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3 years ago

Find x when f(X)=1. (This means find the input that gives an output of 1.)

Mathematics

2 answers:

arlik [135]3 years ago

8 0

There is no solution.

myrzilka [38]3 years ago

3 0

No solution to this

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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

3 years ago

Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many e

andrezito [222]

Pablo : 3(2x) = 6x
Sofia : 2x
Mia : x

Assuming x = 10
Mia : x = 10
Sofia : 2x = 2(10) = 20
Pablo : 3(2x) = 3(20) = 60

10 + 20 + 60 = 90
90/3 = 30 candy eggs per person

Pablo: 60 x 1/2 = 30
Sophia: 30-20 = 10 : 10
Mia : 30 - 10 = 20 : 20

Ratio of eggs given to sophia from pablo's set = 10/60 = 1/6
Ratio of eggs given to mia from pablo's set = 20/60 = 2/6 = 1/3

8 0

3 years ago

On the way to the mall Miguel rides his skateboard to get to the bus stop. He then waits a few minutes for the bus to come, then

professor190 [17]

The answer would be c .

4 0

3 years ago

Read 2 more answers

An amusement park reduced it's admission price to $15.50 per day, but now charges $1.50 per ride. Mark has $26 to spend on admis

gtnhenbr [62]

15.50+1.50x =26
1.50x = 10.50
x = 7
answer: he can ride 7 in one day

4 0