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DochEvi [55]
3 years ago
13

Solve the equation on the interval [0, 2pi) 2 cos^2 (theta/2) - 3 cos theta = 0

Mathematics
1 answer:
Ksivusya [100]3 years ago
3 0
Hello : 
by idetity : 1+cos(2a) = 2cos²(a)
let : a = <span>θ/2
1+cos(2×</span>θ/2)=2cos²(θ/2)
1+cos(θ) = 2cos²(θ/2)
solve :  2 cos^2 (θ/2) - 3 cos(θ) = 0   ......(1)
(1) : 1+cos(θ)-3 cos(θ) =0
2cos(θ)  = 1 

cos(θ) = 1/2
in : [0, 2π<span>[ 
</span>( θ = π/3) or (θ = 5π/3)
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Please answer below :-)
Evgen [1.6K]

Answer:

2\frac{7}{10}

Step-by-step explanation:

First, find the LCM and multiply through:

12(\frac{2x-1}{4} ) +12(\frac{x}{3})=12(2)

The LCM will cancel out the denominators (note that braket symbolizes Multiplication):

:3(2x-1) +4(x)=24

:6x-3+4x=24

Group like terms:

6x+4x=24+3

10x=27

Divide through by 10 to eliminate the coefficient of x

\frac{10x}{10}=\frac{27}{10}

: x=\frac{27}{10}=2\frac{7}{10}

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2 years ago
Henrietta did an experiment. She started out with 700 bacteria cells. She found that the growth rate of the bacteria cells was 5
poizon [28]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have a exponential function of the form

y=a(b^x)

where

y ---> is the population of bacteria

x ---> the number of hours

a is the initial value or y-intercept

b is the base of the exponential function

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b=(1+r)

we have

a=700\ bacteria

r=5\%=5/100=0.05

so

b=1+0.05=1.05

substitute

y=700(1.05^x)

For x=20 hours

substitute in the equation and solve for y

y=700(1.05)^{20} =1,857\ bacteria

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The Flinn Falcons only scored 13 points.
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