Solve the inequality.<br> r −6<br> r

Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations:

1) $x$ must be replaced by $\frac{2\pi\cdot x}{180^{\circ}}$ . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

$\Delta z = \frac{z_{max}-z_{min}}{2}$

$\Delta z = \frac{5+4}{2}$

$\Delta z = \frac{9}{2}$

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

$z_{m} = \frac{z_{min}+z_{max}}{2}$

$z_{m} = \frac{1}{2}$

The new function is:

$z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)$

Given that $z_{m} = \frac{1}{2}$ , $\Delta z = \frac{9}{2}$ and $T = 180^{\circ}$ , the outcome is:

$z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0

2 years ago

Two spinners are spun. One has 5 sections labeled Red, Orange, Purple, Yellow, and Green. The other has three sections labeled 1

quester [9]

Answer:

$S = 15$ possible outcomes

Step-by-step explanation:

For any experiment, the sample space of this experiment is the set of all the possible results of the experiment.

In this case we have two spinners. The first has 5 colors, by spinning the spinner you can get up to 5 different results. Therefore the sample space is $S_1 = 5$

For the second spinner there are 3 possible results. By spinning the spinner you can get the numbers 1, 2 or 3. Then $S_2 = 3$ .

Then, if the two spinners are rotated, the sample space would be:

$S = 5*3$

$S = 15$ possible outcomes.

The tree diagram shown in the attached image shows the 15 possible results

{R, 1} {R, 2} {R, 3} {O, 1} {O, 2} {O, 3} {Y, 1} {Y, 2} {Y, 3} {P, 1} {P, 2} {P, 3} {G, 1}

{G, 2} {G, 3}

4 0

2 years ago

Find the circumference of the given circle 11 ft

nasty-shy [4]

Answer:

69.12

Step-by-step explanation:

5 0

3 years ago

-12-x>-12+4x<br> put the steps too pls thanks

andrey2020 [161]

Answer:

x < 0

Step-by-step explanation:

Firstly put the values with variable x to one side,

; -12 - x > -12 + 4x

; -12 + 12 > 4x + x

; 0 > 5x

then divide both sides by 5,

; (0 ÷ 5) > (5x ÷ 5)

; 0 > x

; Hence the solution to the inequality above,

; x < 0...always remember to reverse the sign when you change the side to which you put the variable of x,

Therefore...( x < 0 )

3 0

3 years ago

How many times does the quadratic function intesect the x axis y=2x^+7x+6

atroni [7]

Answer:

There are two intersections

Step-by-step explanation:

The number of intersections can be found by calculating the delta of the equation

Δ=b²-4ac

if Δ=0, there is 1 intersection

if Δ>0 there are 2 intersections

if Δ=<0, there are no intersections

where the quadratic equation is in the form ax²+bx+c

Δ=7²-4(2)(6)

=1>0

There are two intersections

6 0

3 years ago

Solve the inequality. r −6 r > 6