This expression<span> can not be factored with </span>rational numbers.<span>The </span>polynomial<span> is not factorable with </span>rational numbers
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Answer with Step-by-step explanation:
We are given that 
We have to prove that why the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form and prove that the limit equals to 0.
Because 
and
We know that cos 0=1 and sin 0=0
Substitute the values then we get
We know that 
is indeterminate form
Hence, the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form.
L'hospital rule:Apply this rule and differentiate numerator and denominator separately when after applying 
we get indeterminate form
Now,using L' hospital rule
because 
Now, we get
Hence,
Buckle up, this one was a long one.
I set up 1 / 3(12 + x) as a fraction and set it equal to - 8(6 - x).
Get rid of the parentheses by distributing the integers on the outside. You get 1 / 36 + 3x = - 48 + 8x.
To get rid of the fraction, you multiply both sides by the (36 + 3x) polynomial to get 1 = (- 48 + 8x)(36 + 3x).
Now we do the FOIL method to get 1 = 24x^2 + 288x - 144x - 1728. Combine like terms to get 24x^2 + 144x - 1728 = 1.
Simply again by dividing each term the GCF of 24 to get 24(x^2 + 6x - 72) = 1.
Factor the inside of the parentheses to get 24(x + 12)(x - 6) = 1. Now divide both sides by 24 to isolate the x variables to get (x + 12)(x - 6) = 1/24.
Set each polynomial equal to 1/24 to get you possible answers for what x can be.
x + 12 = 1/24. Subtract 12 from both sides; you get x = - 12 + 1/24 to get x = - 11 23/24.
x - 6 = 1/24. Add 6 to both sides; you get x = 6 + 1/24 to get x = 6 1/24
Answer:
m=-2
Explanation:
If a line passes through the points (4,5) and (2,9): to calculate the slope, use the formula below:
Substituting the points, we have:
The slope of this line is -2.
The answer is 2/5. 2*2=4 and 2*5= 10, 2*3=6 and 3*5=15
