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Marianna [84]
3 years ago
12

PLEASE HELP 46 POINTS!!!

Mathematics
1 answer:
matrenka [14]3 years ago
8 0

Answer:

Step-by-step explanation:

a) Input = -9   ⇒ x = -9

y = x² + 3

Plugin x = (-9),

y = (-9)² + 3  

  =  81 +  3                {(-9)² = -9 * (-9) = 81}

y = 84    ---> Output

y = √x - 2

  = √-9 - 2          { i² = -1}

  = \sqrt{3*3 * i^{2}}-2\\\\=3i -2    

y = 3i - 2  ------> Output

b) Output = 0

y  = x² + 3

x² + 3 = 0

x² = -3

x = \sqrt{-3}=\sqrt{3i^{2}}\\\\x = i \sqrt{3}

y = √x -2

0 = √x - 2

√x = 2

Take square,

(\sqrt{x})^{2}=2^{2}\\\x = 4

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Step-by-step explanation:

0.1 repeating is 1/9, so the number is 4 1/9.

5 0
3 years ago
Find the indicated limit, if it exists.
kondor19780726 [428]

Answer:

d) The limit does not exist

General Formulas and Concepts:

<u>Calculus</u>

Limits

  • Right-Side Limit:                                                                                             \displaystyle  \lim_{x \to c^+} f(x)
  • Left-Side Limit:                                                                                               \displaystyle  \lim_{x \to c^-} f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Limit Property [Addition/Subtraction]:                                                                   \displaystyle \lim_{x \to c} [f(x) \pm g(x)] =  \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)

Step-by-step explanation:

*Note:

In order for a limit to exist, the right-side and left-side limits must equal each other.

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}

<u>Step 2: Find Right-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^+} 5 - x
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} 5 - x = 5 - 5 = 0

<u>Step 3: Find Left-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^-} x + 3
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} x + 3 = 5 + 3 = 8

∴ Since  \displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)  , then  \displaystyle \lim_{x \to 5} f(x) = DNE

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits

5 0
2 years ago
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AysviL [449]

Answer:

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Step-by-step explanation:

Simplify the following:

((3 x)/y)^(-3)

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(y/(3 x))^3

Multiply each exponent in y/(3 x) by 3:

(y^3)/((3 x)^3)

Multiply each exponent in 3 x by 3:

y^3/(3^3 x^3)

3^3 = 3×3^2:

y^3/(3×3^2 x^3)

3^2 = 9:

y^3/(3×9 x^3)

3×9 = 27:

Answer:  y^3/(27 x^3)

6 0
3 years ago
In trapezoid WXYZ, identify WX. PLEASE HELP!!!
matrenka [14]

Answer:

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Step-by-step explanation:

Given that In trapezoid WXYZ, WX║ZY and S and T are the mid points of the sides WZ and XY. We have to find the length of WX.

By trapezoid mid-segment Property,

A mid-segment of a trapezoid join the midpoints of the two non-parallel sides of trapezoid. The length of the mid-segment is the average of the lengths of the two bases and is parallel to the bases of the trapezoid.

∴ ST=\frac{WX+ZY}{2}

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hjlf

Answer:

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8 0
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