Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
A cube has an edge length that is a rational number of centimeters, identifying which measurements will require t by e use of i...Asked by hy
A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
Answers
Answered by
carti
Which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe?
Responses
square root of 3
square root of 3
−3
negative 3
2 3/4
2 and 3 fourths
47
Responses
square root of 3
square root of 3
−3
negative 3
2 3/4
2 and 3 fourths
47
Answered by
carti
How do you show the group of digits that repeat in a repeating decimal?
Answered by
GPT 3.5
One measurement that will require the use of irrational numbers is the diagonal of the cube.
The diagonal of a cube can be found by using the Pythagorean Theorem. Considering the cube's edge length is "a", the diagonal would be the length of the hypotenuse of a right-angled triangle with two side lengths equal to "a".
Using the Pythagorean Theorem, we have:
diagonal^2 = a^2 + a^2
diagonal^2 = 2a^2
To solve for the diagonal, we need to take the square root of both sides:
diagonal = √(2a^2)
Since the edge length "a" is given as a rational number, the square root of 2 (√2) will introduce an irrational number. Thus, the measurement of the diagonal of a cube will require the use of irrational numbers.
The diagonal of a cube can be found by using the Pythagorean Theorem. Considering the cube's edge length is "a", the diagonal would be the length of the hypotenuse of a right-angled triangle with two side lengths equal to "a".
Using the Pythagorean Theorem, we have:
diagonal^2 = a^2 + a^2
diagonal^2 = 2a^2
To solve for the diagonal, we need to take the square root of both sides:
diagonal = √(2a^2)
Since the edge length "a" is given as a rational number, the square root of 2 (√2) will introduce an irrational number. Thus, the measurement of the diagonal of a cube will require the use of irrational numbers.
Answered by
GPT 3.5
The number that could be used to specify how many cups of flour should be used in a bread recipe is 2 3/4. This is a mixed number, representing 2 whole cups and 3/4 of a cup of flour. The other options, square root of 3, -3, and 47, are not appropriate measurements for specifying the amount of flour in cups.
Answered by
GPT 3.5
To show the group of digits that repeat in a repeating decimal, you typically use a horizontal line (or a vinculum) over the digits that repeat. This is called a repeating decimal bar.
For example, if you have the decimal 0.333333..., where the digit 3 repeats infinitely, you would write it as 0.3 with a repeating decimal bar over the digit 3:
0.3
Similarly, for the decimal 0.272727..., where the digits 27 repeat infinitely, you would write it as 0.2 with a repeating decimal bar over the digits 27:
0.2
The repeating decimal bar helps to show which group of digits repeats indefinitely in the decimal representation.
For example, if you have the decimal 0.333333..., where the digit 3 repeats infinitely, you would write it as 0.3 with a repeating decimal bar over the digit 3:
0.3
Similarly, for the decimal 0.272727..., where the digits 27 repeat infinitely, you would write it as 0.2 with a repeating decimal bar over the digits 27:
0.2
The repeating decimal bar helps to show which group of digits repeats indefinitely in the decimal representation.