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Alina [70]
3 years ago
10

Find the solutions to sin2(x) + cos(x) = 1, keeping 0 ≤ x < 2π

Mathematics
1 answer:
frozen [14]3 years ago
3 0
Sin2(x) +cos(x)=1
from the relation: (sin2(x) +cos2(x) =1 )
so , sin2(x)=1-cos2(x)
by subs. in the main eqn.
1-cos2(x) + cos(x) =1
by simplify the eqn.
cos(x) -cos2(x)=0
take cos(x) as a common factor
cos(x)* (1-cos(x))=0
then cos(x)=0 && cos(x)=1
cos(x)=0 if x= pi/2
& cos(x) = 1 if x = 0 , 2*pi
so the solution is x= {0,pi/2 , 2*pi}
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In preperation for an easter egg hunt, 4 blue eggs are filled for every 7 green. How many green eggs will be filled if 100 blue
ivann1987 [24]

Answer:

1. Typed question: 175 green eggs

2. Attached: 22 tables

Step-by-step explanation:

For the question you typed down, it is a ratio and proportion problem. You need to solve for the ratio proportional to the first ratio given.

4 blue eggs are filled for every 7 green. This means that the ratio between blue eggs and green eggs is 4:7.

Now yo need to figure out a ratio proportional to 4:7 if 100 blue eggs were filled. Below is how this is set up:

\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}

Now let's solve for x:

\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}\\\\or\\\\\dfrac{4}{7}=\dfrac{100}{x}\\\\Cross-multiply\\\\4x = (7)(100)\\\\4x = 700\\\\Divide\;both\;sides\;by\;4\\\\\dfrac{4x}{4}=\dfrac{700}{4}\\\\x=175

For your attached problem:

You have a total of 175 people, you need to figure out how many round tables you need if here are 8 chairs for each table You just need to divide the number of people by the number of chairs per table.

175 ÷ 8 = 21.9 tables

Now since you cannot have half a table, you round up to the nearest whole number. (we round up because you need to make sure that all of them are seated)

21.9 ≅ 22 tables.

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4 years ago
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Firdavs [7]
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3 years ago
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natka813 [3]

Answer:

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Step-by-step explanation:

As given, the diatance at any point after t seconds is given by

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At t=2 seconds then

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Since we're not given the units, it may be feet, inches, meters, kilometers, miles etc. Therefore, the diatance is equal to 64 units

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Answer:

Step-by-step explanation:

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