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3 years ago

Determine whether the following numbers are rational or irrational

Mathematics

1 answer:

Leno4ka [110]3 years ago

8 0

Hi! I'm happy to help.

A rational number is a number that repeats, or stops.

First of all, 8/5, in fraction and decimal form (1.6), stops, So it is Rational.

Next, we have pi. This number, doesn't ever stop, or repeat. ( 3.1415926535 897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...) So, pi, is Irrational.

Next, we have 0. This number stops, so it is Rational.

Next, we have $\sqrt{1}$ , the square root of 1, is 1, because 1 squared is one. 1 stops, so it is Rational.

Next, we have 4.46466... This number doesn't stop, and it doesn't seem to repeat, so it is Irrational.

Next, we have -6. -6 stops, so it is Rational.

Finally, we have $\sqrt{2}$ . The square root of 2 is 1.41421356237...

This number doesn't stop, and doesn't repeat, so it is Irrational.

To sum it up: <u>Number 1, 3, 4, and 6 are Rational, and Number 2, 5, and 7 are Irrational.</u>

I hope this was helpful, keep learning! :D

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Metal A has a density of 12.7 g/cm3.

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Using the given information, the density of metal B is 8.58 g/cm³

<h3>Calculating density </h3>

From the question, we are to determine the density of metal B

From the given information,

55 g of metal A is combined with metal B to create an alloy with mass 90 g

∴ Mass of metal B in the alloy = 90 g - 55 g = 35 g

Now, we will determine the volume of metal A in the alloy

Using the formula,

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Volume of metal A in the alloy = 55/12.7

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Then, we will determine the volume of the alloy

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Volume of the alloy = 8.41 cm³

∴ Volume of metal B in the alloy = 8.41 cm³- 4.33 cm³

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Now, for the density of metal B

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2 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

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(a)

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or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

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(b)

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For polar coordinates, x = rcosθ and y = rsinθ. Since
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Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
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3 years ago

There are two numbers, that sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are th

Taya2010 [7]

Answer:

x = 18 (Smaller number)

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Step-by-step explanation:

To solve, begin by setting up a system of equations.

'x' being the smaller number, while

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i hope it will help you!

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3 years ago

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Determine whether the following numbers are rational or irrational​

Determine whether the following numbers are rational or irrational