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solniwko [45]
3 years ago
12

H(x)= 9/x( x^2-49) Determine the domain of the function

Mathematics
1 answer:
Norma-Jean [14]3 years ago
8 0

Answer: The domain of the function h(x) = \frac{9}{x(x^2-49)} is:

Interval Notation: (-∞ , -7) ∪ (-7 , 0) ∪ (0 , 7) ∪ (7, ∞)

Set-Builder Notation: { x | x ≠ 0 , 7 , -7 }

All real numbers besides 0, 7, and -7.

Step-by-step explanation:

In order to find the domain of your rational function, we need to simplify it:

h(x) = \frac{9}{x(x^2-49)} = \frac{9}{(x)(x+7)(x-7)}

Remember, most of the time, the domain of a rational function consists of all real numbers besides zero.

To find the domain, we equal the equations in the denominator to zero.

x=0

x+7=0 --> x=-7

x-7=0 --> x=7

So all real numbers except for 0, -7, and 7 are in the domain of this rational function.

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Answer:

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3 years ago
In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled a
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Answer:

The answer is "\bold{T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5}"

Step-by-step explanation:

Given value:

Temp-maximum=18^{\circ}  

Temp. minimum = 3^{\circ}

It is halfway between 10 am and 10 pm to 4 am.  

The sinus and cosine roles could be used throughout the year to predict fluctuations in climate models. Its type of formula that can be used to model such information is:  

T = A \cos B(t-C) + D, where parameters are A, B , C, D, T is the ° C temperature and t is the time (1-24)

A = amplitude = \frac{(T_{max} - T_{min})}{2}\\\\

                       = \frac{(3 - 18)}{2}\\\\= - \frac{15}{2}\\\\ = -7.5

B = \frac{2 \pi}{24}\\\\

   = \frac{\pi}{12}

C = \text{ units translated to the right}= 4

D = y_{min} + amplitude = units \ translated \ up\\\\

D = 7.5 + 3 = 10.5

Its trigonometric function equation that model temperature T hours after midnight in Johannesburg t.

T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5

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true

Step-by-step explanation:

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