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3 years ago

Simplify 1-cot(x)/tan(x)-1

1 answer:

6 0

$\bf \cfrac{1-cot(x)}{tan(x)-1}\qquad 
\begin{cases}
cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\end{cases}\qquad thus
\\\\\\
\cfrac{1-\frac{cos(x)}{sin(x)}}{\frac{sin(x)}{cos(x)}-1}\implies 
\cfrac{\frac{sin(x)-cos(x)}{sin(x)}}{\frac{sin(x)-cos(x)}{cos(x)}}\\\\
-----------------------------\\\\
recall\implies \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus\\\\
-----------------------------$

$\bf \cfrac{\frac{sin(x)-cos(x)}{sin(x)}}{\frac{sin(x)-cos(x)}{cos(x)}}\implies \cfrac{sin(x)-cos(x)}{sin(x)}\cdot \cfrac{cos(x)}{sin(x)-cos(x)}\implies \boxed{?}$

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Explain why f(x) = x^2+4x+3/x^2-x-2 is not continuous at x = -1.

liberstina [14]

Answer:

The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)

Step-by-step explanation:

We have the following expression

$f(x) = \frac{x^2+4x+3}{x^2-x-2}$

Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.

Now we search that values of x make 0 the denominator factoring the polynomial $x^2-x-2$

We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.

These numbers are -2 and 1

Then the factors are:

$(x-2) (x + 1)$

We do the same with the numerator

$x^2+4x+3$

We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.

These numbers are 3 and 1

Then the factors are:

$(x+3)(x + 1)$

Therefore

$f(x) = \frac{(x+3)(x+1)}{(x-2)(x+1)}$

Note that $\frac{(x+1)}{(x+1)}=1$ only if $x \neq -1$

So since $x = -1$ is not included in the domain the function has a discontinuity in $x = -1$

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Find the next three terms of each geometric sequences. 4,8,16_,_,_

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32 64 128 are the answers

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Aubrey is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks avail

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Answer:

$51

Step-by-step explanation:

do 13*3 because of the 2 kids and the adult then add 12 because of the snacks

hope this helps

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Tommy throws a ball from the balcony of his apartment down to the street. The

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Answer: c

Step-by-step explanation:

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A right triangle with vertices J(4, 0), K(0,0), and L(0,5) is rotated around the x-axis. To the nearest tenth of a unit, what is

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This is the concept of graphs and volume of the solid figures, given that the triangle J,K,L was rotated along the x-axis, the resultant figure was cone with with radius of 5 units and a height of 4 units;
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