The power generated by a wind turbine depends on the wind speed. The expression 800 v^3 gives the power in watts for a certain wind turbine at wind speed v in meters per second. If the wind speed triples, by what factor does the power generated by the wind turbine increase?

2) Can you write the expression 49x^2y^2z^2 using only one exponent? Show how or explain why not?

Question

Kendall Robertson

Mathematics

20 February, 01:42

The power generated by a wind turbine depends on the wind speed. The expression 800 v^3 gives the power in watts for a certain wind turbine at wind speed v in meters per second. If the wind speed triples, by what factor does the power generated by the wind turbine increase?

2) Can you write the expression 49x^2y^2z^2 using only one exponent? Show how or explain why not?

+4

Answers (2)

Know the Answer?

Gia Black · Answer 1

1. it would increase by 27 times

in other words, 3^3 times

2. You can rewrite the expression using one exponent because each variable is being squared and multiplied by each other

if you had 3^2 x 4^2 it would be 144 (9 x 16)

same as if you had (3 x 4) ^2 which is 12^2, which is also 144

the expression would be (7xyz) ^2

Steve Bates · Answer 2

Power = 800v³

If the speed triples, v is replaced by 3v.

Power = 800 * (3v) ³ = 800*27v³ = 27 * (800v³)

The power increases by 27 times.

2) 49x²y²z²

The expression can be written using one exponent

49x²y²z² = 7² * x² * y² * z² = (7xyz) ²

= (7xyz) ²