Find x. A. 44√3 B. 33 C. 33√2 D. 11√3

B

Step-by-step explanation:

Sin 45 = y/(11√6)

1/√2 = y/(11√6)

y= (11√6)/√2

y= 11√3

tan 60 = x/y

√3 = x/y

x = y√3

= (11√3)√3

= 11(3)

= 33

Step-by-step explanation:

The rule for negative exponents is

and that rule goes the other way as well.  We are going to use the reverse of that rule to rewrite the fraction 1/5000 first:

so now the equation looks like this:

That first term will follow the power to power rule which is to multiply the exponents together, giving us

The rule now is that if we are multiplying like bases that we add the exponents.  5000 is our base on the left side, so we will add the exponents:

simplifying gives us

If a base with an exponent is set to equal the same base with an exponent, then the exponents can be set equal to each other.  For us, this gives us

2 = 1  (which is not true, but that's the simplification!)