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4 years ago

Worth 3 marks Please explain with step by step instructions Thanks in advance xx

Mathematics

1 answer:

Anna007 [38]4 years ago

7 0

Have you heard about the triangle sum theorem? Which says that all three angles of a triangle will have a sum of 180. You're gonna use that to find the degrees of the angles in the pentagon by dividing it into the largest triangles you can. You should have created three none lapping triangles. You know that each triangle as a sum of 180 degrees, and you also know that the sum of all of those interior angles are equal to the sum of the interior angles of the pentagon. Next I'll explain the formula you'll use to find how many triangles there will be in a given shape. For two triangles to form you need 4 sides, and from there every side you add will be another triangle. Ok, from there you'll want to figure out for s sided polygon how many none lapping triangles can be formed in the polygon. The formula is number of triangles = 2 + ( s - 4 ) = s - 2. And once you find that out you just need to multiply it by 180 to find the sum of the interior angles of that polygon; 180( s -2 ) = number of triangles. Once you use the formula you find out that there's 540 degrees in a pentagon. Now there's different ways to slice the pentagon, but you should in the end find out that one of the interior of the actual pentagon by using a formula to find one interior angle 180( s - 2 ) / s. Using that you should find that A ( one of the pentagon's interior angles) is 108 degrees. And the angle CFD is equivalent to A, so that means that A's angle degrees is the same for CFD. I'm sorry if it's to confusing. or not what your looking for. I tried my best to explain it thoroughly.

I hope this helps :)

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dybincka [34]

i) The given function is

$f(x)=\frac{(2x+1)(x-5)}{(x-5)(x+4)^2}$

The domain is

$(x-5)(x+4)^2\ne 0$

$(x-5)\ne0,(x+4)^2\ne 0$

$x\ne5,x\ne -4$

ii) For vertical asymptotes, we simplify the function to get;

$f(x)=\frac{(2x+1)}{(x+4)^2}$

The vertical asymptote occurs at

$(x+4)^2=0$

$x=-4$

iii) The roots are the x-intercepts of the reduced fraction.

Equate the numerator of the reduced fraction to zero.

$2x+1=0$

$2x=-1$

$x=-\frac{1}{2}$

iv) To find the y-intercept, we substitute $x=0$ into the reduced fraction.

$f(0)=\frac{(2(0)+1)}{(0+4)^2}$

$f(0)=\frac{(1)}{(4)^2}$

$f(0)=\frac{1}{16}$

v) The horizontal asymptote is given by;

$lim_{x\to \infty}\frac{(2x+1)}{(x+4)^2}=0$

The horizontal asymptote is $y=0$ .

vi) The function has a hole at $x-5=0$ .

Thus at $x=5$ .

This is the factor common to both the numerator and the denominator.

vii) The function is a proper rational function.

Proper rational functions do not have oblique asymptotes.

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I have the answer but I have to show work help?

Marina86 [1]

See attached picture for steps

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3 years ago

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zheka24 [161]

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4 years ago

Read 2 more answers