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3 years ago

What is the length of side c? с 4 3 O A 5 units B. 7 units O C. 16 units O D. 15 units

Mathematics

1 answer:

Savatey [412]3 years ago

4 0

Answer:

Step-by-step explanation:

Pythagorean theorem works for right triangles a²+b² = c²

The Pythagorean theorem might be easier to understand written like this ......

(side 1)² + (side 2)² = (hypotenuse)² hypotenuse is c in this diagram

it can also be written like this just flipping both sides (they are still equal)

(hypotenuse)² = (side 1)² + (side 2)²

using algebra to solve for the hypotenuse

hypotenuse = √[ (side 1)² + (side 2)²] remeber hypotenuse = c

c = √[ (side 1)² + (side 2)²] rewritten with c instead of hypotenuse

= √[ 4² + 3² ]

= √( 16 + 9 ]

= √(25)

What number is the square root of 25?

Or what number times itself equals 25?

Your chooses were ...... A B C or D

A 5x5 = ?

B 7x7 = ?

C 16x16 = ?

D 15x15 = ?

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8 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
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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: $\displaystyle \frac{dy}{dx} = 2$

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

Unit: Implicit Differentiation

Book: College Calculus 10e

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3 years ago

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4 years ago

Read 2 more answers

What are the roots of -12x2 + 11x − 3 = 0?

Nataly_w [17]

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x = -11 +/- √(121 - 144)
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x = -11 +/- √(-23)
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x = -11 +/- i√(23)
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x = -11 + i√(23) x = -11 - i√(23)
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Step-by-step explanation:

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4 years ago

What is the length of side c? с 4 3 O A 5 units B. 7 units O C. 16 units O D. 15 units​

What is the length of side c? с 4 3 O A 5 units B. 7 units O C. 16 units O D. 15 units