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geniusboy [140]
3 years ago
11

What correctly describes the quotient of a nonzero rational number and an irrational number? Always Rational Depends on what the

rational number is Always irrational A combination of irrational and rational
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
7 0

Answer:

Always Irrational

Step-by-step explanation:

An Irrational number is described as a number which cannot in the actual sense be expressed as a ratio between two integers and is not an imaginary number. It means that an irrational number cannot be expressed as a simple fraction.

If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Hence irrational numbers are floating point numbers.

The quotient of a rational number and an irrational number is always irrational.

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Find the limit (enter 'DNE' if the limit does not exist)
vaieri [72.5K]

Answer:

\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)=2

Step-by-step explanation:

We need to first simplify the expression using rationalization(i.e. if a square root term exists in the denominator, then multiply and divide the whole expression by the denominator(but the change the sign of its middle term))

here, we need to find:

\lim\limits_{(x,y)\rightarrow(0,0)}\left(\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\right)

first we'll rationalize our expression:

\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\left(\dfrac{\sqrt{-2x^2-6y^2+1}+1}{\sqrt{-2x^2-6y^2+1}+1}\right)

\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{(\sqrt{-2x^2-6y^2+1}+1)^2-(1)^2}

\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-2x^2-6y^2+1-1}

\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-(2x^2+6y^2)}

\sqrt{-2x^2-6y^2+1}+1

this is our simplified expression, now we can apply our limits:

\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)

\sqrt{-2(0)^2-6(0)^2+1}+1

1+1

2

the limit does exists and it is 2.

5 0
3 years ago
HELP
Solnce55 [7]
12,989 is the answer i believe
3 0
2 years ago
Which expressions are equivalent to -90 - 60w? Choose three. *Hint: On each answer choice below, use the distributive property t
marusya05 [52]

Answer:

a), b), e)

Step-by-step explanation:

<em>a) -30(3 + 2w) = -90 - 60w</em>

<em>b) (-9 − 6w) x 10 = -90 - 60w</em>

c) -3(30 - 20w) = -90 + 60w

d) (6 + 4w) × 15 = 90 + 60w

<em>e) −20(4.5 + 3w) = -90 - 60w</em>

5 0
3 years ago
There are six players on a coed volleyball team. Alter an
julsineya [31]

Answer:

4 girls and 2 boys.

Step-by-step explanation:

8 0
3 years ago
What is the percentage change of 50 to 35 pounds
Artist 52 [7]
30%
hope I helped you with this       
4 0
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