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postnew [5]
3 years ago
5

Solve on the interval [0,2pi] 3(sec x)^2 -4=0

Mathematics
2 answers:
Umnica [9.8K]3 years ago
7 0

Answer:

pi/6, 5pi/6, 7pi/6, 11pi/6

Step-by-step explanation:

3(sec x)^2 -4=0

Add 4 on both sides:

3(sec x)^2=4

Divide 3 on both sides:

(sec x)^2=4/3

Take square root of both sides:

sec x=plus/minus sqrt(4/3)

Reciprocal identity:

cos x=plus/minus sqrt(3/4)

Simplify the radical:

cos x=plus/minus sqrt(3)/2

So we are looking on the unit circle where the first coordinate of the order pair is either sqrt(3)/2 or -sqrt(3)/2.

This happens at pi/6, 5pi/6, 7pi/6, 11pi/6

QveST [7]3 years ago
6 0

Answer:

\sf \boxed{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}

Step-by-step explanation:

A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]

The given equation is ,

\sf\longrightarrow 3(sec x)^2-4=0

This can be written as ,

\sf\longrightarrow 3sec^2x - 4 = 0

Add 4 to both sides of the equation ,

\sf\longrightarrow 3sec^2x = 4

Divide both sides by 3 ,

\sf\longrightarrow sec^2x =\dfrac{4}{3}

Put squareroot on both sides ,

\sf\longrightarrow sec \ x =\sqrt{\dfrac{4}{3} }

Simplify ,

\sf\longrightarrow sec\ x =\pm \dfrac{2}{\sqrt3}

Multiply numerator and denominator by √3 ,

\sf\longrightarrow \bf sec(x) = \dfrac{ 2\sqrt3}{3},-\dfrac{2\sqrt3}{3}

Solve for x ,

\sf\longrightarrow x = \dfrac{\pi}{6} +2\pi n , \dfrac{11\pi}{6}+2\pi n , \textsf{ for any integer n } .

Therefore all the possible solutions are ,

\sf\longrightarrow \boxed{\blue{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}}

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What is the unit rate for 16 ounces (pint) at $3.93?
Juli2301 [7.4K]

Answer:

25 cents/ounce

Step-by-step explanation:

The unit rate means how much is one of the thing you are working with.  In this case, the unit rate of a pint (16 ounces) is how much just one ounce will cost.  So divide $3.93 by 16

$3.93/16 =  $0.245625

Since we're working with money, round to the nearest hundredth

Unit rate is $0.25 per ounce, or 25 cents per ounce

8 0
3 years ago
Read 2 more answers
The growth of a city is described by the population functionwhereis the initial population of the city, t is the time in years,
mamaluj [8]

Complete question:

The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at

Answer:

27,800

Step-by-step explanation:

We need to obtain the initial population(P0) and constant value (k)

Population function : p(t) = P0e^kt

At t = 0, population = 19,000

19,000 = P0e^(k*0)

19,000 = P0 * e^0

19000 = P0 * 1

19000 = P0

Hence, initial population = 19,000

At t = 3; population = 23,000

23,000 = 19000e^(k*3)

23000 = 19000 * e^3k

e^3k = 23000/ 19000

e^3k = 1.2105263

Take the ln

3k = ln(1.2105263)

k = 0.1910552 / 3

k = 0.0636850

At t = 6

p(t) = P0e^kt

p(6) = 19000 * e^(0.0636850 * 6)

P(6) = 19000 * e^0.3821104

P(6) = 19000 * 1.4653739

P(6) = 27842.104

27,800 ( nearest whole number)

3 0
3 years ago
I need help with number 5
Zielflug [23.3K]

Answer:

100.34÷2.9=34.6

Step-by-step explanation:

You will need to move the decimal point to the right one place

5 0
3 years ago
Calculate the speed of a car that went a distance of 125 miles in 2 hours<br> time.
DerKrebs [107]

Answer:

62.5

Step-by-step explanation:

speed = distance / time taken

= 125/2

=62.5miles per hour

5 0
2 years ago
Which statements best describe the dot plot or box plot? Check all that apply
Sveta_85 [38]

Answer:

<h2>The box plot is the only display that can be used to show the variability of the data.</h2><h2>The median appears clearly on the box plot at the line within the box: 10.</h2>

Step-by-step explanation:

When we want to represent variability, we use a box plot instead of a dot plot, because the box plot allow us to observe the range of the data set, that is, the minium and the maximum value.

Remember that variability is about the spread of the dataset, and the range is a measure that can give a pretty good idea of it, shown by a box plot.

Therefore, the last hoice is correct.

On the other hand, according to the dot plot, the median is 10, because there are 13 total values, where the central value is 10.

Therefore, the second choice is correct.

3 0
3 years ago
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