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oksian1 [2.3K]
3 years ago
6

I need some help.. fraction: {5⁷}{5²}

Mathematics
1 answer:
Anvisha [2.4K]3 years ago
3 0

Step-by-step explanation:

\dfrac{5^7}{5^2}\qquad|\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=5^{7-2}=5^5

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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
A CD has a 5% chance of being a smash hit and profiting $5.2 million, a 50% chance of being a modest success and profiting $0.9
Zinaida [17]
The probability of profiting $5.2 million is 5% = 0.05

The probability of profiting $0.9 million is 50% = 0.5

The probability of breaking even, meaning no profit gain, is 45% = 0.45

Expected profit values of the CD is given by
(0.05×5.2) + (0.5×0.9) + (0.45×0) = 0.26+0.45+0 = 0.71 million

3 0
3 years ago
Of the following options, what could be a possible first step in solving the equation 8x + 3 = 2x - 15
Basile [38]
The first step can be subtracting 2x from both sides leaving the equation with 6x + 3 = -15
6 0
3 years ago
Need Help ASAP
iren2701 [21]
The sum of the interior angles of a triangle is 180 degrees

2x-9+3x+x+3=180
6x-6=180
6x=186
x=31

A=2(31)-9
A=62-9
A=53
8 0
3 years ago
Please help with this algebra question
valina [46]

Answer:

i think its

P(x) =  i ^{3}

Step-by-step explanation:

8 0
3 years ago
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