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2 years ago

For each logarithmic equation, write an equivalent equation in exponential form

Mathematics

1 answer:

Montano1993 [528]2 years ago

8 0

Answer:

loga b = c ⇔ a^c = b

Apply the property above:

1. ln 618 = p ⇔ e^p = 618
2. ln q = 2 ⇔ e^2 = q
3. ln 100 = t ⇔ e^t = 100
4. ln (e^3) = 3 ⇔ e^3 = e^3

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Find the missing angle according to the Triangle Exterior Angle Theorem

Alexxandr [17]

Answer:

k = 36

Step-by-step explanation:

By exterior angle theorem:

$k \degree + 110 \degree = 146 \degree \\ \\ k \degree = 146 \degree - 110 \degree \\ \\ k \degree = 36\degree \\ \\ k = 36$

6 0

2 years ago

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Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

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

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate y' terms: $-xy' - 2y' = y$
[Algebra] Factor y': $y'(-x - 2) = y$
[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$

Step 6: Find Slope at Given Point

[Algebra] Substitute in x: $y''(-1) = \frac{8}{(-1+2)^3}$
[Algebra] Evaluate: $y''(-1) =8$

6 0

3 years ago

Read 2 more answers

X+8=17 what is the value of x makes the sentece true

melisa1 [442]

Answer:

x = 9

Step-by-step explanation:

Step 1: Write equation

x + 8 = 17

Step 2: Solve for x

Subtract 8 on both sides: x = 9

Step 3: Check

Plug in x to verify it's a solution.

9 + 8 = 17

17 = 17

7 0

3 years ago

Please help me find the answer!! Picture ⬇️

expeople1 [14]

Answer:

(1) y≥-3x + 4

3 0

2 years ago

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Find the mean of thw data 11,11,12,13,13,13,14,14,15,15,16,16,18

amid [387]

Answer:

the mean is 13

Step-by-step explanation:

The way to find the mean of a set of numbers is to add all the numbers together and divide the sum by the number of numbers. so 11 + 11 + 12 + 13+ 13 + 13 + 14 + 14 + 15 + 15 + 16 + 16 + 18 / 13 = 13.9

4 0

3 years ago