+m) = m-51​
AleksAgata [21]

Answer:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Step-by-step explanation:

pls give branliest if helped you im in 6th grade and i know all this bc im smarter then how smart i should be.

8 0
3 years ago
Convert these decimal into a fraction 0.457, 0.797, 0.815, and 0.242
kogti [31]
.457/100 .797/100 .815/100 .242/100
3 0
3 years ago
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