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adell [148]
2 years ago
7

(01.03. 106, 1.08 HC)

Mathematics
1 answer:
zlopas [31]2 years ago
7 0

Answer:

  A) see attached for a graph. Range: (-∞, 7]

  B) asymptotes: x = 1, y = -2, y = -1

  C) (x → -∞, y → -2), (x → ∞, y → -1)

Step-by-step explanation:

<h3>Part A</h3>

A graphing calculator is useful for graphing the function. We note that the part for x > 1 can be simplified:

  \dfrac{-x^2+x+2}{x^2-3x+2}=-\dfrac{(x-2)(x+1)}{(x-2)(x-1)}=-\dfrac{x+1}{x-1}\quad x\ne 2

This has a vertical asymptote at x=1, and a hole at x=2.

The function for x ≤ 1 is an ordinary exponential function, shifted left 1 unit and down 2 units. Its maximum value of 3^-2 = 7 is found at x=1.

The graph is attached.

The range of the function is (-∞, 7].

__

<h3>Part B</h3>

As we mentioned in Part A, there is a vertical asymptote at x = 1. This is where the denominator (x-1) is zero.

The exponential function has a horizontal asymptote of y = -2; the rational function has a horizontal asymptote of y = (-x/x) = -1. The horizontal asymptote of the exponential would ordinarily be y=0, but this function has been translated down 2 units.

__

<h3>Part C</h3>

The end behavior is defined by the horizontal asymptotes:

  for x → -∞, y → -2

  for x → ∞, y → -1

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 3. So, you have:

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</span> Student N°2=4(2)+7=15
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3 years ago
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.046.0 and
Gala2k [10]

Answer:

The probability of selecting a class that runs between 50.2550.25 and 51.2551.25 minutes is 0.10

Step-by-step explanation:

The Uniform Distribution, also known as Rectangular Distribution, is a type of Continuous Probability Distribution. It has a continuous random variable restricted to a finite interval and its probability function has a constant density during this interval.

The formula of probability if given by:

f(x)=

\left \{ {{\frac{1}{b-a}; \ a \leq x \leq b  } \atop {0}; \ x \ otherwise } \right.

In this exercise a= 46.0 and b= 56.0

The probability of selecting a class that runs between 50.2550.25 and 51.2551.25 minutes is:

\int\limits^{51.25}_{50.25} {\frac{1}{56-46} } \, dx = \int\limits^{51.25}_{50.25} {\frac{1}{10} } \, dx = \frac{1}{10} \times (51.25 - 50.25)=\frac{1}{10}=0.1

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3 years ago
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3 years ago
Read 2 more answers
Based on the side lengths given (a, b, and c), which triangles are right triangles?
Mekhanik [1.2K]

Answer:

B & C

Step-by-step explanation:

Use the Pythagorean Theorem:   a^2 + b^2 = c^2

A) 18^2 + 24^2 = 2,088   |   42^2 = 1,764     [NOT A]

B) 33^2 +56^2 = 4,225   |   65^2 = 4,225     [B IS CORRECT]

C) 19^2 + 180^2 = (32,761) = 181^2 = (32,761)     [C IS CORRECT]

D) 3^2 + 4^2 = 25  |   7^2 = 49     [NOT D]

I hope this helped you ! In return, please deem this the most brainliest answer.

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