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Trava [24]
3 years ago
13

Which expression is equivalent to ^3√x^5y?a)x5/3b)x5/3y1/3c)x3/5 yd)x3/5 y3​

Mathematics
1 answer:
Illusion [34]3 years ago
7 0

Answer:

(x^5y)^{\frac{1}{3}}= x^{\frac{5}{3}} \times y^{\frac{1}{3}}

Step-by-step explanation:

We are given our expression as

\sqrt[3]{x^5y}

The property of exponent says that

\sqrt[n]{x} =x^{\frac{1}{n}}

Hence

\sqrt[3]{x^5y}= (x^5y)^{\frac{1}{3}}

Another property says

(ab)^n=a^n \times b^n

Hence

(x^5y)^{\frac{1}{3}}= x^{\frac{5}{3}} \times y^{\frac{1}{3}}

Hence option B is correct.

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graph the function f (x) = x^2 + 4x -5. on the coordinate plane. (a) What are the x-intercepts? (b) What are the y-intercepts? (
Butoxors [25]

Answer:

a) (-5,0) and (1,0)

b) (0,-5)

c) minimum

See attached graph.

Step-by-step explanation:

To graph the function, find the vertex of the function find (-b/2a, f(-b/2a)). Substitute b = 4 and a = 1.

-4/2(1) = -4/2 = -2

f(-2) = (-2)^2 + 4(-2) - 5 = 4 - 8 - 5 = -4 - 5 = -9

Plot the point (-2,-9). Then two points two points on either side like x = -1 and x = -3. Substitute x = -1 and x = -3

f(-1) = (-1)^2 + 4 (-1) - 5 = 1 - 4 - 5 = -8

Plot the point (-1,-8).

f(-3) = (-3)^2 + 4(-3)  - 5 = 9 - 12 - 5 = -8

Plot the point (-3,-8).

See the attached graph.

The features of the graph are:

a) (-5,0) and (1,0)

b) (0,-5)

c) minimum

5 0
3 years ago
Y= -4/3x - 5/2<br><br>y-intercept:<br><br>slope:​
CaHeK987 [17]

Answer:the answer is Y= -4/3x - 5/2

Step-by-step explanation:

3 0
3 years ago
Can anybody help plzz?? 65 points
Yakvenalex [24]

Answer:

\frac{dy}{dx} =\frac{-8}{x^2} +2

\frac{d^2y}{dx^2} =\frac{16}{x^3}

Stationary Points: See below.

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Equality Properties

<u>Calculus</u>

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

  • 1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef
  • 2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Quotient Rule: \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

f(x)=\frac{8}{x} +2x

<u>Step 2: Find 1st Derivative (dy/dx)</u>

  1. Quotient Rule [Basic Power]:                    f'(x)=\frac{0(x)-1(8)}{x^2} +2x
  2. Simplify:                                                      f'(x)=\frac{-8}{x^2} +2x
  3. Basic Power Rule:                                     f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}
  4. Simplify:                                                     f'(x)=\frac{-8}{x^2} +2

<u>Step 3: 1st Derivative Test</u>

  1. Set 1st Derivative equal to 0:                    0=\frac{-8}{x^2} +2
  2. Subtract 2 on both sides:                         -2=\frac{-8}{x^2}
  3. Multiply x² on both sides:                         -2x^2=-8
  4. Divide -2 on both sides:                           x^2=4
  5. Square root both sides:                            x= \pm 2

Our Critical Points (stationary points for rel max/min) are -2 and 2.

<u>Step 4: Find 2nd Derivative (d²y/dx²)</u>

  1. Define:                                                      f'(x)=\frac{-8}{x^2} +2
  2. Quotient Rule [Basic Power]:                  f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2
  3. Simplify:                                                    f''(x)=\frac{16}{x^3} +2
  4. Basic Power Rule:                                    f''(x)=\frac{16}{x^3}

<u>Step 5: 2nd Derivative Test</u>

  1. Set 2nd Derivative equal to 0:                    0=\frac{16}{x^3}
  2. Solve for <em>x</em>:                                                    x = 0

Our Possible Point of Inflection (stationary points for concavity) is 0.

<u>Step 6: Find coordinates</u>

<em>Plug in the C.N and P.P.I into f(x) to find coordinate points.</em>

x = -2

  1. Substitute:                    f(-2)=\frac{8}{-2} +2(-2)
  2. Divide/Multiply:            f(-2)=-4-4
  3. Subtract:                       f(-2)=-8

x = 2

  1. Substitute:                    f(2)=\frac{8}{2} +2(2)
  2. Divide/Multiply:            f(2)=4 +4
  3. Add:                              f(2)=8

x = 0

  1. Substitute:                    f(0)=\frac{8}{0} +2(0)
  2. Evaluate:                      f(0)=\text{unde} \text{fined}

<u>Step 7: Identify Behavior</u>

<em>See Attachment.</em>

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

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What is the area of each piece of paper that Jodi is cutting out
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The simplest (and most commonly used) area calculations are for squares and rectangles. To find the areaof a rectangle multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself tofind the area.
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Solve -3/4(8k-24)&gt;-12
lisabon 2012 [21]

-\dfrac{3}{4}(8k-24) > -12\ \ \ \ |\teext{change the signs}\\\\\dfrac{3}{4}(8k-24) < 12\ \ \ \ |\cdot\dfrac{4}{3}\\\\8k-24 < 12\cdot\dfrac{4}{3}\\\\8k-24 < 4\cdot4\\\\8k-24 < 16\ \ \ \ |+24\\\\8k < 40\ \ \ \ |:8\\\\k < 5\to k\in(-\infty;\ 5)

7 0
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