Solve each equation for the unknown 1. 5 + y = 7.2. 3.8 = a + 2.55. + p = 9 1/3

Mathematics

2 answers:

natima [27]3 years ago

8 0

1. Y=2

2.A=1.3

5.p=28/3

Alexxandr [17]3 years ago

3 0

Answer:

1. 5 + y = 7

⇒ y = 7 - 5

⇒y = 5

2. 3.8 = a + 2.5

⇒ a = 2.5 - 3.8

⇒ a = -1.3

3. 5 + p = 9 1/3 

⇒ p = 9 1/3 - 5

⇒ p = 28/3 - 5

⇒ p = 28/3 - 15/3

⇒ p = 13/3

⇒ p = 4 1/3

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Answer:

$\displaystyle f'(x) = \frac{4}{x^2}$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Differentiation

Derivatives
Derivative Notation

The definition of a derivative is the slope of the tangent line: $\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle f(x) = -\frac{4}{x}$

Step 2: Differentiate

[Function] Substitute in x: $\displaystyle f(x + h) = -\frac{4}{x + h}$
Substitute in functions [Definition of a Derivative]: $\displaystyle f'(x) = \lim_{h \to 0} \frac{-\frac{4}{x + h} - \big( -\frac{4}{x} \big)}{h}$
Simplify: $\displaystyle f'(x) = \lim_{h \to 0} \frac{4}{x(x+ h)}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle f'(x) = \frac{4}{x(x+ 0)}$
Simplify: $\displaystyle f'(x) = \frac{4}{x^2}$