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3 years ago

Is the Square root of 18 divided by 3 a rational or irrational number? explain using full sentences

Mathematics

1 answer:

weeeeeb [17]3 years ago

6 0

Answer:

irrational

Step-by-step explanation:

$\sqrt{18}$ = $\sqrt{9}$ · $\sqrt{2}$ which is the same as 3 $\sqrt{2}$

3 $\sqrt{2}$ divided by 3 equals $\sqrt{2}$ , which is irrational

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Who can help me to solve these questions please?

ankoles [38]

Using the given information, length of QR = 16.6 cm

The area of the trapezium is 304.5 cm²

<h3>Calculating area of a trapezium</h3>

From the question we are to calculate the length of QR and the area of trapezium PQRS

In the given diagram,

Let the midpoint of PS be T

Then, we can write that

|OP|² = |OT|² + |PT|² (<em>Pythagorean theorem</em>)

|OP| = radius = 13 cm

|PT| = 1/2 × PS = 1/2 × 24 cm = 12 cm

∴ 13² = |OT|² + 12²

169 = |OT|² + 144

|OT|² = 169 -144

|OT|² = 25

|OT| = √25

|OT| = 5 cm

Also, let the midpoint of QR be U

Then, we can write that

|OQ|² = |OU|² + |QU|² (<em>Pythagorean theorem</em>)

|OQ| = radius = 13 cm

From the given information,

The distance of QR from O is twice the distance of PS from O

∴ |OU| = 2 × |OT|= 2 × 5 cm = 10cm

Thus,

13² = ||² + 12²

169 = 10² + |QU|²

|QU|² = 169 -100

|QU|² = 69

|QU| = √69

|QU| = 8.3 cm

Now,

Length of QR = 2 × |QU| = 2 × 8.3 cm

Length of QR = 16.6 cm

Area of the trapezium = 1/2(|QR| + |PS|) × |TU|

Area of the trapezium = 1/2(16.6 + 24) × 15

NOTE: |TU| = |OT| + |OU|

Area of the trapezium = 1/2(40.6) × 15

Area of the trapezium = 20.3 × 15

Area of the trapezium = 304.5 cm²

Hence, the area of the trapezium is 304.5 cm²

Learn more on Calculating area of trapezium here: brainly.com/question/3435635

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2 years ago

Write a rational function that meets the following criteria:

Sliva [168]

You can get a vertical asymptote at x=1 using y = 1/(x-1)
You can generate a hole at x=3 by multiplying by (x - 3/(x - 3) which is undefined at x=3 but otherwise equals 1
You can move the horizontal asymptote up to y=2 by adding 2

y = (x - 3)/((x - 1)(x - 3)) + 2

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3 years ago

Write 7:30 in two ways pertaining to time

Vanyuwa [196]

Seven-thirty.
A half an hour past seven o'clock.

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4 years ago

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A cube has a volume of 64 m3<br> What are its height, width and length?

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The answer above is correct

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Apply Laws of Exponents to write an equivalent expression.<br> (3y)-4. (2z)-4

Stels [109]

After Applying Laws of Exponents we can write as $(6yz)^{-4}$

<h3>What is law of exponents ?</h3>

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

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