Answer:
Step-by-step explanation:
Let f(x) be the polynomial function of minimum degree with real coefficients whose zeros are 5, -3, and -1 + 3i be f(x).
By the complex conjugate property of polynomials, -1-3i is also a root of this polynomial.
Therefore the polynomial in factored form is
We expand to get:
We expand further to get:\
First: Equations are solved. is an expression, and expressions can be simplified.
Now suppose . Imagine a right triangle with one angle (not the one opposite the hypotenuse, of course) labeled . This relation suggests that
and under the hood, we're assuming that , because otherwise we wouldn't be able to properly alternate from to so seamlessly.
Now,
so the given expression is the same as the tangent of that same angle .
If , then in the triangle, the leg opposite the angle occurs with the length of the hypotenuse in a ratio of to 2. By the Pythagorean theorem, the remaining side - call it - satisifies
and we have
Answer:
Step-by-step explanation:
Since the height of each bounce is 3/4 of its last peak height we can use a geometric sequence to find the bounce height for any number of bounces.
h=12(3/4)^b
h(5)=12(3/4)^5
h(5)=2.85m
Answer:
As of this writing, 964 babies were born to parents using the new method, and 888 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby ...
Step-by-step explanation:As of this writing, 964 babies were born to parents using the new method, and 888 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby ...