1 kilogram = 2.205 pounds
5 kg * 2.205 lbs = 11.0231 pounds
Round to pounds = 11
Round to tenths/1 decimal = 11
Round to hundredths/2 decimals = 11.02
Since there are 43560 feet in an acre, 285 feet is 0.654% of an acre.
Hope this helps!
Answer:
(x+1)(3x+2) is the answer
The value of -7² is less than zero which is the correct answer would be an option (D)
<h3>What is the fraction?</h3>
A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
<h3>What are Arithmetic operations?</h3>
Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
To determine the value is less than zero
Option A: (-6)² ⇒ 36
So this value is greater than zero
Option B: 1/3 × 2 ⇒ 2/3
So this value is greater than zero
Option C: 0.5² ⇒ 0.25
So this value is greater than zero
Option D: -7² ⇒ -49
So this value is less than zero
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The derivatives of the functions are listed below:
(a)
(b) 
(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²
(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]
(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶
(f)
(g)
(h) f'(x) = cot x + cos (㏑ x) · (1 / x)
<h3>How to find the first derivative of a group of functions</h3>
In this question we must obtain the <em>first</em> derivatives of each expression by applying <em>differentiation</em> rules:
(a) ![f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%20%5Ccdot%20x%5E%7B-%5Cfrac%7B7%7D%7B2%7D%20%7D%20-%20x%5E%7B2%7D%20%2B%204%20%5Ccdot%20x%20-%20%5Cfrac%7Bx%7D%7B5%7D%20%2B%20%5Cfrac%7B5%7D%7Bx%7D%20-%20%5Csqrt%5B11%5D%7B2022%7D)
Given
Definition of power
Derivative of constant and power functions / Derivative of an addition of functions / Result
(b) ![f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%20%2B%203%7D%20%5Ccdot%20%5Csqrt%5B3%5D%7Bx%20%2B%205%7D)
Given
Definition of power
Derivative of a product of functions / Derivative of power function / Rule of chain / Result
(c) f(x) = (sin x - cos x) / (x² - 1)
- f(x) = (sin x - cos x) / (x² - 1) Given
- f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)² Derivative of cosine / Derivative of sine / Derivative of power function / Derivative of a constant / Derivative of a division of functions / Result
(d) f(x) = 5ˣ · ㏒₅ x
- f(x) = 5ˣ · ㏒₅ x Given
- f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)] Derivative of an exponential function / Derivative of a logarithmic function / Derivative of a product of functions / Result
(e) f(x) = (x⁻⁵ + √3)⁻⁹
- f(x) = (x⁻⁵ + √3)⁻⁹ Given
- f'(x) = - 9 · (x⁻⁵ + √3)⁻⁸ · (- 5) · x⁻⁶ Rule of chain / Derivative of sum of functions / Derivative of power function / Derivative of constant function
- f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶ Associative and commutative properties / Definition of multiplication / Result
(f) 
Given
Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions
Distributive property / Result
(g) 
Given
Derivative of the subtraction of functions / Derivative of arccosine / Derivative of arctangent / Rule of chain / Derivative of power functions / Result
(h) f(x) = ㏑ (sin x) + sin (㏑ x)
- f(x) = ㏑ (sin x) + sin (㏑ x) Given
- f'(x) = (1 / sin x) · cos x + cos (㏑ x) · (1 / x) Rule of chain / Derivative of sine / Derivative of natural logarithm /Derivative of addition of functions
- f'(x) = cot x + cos (㏑ x) · (1 / x) cot x = cos x / sin x / Result
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