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2 years ago

Which binomial is a factor of 100x2 – 49?

Mathematics

1 answer:

pentagon [3]2 years ago

6 0

Answer:

Step-by-step explanation:

What you have here is called "the difference of two squares"

Difference means subtraction and both 100x2 and 49 are perfect squares.

The factored form of 100x2-49 is

(10x+7)(10x-7)

Because 10x times 10x is 100x2 and 7 times 7 is 49

One factor has a + and

One factor has a -

It is a pattern worth memorizing!

So 10x + 7 is the factor you're looking for.

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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

2 years ago

Decide whether there is enough information to prove that ab. If so, state the theroem you would use.

Triss [41]

Answer - Yes, corresponding angles converse

5 0

2 years ago

Solve this problem in your notebook using all four steps. Harvey is 3 times as old as Jane. The sum of their ages is 48 years. F

JulsSmile [24]

Harvey is 3 times as old as Jane."
h = 3j 

"The sum of their ages is 48 years." 
h + j = 48 

substitution 
(3j) + j = 48 
4j = 48 
j = 12 
h = 3j = 36

3 0

3 years ago

How do you solve(through/with elimination)?

Tasya [4]

Which question did you need help on?

5 0

3 years ago

What is the area of parallelogram RSTU?

sergiy2304 [10]

The answer
to find the area of this parallelogram, first, we must find the value of its length and width

The area can be found with the formula A = L x W
L = length
W= width
according to the image, the dimensions are L =UT and W= UR

vector UT = (6,2) and vector UT= (-4,4)

so L= length of vector UT = sqrt (6²+2²)=sqrt(40) =2 √10

and W= length of vector UR= sqrt(4²+4²)=sqrt(32) =4√2

4 0

3 years ago