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2 years ago

Determine if 0.4744335042096347... is rational or irrational and give a reason for your answer.

Mathematics

1 answer:

Marina86 [1]2 years ago

7 0

Answer: Irrational

Explanation:

Based on what is shown so far, there isn't any clear pattern of the digits. And the digits don't seem to repeat. Because of this, it's very likely that the number is irrational.

If in contrast we had something like 0.47474747, where the "47"s repeat forever", then it would be rational. We would be able to use algebra to show that 47/99 = 0.4747474747...

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For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inel

adelina 88 [10]

Answer:

Demand is inelastic at p = 9 and therefore revenue will increase with

an increase in price.

Step-by-step explanation:

Given a demand function that gives <em>q</em> in terms of <em>p</em>, the elasticity of demand is

$E=|\frac{p}{q}\cdot \frac{dq}{dp} |$

If E < 1, we say demand is inelastic. In this case, raising prices increases revenue.
If E > 1, we say demand is elastic. In this case, raising prices decreases revenue.
If E = 1, we say demand is unitary.

We have the following demand equation $D(p)=-\frac{3}{4}p+29$ ; p = 9

Applying the above definition of elasticity of demand we get:

$E(p)=\frac{p}{q}\cdot \frac{dq}{dp}$

where

p = 9
q = $-\frac{3}{4}p+29$
$\frac{dq}{dp}=\frac{d}{dp}(-\frac{3}{4}p+29)$

$\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{d}{dp}\left(\frac{3}{4}p\right)+\frac{d}{dp}\left(29\right)\\\\\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{3}{4}$

Substituting the values

$E(9)=\frac{9}{-\frac{3}{4}(9)+29}\cdot -\frac{3}{4}\\\\E(9)=\frac{36}{89}\cdot -\frac{3}{4}\\\\E(9)=-\frac{27}{89}\approx -0.30337$

$|E(9)|=|\frac{27}{89}| < 1$

Demand is inelastic at p = 9 and therefore revenue will increase with an increase in price.

6 0

2 years ago

PLEASE HELP! for 10 pionts!

erastovalidia [21]

Answer: The answer is A.|7 + -2 + 5 + - 8|

Step-by-step explanation:

|7−2+5−8|

=|5+5−8|

=|10−8|

=|2|

4 0

2 years ago

Read 2 more answers

100 km per hour equals how many mph?

trasher [3.6K]

Answer:

62.1371

To obtain an approximate result, divide the speed value by 1.609

8 0

2 years ago

Read 2 more answers

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) $f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}$

$f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}$ Given
$f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4\cdot x - \frac{x}{5} + 5 \cdot x^{-1} - \sqrt[11]{2022}$ Definition of power
$f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}$ Derivative of constant and power functions / Derivative of an addition of functions / Result

(b) $f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}$

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

(c) f(x) = (sin x - cos x) / (x² - 1)

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

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

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

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

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

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

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7 0

1 year ago

The students in Gwen's class got to choose between pizza and burgers for the celebration on

Oksana_A [137]

Answer:

80% of the class picked the pizza

Step-by-step explanation:

In order to find a percentage, you are supposed to divide the amount of how much someone has picked by the total amount (in this case pizza's). Here is how I got 80%,

28/35 = 0.8

0.8*100 = 80

So the answer is 80%

4 0

2 years ago