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docker41 [41]
3 years ago
11

Solve for x. Round your answer to the nearest tenth if necessary.

Mathematics
1 answer:
Umnica [9.8K]3 years ago
8 0

Answer:

30.5

Step-by-step explanation:

cos18=29/x --> reciprocate for simplicity : 1/cos18=x/29 --> solve for x

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Abigail's mom asked her to go to the store and purchase 5 kilograms (kg) of potatoes. When she got to the store, she saw the pot
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Round to pounds = 11
Round to tenths/1 decimal = 11
Round to hundredths/2 decimals = 11.02
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What percentage is 285 feet of an acre
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Hope this helps!
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Please help me do this i need it​
Darya [45]

Answer:

(x+1)(3x+2) is the answer

6 0
2 years ago
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Which of the following has a value this is less than zero? A:(-6)^2 B:1/3 x 2 C:0.5^2 D:-7^2
solniwko [45]

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

Learn more about the fraction here:

brainly.com/question/10708469

#SPJ1

8 0
2 years ago
Question in pictures
yan [13]

The derivatives of the functions are listed below:

(a) f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}    

(b) f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }

(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) f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}]

(g) f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) -  \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2}  \cdot x^{-\frac{1}{2} }\right)

(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}

  1. f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}        Given
  2. f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4\cdot x - \frac{x}{5} + 5 \cdot x^{-1} - \sqrt[11]{2022}      Definition of power
  3. f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}       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}

  1. f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}              Given
  2. f(x) = (x + 3)^{\frac{1}{3} }\cdot (x + 5)^{\frac{1}{3} }           Definition of power
  3. f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }        Derivative of a product of functions / Derivative of power function / Rule of chain / Result

(c) f(x) = (sin x - cos x) / (x² - 1)

  1. f(x) = (sin x - cos x) / (x² - 1)          Given
  2. 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

  1. f(x) = 5ˣ · ㏒₅ x             Given
  2. 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

  1. f(x) = (x⁻⁵ + √3)⁻⁹          Given
  2. 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
  3. f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶     Associative and commutative properties / Definition of multiplication / Result

(f) f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}

  1. f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}         Given
  2. f'(x) = 7^{x\cdot\ln x} \cdot \ln 7 \cdot (\ln x + 1) + 7\cdot (x\cdot \ln x)^{6}\cdot (\ln x + 1)         Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions
  3. f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}]        Distributive property / Result

(g) f(x) = \arccos^{2} x - \arctan (\sqrt{x})

  1. f(x) = \arccos^{2} x - \arctan (\sqrt{x})        Given
  2. f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) -  \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2}  \cdot x^{-\frac{1}{2} }\right)      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)

  1. f(x) = ㏑ (sin x) + sin (㏑ x)          Given
  2. 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
  3. f'(x) = cot x + cos (㏑ x) · (1 / x)      cot x = cos x / sin x / Result

To learn more on derivatives: brainly.com/question/23847661

#SPJ1

7 0
1 year ago
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