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klasskru [66]
3 years ago
7

When is the product of the square root of a prime number and a nonzero rational number a rational number?

Mathematics
1 answer:
Nookie1986 [14]3 years ago
8 0

Answer:

The square root of a prime number is always an irrational number, then the product of the square root of a prime number and a nonzero rational number is equivalent to:

"the product of an irrational number and a rational number different than zero...."

We know that the product of an irrational number and a rational number (different than zero) is ALWAYS an irrational number.

Then "When is the product of the square root of a prime number and a nonzero rational number a rational number?"

Never, the product will always be irrational.

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Find the exact value of cos(arcsin(1/4)). For full credit, explain your reasoning.
Westkost [7]
First way
arcsin(1/4) means that 1/4 sin of the angle.

sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4

<span>Second way
</span>
sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4

For one value of sinα, possible 2 values of cosα.

5 0
2 years ago
KEVIN'S GAS TANK IS 1/6 FULL. AFTER HE BUYS 14 GALLONS OF GAS, IT IS 3/4 FULL. HOW MANY GALLONS CAN KEVIN'S TANK HOLD?
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\frac 1 6 t  + 14 = \frac 3 4 t


14 = (\frac 3 4 - \frac 1 6)t = (\frac 9{12} - \frac{2}{12}) t = \frac {7}{12} t


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