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4 years ago

Another way to write the value absolute value inequality |p|<12

Mathematics

2 answers:

mote1985 [20]4 years ago

5 0

Answer:

-12 <p <12

Step-by-step explanation:

|p|<12

We can write this without the absolute values

Take the equation with the positive value on the right hand side and take the equation with a negative value on the right side remembering to flip the inequality. Since this is less than we use and in between

p < 12 and p >-12

-12 <p <12

Lady bird [3.3K]4 years ago

4 0

Step-by-step explanation:

$For\ a>0\\\\|x|a\Rightarrow x>a\ \wedge\ x$

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the length of a string in yards is a function f(n) of the length n in inches. write a function rule for this situation. a) f(n)

Vera_Pavlovna [14]

The answer would be b. f(n)=n/12/c)

3 0

3 years ago

A number, X, rounded to 1 decimal place is 3,7 Write down the error interval for x,

sp2606 [1]

Answer:

The error interval for x is:

[3.65,3.74]

Step-by-step explanation:

The number after rounding off is obtained as:

3.7

We know that any of the number below on rounding off the number to the first decimal place will result in 3.7:

3.65 3.66 3.67 3.68 3.69 3.70 3.71 3.72 3.73 3.74

( Because if we have to round off a number present in decimals to n place then if there is a number greater than or equal to 5 at n+1 place then it will result to the one higher digit at nth place on rounding off and won't change the digit if it less than 5 )

Hence, the error interval is:

[3.65,3.74]

6 0

3 years ago

The problem is attached, thanks.

NeX [460]

Answer:

$\displaystyle \frac{dy}{dx} \bigg| \limit_{(1, 4)} = 2$

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)
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Implicit Differentiation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle \sqrt{x} - \sqrt{y} = -1$

Point (1, 4)

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle x^{\frac{1}{2}} - y^{\frac{1}{2}} = -1$
[Implicit Differentiation] Basic Power Rule: $\displaystyle \frac{1}{2}x^{\frac{1}{2} - 1} - \frac{1}{2}y^{\frac{1}{2} - 1}\frac{dy}{dx} = 0$
[Implicit Differentiation] Simplify Exponents: $\displaystyle \frac{1}{2}x^{\frac{-1}{2}} - \frac{1}{2}y^{\frac{-1}{2}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Isolate y terms: $\displaystyle -\frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = \frac{2y^{\frac{1}{2}}}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Simplify: $\displaystyle \frac{dy}{dx} = \frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}}$

Step 3: Evaluate

Substitute in point [Derivative]: $\displaystyle \frac{dy}{dx} = \frac{(4)^{\frac{1}{2}}}{(1)^{\frac{1}{2}}}$
Exponents: $\displaystyle \frac{dy}{dx} = \frac{2}{1}$
Division: $\displaystyle \frac{dy}{dx} = 2$