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3 years ago

The price of an item has been reduced by 40%. The original price was $60. What is the price of the item now?

1 answer:

4 0

To reduce the item by 40%, you first need to find the 40% of 60. Multiply 0.4*60 and you will get 24. That is 40%. Now you need to subtract that from the original. 60-24 is 36 dollars and that is your answer.

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210

seropon [69]

The answer is The second one because I took this test before and I got it right

4 0

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

3 0

1 year ago

In the xy-plane, a line crosses the y-axis at the point (0, 3) and passes through the point (4, 5). Which is the equation of the

Gelneren [198K]

Answer:D

Step-by-step explanation:

4 0

2 years ago

Determine whether the value given below is from a discrete or continuous data set. The volume of cola in a can is 11.5 oz. Nothi

AnnyKZ [126]

Volume will represent a continuous data set.

Why? because you can have any measurement (1 oz, 0.1 oz, 0.001 oz, etc)

A discrete data set is when you cannot have a "part" of the whole. An example would be if the data set is the number of people ... you can't have 1/2 of a person. Another example would be a product (tv, laptop, etc) ... you can't have a part of the product. you either have 1 or 2 or 3, etc.

Answer: Continuous

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3 years ago

Read 2 more answers

Expanding Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as a sum, difference,

aev [14]

Answer:

The simplified expression is:

$\ln{x} + \frac{\ln{(x-1)}}{2}$