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morpeh [17]
2 years ago
9

How many solutions does the equation cos(6x)=1/2 have on the interval (0, 2pi)?

Mathematics
2 answers:
Lina20 [59]2 years ago
6 0
Cos( 6 x ) = 1/2          
6 x = 60°  ⇒ x 1 = 10°
6 x = 300° ⇒ x 2 = 50°
6 x = 420° ⇒ x 3 = 70°
6 x  = 660° ⇒ x 4 = 110°
x 5 = 130°,  x 6 = 170°,  x 7 = 190° , x 8 = 230°, x 9 = 250°,
x 10 = 290°, x 11 = 310°, x 12 = 350°
Answer: there are 12 solutions on the interval ( 0 , 2π ).
Kaylis [27]2 years ago
3 0

Answer:

The number of possible solution of the trignometric equation are:

12

Step-by-step explanation:

We have to find the solution of the trignometric equation which is given as:

\cos(6x)=\dfrac{1}{2}

Now, the solution of the trignometric equation is the possible value of x such that the equation holds true.

Now we know that:

\cos(\dfrac{\pi}{3})=\dfrac{1}{2}

Also,

\cos(2\pi-\dfrac{\pi}{3})=\dfrac{1}{2}\\\\i.e.\\\\\cos(\dfrac{5\pi}{3})=\dfrac{1}{3}

We are given that:

0<x<2π.

this means that:

0<6x<12π.

Now, we have the solution as:

6x=\dfrac{\pi}{3}\\\\\\i.e\\\\x=\dfrac{\pi}{18}

and:

6x=\dfrac{5\pi}{3}\\\\x=\dfrac{5\pi}{18}

6x=2\pi+\dfrac{\pi}{3}=\dfrac{7\pi}{3}\\\\6x=4\pi-\dfrac{\pi}{3}=\dfrac{11\pi}{3}\\\\6x=4\pi+\dfrac{\pi}{3}=\dfrac{13\pi}{3}\\\\6x=6\pi-\dfrac{\pi}{3}=\dfrac{17\pi}{3}\\\\6x=6\pi+\dfrac{\pi}{3}=\dfrac{19\pi}{3}\\\\6x=8\pi-\dfrac{\pi}{3}=\dfrac{23\pi}{3}\\\\6x=8\pi+\dfrac{\pi}{3}=\dfrac{25\pi}{3}\\\\6x=10\pi-\dfrac{\pi}{3}=\dfrac{29\pi}{3}\\\\6x=10\pi+\dfrac{\pi}{3}=\dfrac{31\pi}{3}\\\\6x=12\pi-\dfrac{\pi}{3}=\dfrac{35\pi}{3}

Hence, the number of possible solution of the trignometric equation are:

12

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Answer: 22.5 yards

Step-by-step explanation:

There are a total of 20 parts yarn. This means that 3/20 of the carpet is silver. So in order to compare this to the 150 meters of total yarn, you would set up this equation:

3/20 = x/150

Next, you cross multiply:

3*150 = 20*x or simplified would be 450 = 20x

Next, you divide both sides by 20 to get x by itself.

450/20 = 22.5, so x is equal to 22.5

This means you have 22.5 yards of silver in the carpet.

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3 years ago
In a recent semester at a local university, 490 students enrolled in both General Chemistry and Calculus I. Of these students, 6
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I marked all 3 parts. I need to know part C (the shaded part). anybody mind helping?​
Mnenie [13.5K]

Answer:

Area of shaded part ABCEF = 66 sq.cm

Step-by-step explanation:

AB = 8cm

CD = 8cm

Let DE = x cm

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CD =  CE + DE = 8cm

        x + 3x = 8

4x = 8

x = 8/4 = 2 cm

DE = 2cm

CE = 3 * 2 = 6 cm

Area of triangle ADE = 1/2 * base * height

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                                    = 1/2 * 2 * 11 = 11 sq. cm

Area of triangle AEF = Area of triangle ADE = 11 sq. cm

Area of Rectangle ABCD =  l * b = 8 * 11 = 88 sq.cm

Area of shaded part ABCEF =  Area of Rectangle ABCD - (Area of triangle AEF + Area of triangle ADE)

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6 0
3 years ago
2. Consider the function, f(x)=x^3+x^2-9x-9
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The intercepts of the graph are:

x-axis interception: \left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right).

y-axis interception: \left(0,\:-9\right).

See the graph of the function f(x)=x^3+x^2-9x-9  in the attached image.

<h3>Constructing a graph</h3>

For constructing a graph we have the following steps:

  • Determine the range of values for x of your graph.

For this exercise, for example, we can define a range -4<x<4.  In others words, the values of x will be in this interval.

  • Determine the points

Replace these x-values in the given equation. For example:

When x=-4, we will have: \left(-4\right)^3+\left(-4\right)^2-9\left(-4\right)-9=-21.  Do this for the all x-values of your ranges.

See the results for this step in the attached table.

  • Draw the graph

Mark the points <u>x</u> and<u> y</u> that you found in the last step. After that, connect the dots to draw the graph.

The attached image shows the graph for the given function.

<h3>Find the x- and y-intercepts</h3>

The intercepts are points that crosses the axes of your plot. From your graph is possible to see:

x-axis interception points (y=f(x)=0)  are: \left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right).

y-axis interception point (x=0) is: \left(0,\:-9\right).

Learn more about intercepts of the graph here:

brainly.com/question/4504979

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2 years ago
What is the exact distance from (8, 5) to (−1, 3)? (Round to the nearest tenth)
alexira [117]

Answer:

About 9.2 units

Step-by-step explanation:

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81+4

sqrt(85)

9.2

Brainliest appreciated :)

4 0
2 years ago
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