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Solve the trigonometric equation:
Restriction for the solution:
Square both sides of
(i):
![\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2%5Ccdot%20%281-sin%5E2%5C%2Cx%29-sin%5C%2Cx%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2-2%5C%2Csin%5E2%5C%2Cx-sin%5C%2Cx%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B-%5C%2C%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2%5C%2Csin%5E2%5C%2Cx%2Bsin%5C%2Cx-2%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Bsin%5C%2Cx%5Ccdot%20%5Cleft%5B2%5C%2Csin%5E2%5C%2Cx%2Bsin%5C%2Cx-2%20%5Cright%5D%3D0%7D)
Let
So the equation becomes
Solving the quadratic equation:
You can discard the negative value for
t. So the solution for
(ii) is
Substitute back for
t = sin x. Remember the restriction for
x:
where
k is an integer.
I hope this helps. =)
The correct answer is C.
You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.
f(x) = x^4 + x^3 - 2x^2
Since each term has at least x^2, we can factor it out.
f(x) = x^2(x^2 + x - 2)
Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.
f(x) = x^2(x + 2)(x - 1)
Now we can also separate the x^2 into 2 x's.
f(x) = (x)(x)(x + 2)(x - 1)
To find the zeros, we need to set them all equal to 0
x = 0
x = 0
x + 2 = 0
x = -2
x - 1 = 0
x = 1
Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.
It would be 20 points bcuz it says each week it costs 20 points for unlimited bus rides
question number 36 the answer is always true because rational numbers are numbers that can be turned into fractions or simple fractions easily and any integers that is positive added together will provide a positive answer.
37. the answer is always true because and a negative integer and a negative integer added together will give a negative answer.
38. sometimes true. a positive intergee plus a negative interger can give a positive or negative answer. eg -3+2=-1 but -4+8=4
39. always true. + multiply + =+
40. never true. - multiply - = +
Answer:
The polygon with the smallest perimeter is the megagon
The polygon with the largest perimeter is the triangle
Step-by-step explanation:
An equilateral triangle with area = 20 has
0.5× a²×sin60 = 20
a= 6.796
Hence, perimeter = 20.39
A square of area 20 has perimeter= 4×√20 = 17.9
A regular pentagon of area = 20 has perimeter = 3.41 × 5 = 17.05
Hence as the number of sides is increasing, the ratio of the Area to the Perimeter also increases
Therefore, a triangle has the largest perimeter with an area of 20 while a megagon with a million sides has the smallest perimeter with an area of 20.
