Write the fraction 6/6 as a sum of fractions three different ways.
2 answers:
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We know that (-3,5) is the location of one of the endpoints.... and we know the midpoint is at (2,-6)... .now.. what's the distance between those two guys?
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 5}})\quad % (c,d) &({{ 2}}\quad ,&{{ -6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[2-(-3)]^2+[-6-5]^2}\implies d=\sqrt{(2+3)^2+(-6-5)^2} \\\\\\ d=\sqrt{5^2+(-11)^2}\implies d=\sqrt{25+121}\implies d=\sqrt{146}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%28%7B%7B%20-3%7D%7D%5Cquad%20%2C%26%7B%7B%205%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0A%26%28%7B%7B%202%7D%7D%5Cquad%20%2C%26%7B%7B%20-6%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B%5B2-%28-3%29%5D%5E2%2B%5B-6-5%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%282%2B3%29%5E2%2B%28-6-5%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B5%5E2%2B%28-11%29%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B25%2B121%7D%5Cimplies%20d%3D%5Csqrt%7B146%7D)
so, the distance "d" from the midpoint to that endpoint is that much. And the distance from the midpoint to the other endpoint is the same "d" distance, because the midpoint is half-way in between both endpoints.
so, the length of AB is twice that distance, or
so, the distance "d" from the midpoint to that endpoint is that much. And the distance from the midpoint to the other endpoint is the same "d" distance, because the midpoint is half-way in between both endpoints.
so, the length of AB is twice that distance, or
Answer:
The imaginary part is 0
Step-by-step explanation:
The number given is:
First, we can expand this power using the binomial theorem:
After that, we can apply De Moivre's theorem to expand each summand:
The final step is to find the common factor of i in the last expansion. Now:
The last part is to multiply these factors and extract the imaginary part. This computation gives:
(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)
A calculator simplifies the imaginary part Im(x⁶) to 0
Answer:
<u>Potential roots:</u>
Step-by-step explanation:
Simply put, the rational roots theorem tells us that if there are any rational roots of a polynomial function, they must be in the form
±
Where
a_n is the number before the highest power of the polynomial, and
a_0 is the constant in the polynomial
<em>From the polynomial shown, we have a_n = 9 and a_0 = 4</em>
<em />
<em>The factors of 9 are 9, 3, 1</em>
<em>and</em>
<em>The factors of 4 are 4,2,1</em>
<em />
So, if there are any rational roots, they would be:
±
±
Which is ± 9/4, 9/2, 9/1, 3/4, 3/2, 3/1, 1/4, 1/2, 1/1
or
Answer:
To the right
Step-by-step explanation:
The negatives on a number line are on the left side and the positives on the right.
see this as an example:
