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Flauer [41]
2 years ago
6

The domain and the range of the reciprocal function are the set of all real numbers. True or false?.

Mathematics
1 answer:
Elodia [21]2 years ago
6 0

False. All real numbers, with the exception of 0 because f (0) = 1 0, fall inside the reciprocal function's domain and range. Y cannot be 0 if x cannot, either.

<h3>What are real numbers?</h3>

In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are used in measurements of continuously varying quantities such as size and time. They are distinguished from imaginary numbers, which use the symbol I or the square root of 1, by the word "real." A complex number has a real (1) and an imaginary I component, like 1 + i. The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.

Contrary to rational numbers, whose decimal expansions always contain a digit or group of digits that repeats itself, such as 1/6 = 0.16666... or 2/7 = 0.285714285714, irrational numbers have decimal expansions that do not repeat themselves. Since there is no regularly repeating group in the decimal produced as 0.42442444244442, it is irrational.

To learn more about the, real numbers visit:

brainly.com/question/9876116

#SPJ4

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Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen
3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

<em></em>

Step-by-step explanation:

Given

Surface\ Area = 181.5cm^2

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

Volume =x^2 * h

Volume =x^2h

181.5 =x^2h

The surface area (S) is calculated as this:

S = 2(x^2 + xh + xh)

S = 2(x^2 + 2xh)

S = 2x^2 + 4xh

Substitute 181.5 for S

181.5 = 2x^2 + 4xh

Make h the subject:

4xh = 181.5 - 2x^2

h = \frac{181.5 - 2x^2}{4x}

Substitute h = \frac{181.5 - 2x^2}{4x} in Volume =x^2h

V = x^2(\frac{181.5 - 2x^2}{4x})

V = x(\frac{181.5 - 2x^2}{4})

V = \frac{1}{4}(x)(181.5 - 2x^2)

V = \frac{181.5x}{4} - \frac{2x^3}{4}

V = \frac{181.5x}{4} - \frac{x^3}{2}

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

dV = \frac{181.5}{4} - \frac{3x^2}{2}

Set to 0

0 = \frac{181.5}{4} - \frac{3x^2}{2}

\frac{3x^2}{2} = \frac{181.5}{4}

Multiply through by 4

4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4

2*3x^2 = 181.5

6x^2 = 181.5

x^2 = \frac{181.5}{6}

x^2 = 30.25

x = \sqrt{30.25

x = 5.5

Recall that:

h = \frac{181.5 - 2x^2}{4x}

h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}

h = \frac{181.5 - 60.5}{22}

h = \frac{121}{22}

h = 5.5

So, we have:

h = 5.5

x = 5.5

<em>Hence, the base and height of the solid is 5.5cm</em>

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4 years ago
PLS HELP DUE IN 10MINS!!!!! 67 POINTS AND BRAINLIEST!!!!!
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Answer:

a

Step-by-step explanation:

4 0
3 years ago
The area of a circle is 100π ft². What is the circumference, in feet? express your answer in terms of \piπ
Bond [772]

Answer:

20π ft

Step-by-step explanation:

To find the circumference of the circle given its area, first find its radius.

\textcolor{steelblue}{\boxed{\text{Area of circle =}\pi  {r}^{2} }}

Substitute given area into the formula:

100π= πr²

Divide both sides by π:

100= r²

Square root both sides:

r =  \sqrt{100}

r= 10 ft

\textcolor{steelblue}{\boxed{\text{Circumference of circle = }2\pi  {r}}}

Since we have found the value of the radius, we can substitute r= 10 into the formula above to find the circumference.

Circumference of circle

= 2(π)(10)

= 20π ft

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2 years ago
What 3 ratios are equivalent to 20:36
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Nov 3, 2014 - <span>Math - Ms. Sue, Monday, November </span>3, 2014 at 4:29pm. 36:20 = 9/ ... Also, keep in mind that 36/20, 36<span>:20, and 36 to 20 are the same.</span>
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4 years ago
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How do you graph y=2x-3 and y=x+2
nadya68 [22]
Start from -3 and do rise over run and the same thing for the other equation but instead of -3 start from 2
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