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motikmotik
3 years ago
8

Suppose that l lines are drawn through a circle and these lines form p points of intersection (involving exactly two lines at ea

ch intersection). How many regions r are formed inside the circle by these lines? Assume that the lines end at the edge of the circle at 2l distinct points.
Mathematics
1 answer:
zhenek [66]3 years ago
8 0

Over which interval(s) is the function decreasing?


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Ksju [112]

Answer:

it's  A

Step-by-step explanation:

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3 years ago
Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side
maria [59]

Answer:

cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = -\frac{1}{3}

cos(b) = -\frac{1}{4}

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = -\sqrt{1-(-\frac{1}{3})^2} [Since, sin(a) = \sqrt{(1-\text{cos}^2a)}]

         = -\sqrt{\frac{8}{9}}

         = -\frac{2\sqrt{2}}{3}

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be  negative.

sin(b) = -\sqrt{1-(-\frac{1}{4})^2}

         = -\sqrt{\frac{15}{16}}

         = -\frac{\sqrt{15}}{4}

By substituting these values in the identity,

cos(a + b) = (-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})

                = \frac{1}{12}-\frac{\sqrt{120}}{12}

                = \frac{1}{12}(1-\sqrt{120})

                = \frac{1}{12}(1-2\sqrt{30})

Therefore, cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

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3 years ago
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3 years ago
Solve the following 3 × 3 system. Enter the coordinates of the solution below.
defon

9514 1404 393

Answer:

  (x, y, z) = (-1, 0, -3)

Step-by-step explanation:

We notice that the coefficients of z are such that elimination of the z term from the equations is made easy.

Adding equations 1 and 2:

  (2x -3y -2z) +(x +3y +2z) = (4) +(-7)

  3x = -3

  x = -1

Adding equations 2 and 3:

  (x +3y +2z) +(-4x -4y -2z) = (-7) +(10)

  -3x -y = 3

Substituting for x, we get ...

  (-3)(-1) -y = 3

 0 = y . . . . . . . . . . . add y-3 to both sides

Then z can be found from any equation. Substituting for x and y in the second equation gives ...

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The solution is (x, y, z) = (-1, 0, -3).

3 0
3 years ago
Given that 3+√5/4−√5 = a + b√5, find the values of “a” and “b”<br>URGENT PLZ ANSWER!
Vikki [24]

Answer:

Step-by-step explanation:

hello :

√(5/4)= √5/ √4 =√5/2 = (1/2)√5

3+√5/4−√5 = 3+(1/2)√5   so : a=3  and  b= 1/2

6 0
3 years ago
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