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patriot [66]
3 years ago
5

Determine the slope-intercept form of the equation of the line parallel to y = -4/3 x + 11 that passes through the point (–6, 2)

. y = x +
Mathematics
1 answer:
rewona [7]3 years ago
6 0

Answer: -4/3x - 6

Step-by-step explanation:

First, let's find the slope of the line

y=- -4/3x+11

As the equation is already in slope-intercept form y=mx+c ,

Slope = -4/3

Let a point (x,y) be on the new line.

By finding the slope again,

y−2/x+6= -4/3

y−2= -4/3(x+6)

y−2= -4/3x−8

y = -4/3x - 6

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Find the measure of 1 in the​ figure, shown to the right.
Aleks04 [339]

Answer:

∠1 = 81°

Step-by-step explanation:

∠1 and 81° are corresponding angles and corresponding angles are equal to each other.

3 0
3 years ago
A fluid has density 860 kg/m3 and flows with velocity v = z i + y2 j + x2 k, where x, y, and z are measured in meters and the co
ehidna [41]

You can use the divergence theorem:

\vec v=z\,\vec\imath+y^2\,\vec\jmath+x^2\,\vec k

has divergence

\mathrm{div}\vec v=\dfrac{\partial z}{\partial x}+\dfrac{\partial y^2}{\partial y}+\dfrac{\partial x^2}{\partial z}=2y

Then the rate of flow out of the cylinder (call it <em>R</em>) is

\displaystyle\iint_{\partial R}\vec v\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec v\,\mathrm dV

(by divergence theorem)

=\displaystyle2\int_0^{2\pi}\int_0^5\int_0^1r^2\sin\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta

(after converting to cylindrical coordinates)

whose value is 0.

6 0
3 years ago
What is the derivative of 1/square root 4x.
Bumek [7]

Answer:

\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

Exponential Properties

  • Exponential Property [Rewrite]:                                                                   \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Property [Root Rewrite]:                                                           \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)  

Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]

<u>Step 2: Differentiate</u>

  1. Simplify:                                                                                                         \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'
  2. Rewrite [Derivative Property - Multiplied Constant]:                                   \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'
  3. Rewrite [Exponential Rule - Root Rewrite]:                                                 \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'
  4. Rewrite [Exponential Rule - Rewrite]:                                                           \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'
  5. Derivative Rule [Basic Power Rule]:                                                             \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)
  6. Simplify:                                                                                                         \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}
  7. Rewrite [Exponential Rule - Rewrite]:                                                           \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}

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

Unit: Differentiation

5 0
3 years ago
Kyree needs to fill up his truck with gasoline to drive to and from school. Gas costs $2.79 per gallon, and his truck holds a ma
Lunna [17]

Let x represent the cost per gallon of gasoline.

Let y or f(x) represent the cost of x gallons of gasoline.

Given that the cost per gallon is $2.79,

The function would be

f(x) = 2.79x

The domain refers to all possible values of x that can fit into the function. Given that the truck holds a maximum of 28 gallons, the maximum value of x is 28. When the truck is empty, the minimum value of x is 0. Therefore, the domain is 0 to 28

The range refers to all possibel values of y or f(x) that can satisfy the function.

When x = 0, f(x) = 2.79 * 0 = 0

When x = 28, f(x) = 2.79 * 28 = 78.12

The range would be 0 to 78.12

Domain: 0 to 28

Range: 0 t0 78.12

4 0
1 year ago
Evaluate the expression x ÷ y for x = 8 and y = 16.
daser333 [38]

Answer:

Step-by-step explanation:

hello :

x ÷ y for x = 8 and y = 16 means : 8/16 = 8/(2×8) = 1/2

7 0
4 years ago
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