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2 years ago

F(x) = 3 - 2x and g(x) = 1/X+5 what is the value of (f/g)(8)

Mathematics

1 answer:

Nina [5.8K]2 years ago

8 0

9514 1404 393

Answer:

(f/g)(8) = -104/41

Step-by-step explanation:

Fill in the value for x and do the arithmetic.

f(8) = 3 -2·8 = 3 -16 = -13

g(8) = 1/8 +5 = (1+40)/8 = 41/8

Then the ratio is ...

(f/g)(8) = f(8)/g(8) = -13/(41/8) = -13(8)/41

(f/g)(8) = -104/41

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A geologist studying the depths of water in a mountain lake finds that it has changed from 8,300 ft to 8,881 ft over a period of

grigory [225]

Answer:

7.0%

Step-by-step explanation:

Here, we want to get the value of the percentage increase

mathematically, we have the formula for this as follows ;

(new value - old value/old value * 100%

from the question, old value is 8,300 ft and the new value is 8,881 ft

So we have the percentage increase as follows;

(8,881 - 8,300)/8,300 * 100%

= 7.0%

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2 years ago

What is the price of 0.75 m of fabric if the meter costs 31,500

skad [1K]

Look up what is 75% of 31,500

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2 years ago

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

natima [27]

Answer:

The equation 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:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate
y₁ - y coordinate
m - slope

Calculus

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 slope of the tangent line.

Step 1: Define

Identify given.

$\displaystylef(x) = e^{-x} \\x = -1$

Step 2: Differentiate

[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]:
$\displaystyle f'(x) = -e^{-x}$

Step 3: Find Tangent Slope

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

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

Step 4: Find Equation

[Function] Substitute in x = 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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2 years ago

Bag of candy contains 4 strawberry

Andreas93 [3]

There are 9 candies in total, with 5 being orange. Think of it. For the first grab, you have a 5/9 chance of it being orange flavored. Now there are 4 orange flavored candies, and 8 total candies in the bag. Grabbing a second candy, Billy has a 4/8 chance of grabbing an orange flavored candy. So your two fractions are...

5/9, 4/8

Can you combine these two fractions for a final answer?

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3 years ago

Which expression is equivalent to xy^((2)/(9))?

bonufazy [111]

Pretty sure it's D. When you have a fractional exponent, the root number is always on the bottom, while the exponent on the top. Since x and y are not grouped together in a parentheses, we can assume that only "y" is being raised to the 2/9 power. That means "x "will stay out in front and y will be in the 9th root being raised to the 2nd power.

7 0

2 years ago

Read 2 more answers