Answer:
In the picture I send above shows the step by step how to get the answers. Cheers!
Answer:
Long leg = 3√30 yards.
Step-by-step explanation:
Ratio of the long leg to the hypotenuse = √3 to 2.
So (6√10) / x = 2 / √3
2x = 6√10√3
x = 3√10√3
x = 3√30
a) The polynomial in expanded form is
.
b) The slant asymptote is represented by the linear function is
.
c) There is a discontinuity at
with a slant asymptote.
a) In this question we are going to use the Factor Theorem, which establishes that polynomial are the result of products of binomials of the form
, where
is the i-th root of the polynomial and the grade is equal to the quantity of roots. Therefore, the polynomial
has the following form:

And the expanded form is obtained by some algebraic handling:



(1)
The polynomial in expanded form is
.
b) In this question we divide the polynomial found in a) (in factor form) by the polynomial
(also in factor form). That is:

(2)
The slant asymptote is defined by linear function, whose slope (
) and intercept (
) are determined by the following expressions:
(3)
(4)
If
, then the equation of the slant asymptote is:







The slant asymptote is represented by the linear function is
.
c) The number of discontinuities in rational functions is equal to the number of binomials in the denominator, which was determined in b). Hence, we have a discontinuity at
with a slant asymptote.
We kindly invite to check this question on asymptotes: brainly.com/question/4084552
Answer: 1.) Irrational (because its not terminal)
2.) 