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pashok25 [27]
3 years ago
7

the spinner at the right is spun once.find the probability of each event.write each answer as a fraction, percent, and decimal

Mathematics
1 answer:
coldgirl [10]3 years ago
5 0
Im sure it has more but what you have to do is divide or multiply to get your answer not really sure

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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]:

  1. f(x) = cxⁿ
  2. 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>

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

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

  1. [Derivative] Substitute in <em>x</em> = 1:
    \displaystyle f'(1) = -e^{-1}
  2. 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>

  1. [Function] Substitute in <em>x</em> = 1:
    \displaystyle f(1) = e^{-1}
  2. 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.

---

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

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

---

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

Unit: Differentiation

3 0
2 years ago
Cory predicts it will take him 64 minutes to travel to Baltimore from Washington D.C. If the trip actually took 74 minutes, what
n200080 [17]

Answer:13.5



Step-by-step explanation:

the answer is 13.5


6 0
3 years ago
WILL GIVE BRAINLIEST
wlad13 [49]

A) Tonya bought 3 games at X price, so 3X would be total amount.

B) Tony's cost was 0.50 less than X, so x-0.50, he bought 4 games, so he spent 4(x-0.50).

C) Set those to equal to solve for x:

3x = 4(x-0.50)

D) Solve:

3x = 4(x-0.50)

Distribute:

3x = 4x - 2

Subtract 4x from both sides:

-X = -2

Multiply both sides by -1:

X = 2

E) Since X is the amount Tonya paid per game, Tony paid X - 0.50, so Tony paid 2 - 0.50 = $1.50 per game.

Check:

Tonya:  3x = 3(2) = $6 total

Tony: 4(x-0.50) = 4(2.00 - 0.50) = 4(1.50) = $6 total

8 0
3 years ago
Read 2 more answers
The ratio of the number of left handers to the number of right handers in a middle school is 6:15. If there are 120 left handers
fiasKO [112]

Answer:

300

Step-by-step explanation:

there are 9 15's in 120 which means its going by 15's 3 x 5= 15 and if it says 6 that means its timesed by 2. 15 x 2= 30 then 30 x 10= 300

8 0
3 years ago
4x • 7y = 4.7.x.y<br> Property<br> What is this property
patriot [66]

Answer: puppy love is the best love and thats on periodt

Step-by-step explanation: gimme all your love tonight and i will right by your side allll night long do do do do

5 0
3 years ago
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