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Roman55 [17]
3 years ago
5

ASAPFind all solutions to the equation.7 sin^2 x - 14 sin x + 2 = -5

Mathematics
1 answer:
matrenka [14]3 years ago
3 0

Answer:

{-π/2, π/2}

Step-by-step explanation:

Rewrite this as:

7sin^2 x - 14sin x + 7 = 0.  Reduce this result by dividing all terms by 7:

sin^2 x - 2sin x + 1

Temporarily replace "sin x" with y:

y^2 - 2y + 1 = 0

Solve this through factoring:  (y - 1)^2 = 0, or y - 1 = ± 0, or y = ±1

Recalling that y = sin x, we write

sin x = ±1, whose solutions are sin x = 1 and sin x = -1

The solution of sin x = 1 is π/2 and that of sin x = -1 is -π/2

and so the solution set is {-π/2, π/2}

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Answer:

a.

Month\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Pop(whole \ ant)\\month1 => x_1=80\times0.94^1=1128\\month2=>x_2=1200\times0.94^2=1060\\month3=>x_3=1200\times0.94^3=996\\month4=>x_4=1200\times0.94^4=936

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week Number\ \ \ \ \ \ \ \ \ \ \ \ \ \ Mass(g)\\week1 => x_1=80\times1.1^1=88g\\week2=>x_2=80\times1.1^2=96.8g\\week3=>x_3=80\times1.1^3=106.48g\\week4=>x_4=80\times1.1^4=117.128g

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a. From the information provided, we can deduce that the population death's follows a Geometric sequence in the form (a,ar,ar^2,ar^3...) where a-first \ term and r-common \ ratio

#Since the population is reducing, r can is obtained as r=1-r=0.94

#The n^t^h term is obtained using the formula x_n=ar^(^n^-^1^), given a=1200

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Month\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Pop(whole \ ant)\\month1 => x_1=80\times0.94^1=1128\\month2=>x_2=1200\times0.94^2=1060\\month3=>x_3=1200\times0.94^3=996\\month4=>x_4=1200\times0.94^4=936

The ant's alive after 4 months is obtained as the value of x_5

x_n=ar^(^n^-^1^)\\1-x_5=1-1200\times 0.94^4=936.89\\\approx 936

Hence, 936 ants are alive after 4 months.

b. As with the above question, the kitten population follows a geometric sequence: (a,ar,ar^2,ar^3...).

#Since it's a growing population , the common ration is the sum of 100% + the growth rate,

r=1.1 and a=80 and x_n=ar^(^n^-^1^)

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week Number\ \ \ \ \ \ \ \ \ \ \ \ \ \ Mass(g)\\week1 => x_1=80\times1.1^1=88g\\week2=>x_2=80\times1.1^2=96.8g\\week3=>x_3=80\times1.1^3=106.48g\\week4=>x_4=80\times1.1^4=117.128g

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