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2 years ago

Which is bigger? 92^7 or 3^81? Hint: can you write 9^27 as an exponential expression with a base of 3?

Mathematics

1 answer:

Vera_Pavlovna [14]2 years ago

7 0

Answer:

${3}^{81}$ is bigger.

Step-by-step explanation:

${9}^{27} = ( {3}^{2} )^{27} = {3}^{2 \times 27} = {3}^{54} \\$

If we compare the exponents of ${3}^{54}$ and ${3}^{81}$ it can be concluded that:

${3}^{81}$ > ${3}^{54}$

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The height of a wooden pole, h, is equal to 15 feet. Ataut wire is stretched from a point on the ground to the top of the pole.

Taya2010 [7]

The question is incomplete. Here is the complete question:

The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?

Answer:

Length of wire = 17 feet

Step-by-step explanation:

Given:

The height of the wooden pole is, $h=15\ ft$

The distance from the base of the pole to this point on the ground is, $b=8\ ft$

Let the length of the wire be 'l'.

Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.

Using Pythagorean theorem, we can find the hypotenuse.

$(Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2$

Plug in the given values and solve for 'l'. This gives,

$l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17$

As length can never be negative, we ignore the negative result.

Therefore, the length of the wire is 17 feet.

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3 years ago

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2 years ago

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Step-by-step explanation:

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2 years ago

If 3x is one factor of 3x^2-9x, what is the other factor?

Rudik [331]

The answer is: " (x² − 3) " .
_________________________________
Explanation:
_________________________________

Given: 3x² <span>− 9x ; factor out a "3x" ;
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</span>→ 3x (x² − 3) ;
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The answer is: " (x² − 3) " .
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3 years ago

Which is bigger? 92^7 or 3^81? Hint: can you write 9^27 as an exponential expression with a base of 3?​

Which is bigger? 92^7 or 3^81? Hint: can you write 9^27 as an exponential expression with a base of 3?