Answer:
Eccentricity = 5/6
Type of conic section; Ellipse
Directrix; x = -11/5
Step-by-step explanation:
The first step would be to write the polar equation of the conic section in standard form by multiplying the numerator and denominator by 1/6;
The polar equation of the conic section is now in standard form;
The eccentricity is given by the coefficient of cos theta in which case this would be the value 5/6. Therefore, the eccentricity of this conic section is 5/6.
The eccentricity is clearly between 0 and 1, implying that the conic section is an Ellipse.
Since the conic section is in standard form, the numerator is the product of eccentricity and the value of the directrix, that is;
e*d = 11/6
5/6*d = 11/6
d = 11/5
Since the denominator has a minus sign then the ellipse opens towards the right and thus the equation of its directrix is;
x = -11/5
Answer:
45.21960784 or 45.2
Step-by-step explanation:
Yes as long as the length remained the same each time
Answer:
f(x) = (3x -2)(2x +1)
Step-by-step explanation:
The procedure for factoring expression of the form ...
ax² +bx +c
is to look for factors of a·c that have a sum of b.
The product a·c is 6·(-2) = -12. You are looking for factors that have a sum of b = -1. From your familiarity with multiplication tables, you know ...
-12 = 1(-12) = 2(-6) = 3(-4)
The sums of the factor pairs in this list are -11, -4, -1. So, the last pair of factors, {3, -4} is the one we're looking for.
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At this point, there are several ways to proceed. Perhaps the simplest is to rewrite the linear term as the sum of terms involving these factors:
-x = 3x -4x
f(x) = 6x² +3x -4x -2
Now, the expression can be factored 2 terms at a time:
f(x) = (6x² +3x) -(4x +2) . . . . . pay attention to signs
f(x) = 3x(2x +1) -2(2x +1) . . . . factor each pair
f(x) = (3x -2)(2x +1) . . . . . . . . factor out the common factor of (2x+1)
Answer:
11 + 4
Step-by-step explanation:
11 - (-4) = 11 + 4
