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2 years ago

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Statements showing a relationship between numbers that are not necessarily equal using the symbols >, <, ≥, ≤, or ≠ are ca

lled _____. 1. inferences 2.inconsistencies 3.inequalities 4.unequals

1 answer:

likoan [24]2 years ago

7 0

3.) Inequalities.
Hope it helped.

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How much would the sales tax be on a $66 meal?

vovangra [49]

Answer:

$71.61

Step-by-step explanation:

66/22 = 3

3 · $1.87 = $5.61

$66 + $5.61 = $71.61

OR

$23.87 · 3 = $71.61

Sorry if this is wrong!

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2 years ago

Can someone help me answer this question

lubasha [3.4K]

Answer:

253.89 pounds

Step-by-step explanation:

$1 = 0.74 pounds

345 * 0.74 = 253.89

$345 = 253.89 pounds

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1 year ago

F(x) = e^-x . Find the equation of the tangent to f(x) at x=-1

natima [27]

Answer:

The <em>equation</em> of the tangent line is given by the following equation:

$\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)$

General Formulas and Concepts:

<u>Algebra I</u>

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate
y₁ - y coordinate
m - slope

<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]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
$\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the <em>slope of the tangent line</em>.

<u>Step 1: Define</u>

<em>Identify given.</em>

<em /> $\displaystylef(x) = e^{-x} \\x = -1$

<u>Step 2: Differentiate</u>

[Function] Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
$\displaystyle f'(x) = e^{-x}(-x)'$
[Derivative] Rewrite [Derivative Rule - Multiplied Constant]:
$\displaystyle f'(x) = -e^{-x}(x)'$
[Derivative] Apply Derivative Rule [Derivative Rule - Basic Power Rule]:
$\displaystyle f'(x) = -e^{-x}$

<u>Step 3: Find Tangent Slope</u>

[Derivative] Substitute in <em>x</em> = 1:
$\displaystyle f'(1) = -e^{-1}$
Rewrite:
$\displaystyle f'(1) = \frac{-1}{e}$

∴ the slope of the tangent line is equal to $\displaystyle \frac{-1}{e}$ .

<u>Step 4: Find Equation</u>

[Function] Substitute in <em>x</em> = 1:
$\displaystyle f(1) = e^{-1}$
Rewrite:
$\displaystyle f(1) = \frac{1}{e}$

∴ our point is equal to $\displaystyle \bigg( 1, \frac{1}{e} \bigg)$ .

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

$\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }$

∴ we have our final answer.

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Learn more about derivatives: brainly.com/question/27163229

Learn more about calculus: brainly.com/question/23558817

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

Unit: Differentiation

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