A taxi charges a fee, plus $1.80 per mile. how far can you go for $12?

If the gradient of the tangent to

Marizza181 [45]

Answer:

Point A(9, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

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:

Step 1: Define

Identify

$\displaystyle y = \sqrt{x}$

$\displaystyle y' = \frac{1}{6}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = x^{\frac{1}{2}}$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}$
Simplify: $\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x}}$

Step 3: Solve

Find coordinates of A.

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}$
[Multiplication Property of Equality] Cross-multiply: $\displaystyle \sqrt{x} = 3$
[Equality Property] Square both sides: $\displaystyle x = 9$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{9}$
[√Radical] Evaluate: $\displaystyle y = 3$

∴ Coordinates of A is (9, 3).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

7 0

3 years ago

NEEED HELP FROM BRAINLIEST??????

Leno4ka [110]

Answer:

A

Step-by-step explanation:

5 0

3 years ago

En un consultorio medico infanfil se consultas mensualmente a 160 pacientes si la razon de cada 8 paciente 5 son niñas A ¿cuanto

Rainbow [258]

Answer: 60 of the patients are boys.

Step-by-step explanation: According to what is described, 5 in 8 patients are girls, then: 8 - 5 = 3, i.e., 3 in 8 are boys.

Mathematically the proportionality is $\frac{3}{8}$

If 160 patients have appointments per month and $\frac{3}{8}$ are boys:

160. $\frac{3}{8}$ = 60

Per month, 60 boys have appointments at the medical office.

6 0

3 years ago

5/6-1/8 Solve by finding a common denominator A)30/48 B)34/48 C)38/48 D)42/48

GrogVix [38]

Answer:

B) 34/48

Step-by-step explanation:

The easiest common denominator to find is the product of the denominators you have.

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The difference is ...

$\dfrac{5}{6}-\dfrac{1}{8}=\dfrac{5}{6}\cdot\dfrac{8}{8}-\dfrac{1}{8}\cdot\dfrac{6}{6}\\\\=\dfrac{40-6}{48}=\boxed{\dfrac{34}{48}}$

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Additional comment

The difference numerator and denominator have a common factor of 2, so can be reduced to 17/24. The denominator 24 could have been used as the common denominator from the start.

5/6 -1/8 = 20/24 -3/24 = 17/24 . . . . reduced result

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Using the least common denominator does not always result in a reduced sum or difference. If some other denominator is used (as here), then you can be assured that the result will need to be reduced to get to lowest terms.

8 0

2 years ago

What fraction of 1 quart is 3 cups

Rasek [7]

There are two cups in one pint and there are two pints in one quart. That means that there are four cups in one quart. Three cups would be 3/4 of a quart.

Hope that helped =)

5 0

3 years ago