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Vlada [557]
3 years ago
6

Solve on the interval [0,2pi): 2 sin^2 x-3 sin x + 1 = 0

Mathematics
1 answer:
erica [24]3 years ago
7 0

Answer:

How do you solve #2sin^2x+3sinx+1=0# and find all solutions in the interval #[0,2pi)#?

Trigonometry Trigonometric Identities and Equations Solving Trigonometric Equations

Answer:

Explanation:

We may identify this as a quadratic equation in #sinx# and factorise it as a trinomial to obtain the solutions as

<h3>#(2sinx+1)(sinx+1)=0#</h3>

<h3>#thereforesinx=-1/2 or sinx=-1#</h3>

<h3>#therefore x= (7pi)/6 or (11pi)/6 or (3pi)/2#</h3>

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Answer:

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Step-by-step explanation:

4 0
3 years ago
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A bike shop rents each of its mountain bikes for a one time $4.00 insurance charge plus $2.50 per hour create an equation that r
egoroff_w [7]

Answer:

y=2.50x+4.00

Step-by-step explanation:

Let

x -----> the number of hours

y ----> the total cost to rent a bike in dollars

we know that

The equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope or the unit rate of the linear equation

b is the y-intercept or the initial value

In this problem we have

The unit rate or slope is equal to

m=\$2.50\ per\ hour

The y-intercept (value of y when the value of x is equal to zero) is equal to

b=\$4.00 ----> (fee charge)

substitute the values

y=2.50x+4.00

5 0
4 years ago
Molly owes her brother $300.She works for $10 per hour as a checker at the local grocery store.Molly plans to repay her brother
gavmur [86]

Answer: The expression which represents the condition described is given as  4x=300

Step-by-step explanation:

Since we have given that

Amount that Molly owes her brother = $300

Let the number of hours she worked as a checker be x

Cost of per hour = $10

Amount she get after doing work for x hours is given by

10x

Rate of tax are taken out = 80%

So, amount she left with is given by

\frac{100-20}{100}\times 10x\\\\=\frac{80}{100}\times 10x\\\\=8x

So, Molly plans to repay her brother half of what she earns is given by

\frac{8x}{2}=4x

According to question,

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So, the expression which represents the condition described is given as

4x=300

3 0
4 years ago
Read 2 more answers
PLEASE HELP!<br>Calculate $40^{13} \pmod{85}.$
SVEN [57.7K]
In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85

Notice

40*40*40=64,000

so we check how many time does 85 fit into 64,000:

64,000/85=752.94

85*753=64,005;       64000-64,005=-5

this means that 

40^{3} =-5\pmod{85}

thus

40^{13} =40^{3*4+1}={(40^{3})}^{4}*40=(-5)^{4}*40 \pmod{85}=\\\\625*40\pmod{85}=(7*85+30)*40\pmod{85}=30*40\pmod{85}\\\\=1200\pmod{85}=(14*85+10)\pmod{85}=10\pmod{85}


Answer: 10 (mod85)

Remark, the set of all solutions is:

{......-75, 10, 95, .....}, that is 85k +10
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3 years ago
Eric noticed that his basil plant grows 5 cm every day. He starts recording the height when the plant is 22 cm tall. He wants to
slava [35]
The answer is B because you multiply 14 days (2 weeks) to 5 which is 70 then you add the other 22cm and that's how you would end up with 92cm
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