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3 years ago

Solve [0, 2pi) 3 Cos(2x) = 5 Sin(x) - 1

Mathematics

1 answer:

erastovalidia [21]3 years ago

7 0

Given :

Solve [0, 2π)

3cos(2x) = 5sin(x) - 1

To Find :

The value of x in range [0,2π).

Solution :

We know, cos(2x) = 1 - sin²x .

3( 1 - 2sin²x ) = 5sinx - 1

3 - 6sin²x = 5sinx - 1

6sin²x + 5sinx - 4 = 0

6sin²x + 8sinx - 3sinx - 4 = 0

2sinx( 3sinx + 4 ) - 1( 3sinx + 4) = 0

sin x = 1/2 and sin x = -4/3 .

Since, sin x ≤ 1.

So, sin x = 1/2 .

x = π/6 .

Therefore, value of x is π/6.

Hence, this is the required solution.

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Solve the system of linear equations by graphing. Round the solution to the nearest tenth as needed. Y + 2.3 = 0.45x and -2y = 4

HACTEHA [7]

Answer:

(2.4, -1.2)

Step-by-step explanation:

Start by moving the x and the y to the same side and moving the number across the equal sign in both equations. We should now have y-0.45x=-2.3 and 2y+4.2x=7.8. We can use the elimination method by multiplying the first equation by -2 to get -2y+0.9x=4.6 and 2y+4.2x=7.8. From there, add the two equations together, eliminating y (-2+2=0). We now have 5.1x=12.4; divide both sides by 5.1 to get x=2.4. Then, in any of the two equations, let's use y-0.45x=-2.3, substitute x with 2.4. Now we have y-1.08=-2.3. Add 1.08 to both sides to get y=-1.22; round that to the nearest tenth to get -1.2.

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3 years ago

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Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−13x+4.

lilavasa [31]

Answer:

y = -13x + 55

Step-by-step explanation:

perpendicular formula : m1 × m2 = -1

y = -13x + 4

now we take the grafient of the equation which is 13 :

m × 13 = -1

m = -13

so now we hv a new gradient then we can find the equation use the formula y = mx + c :

m = -13 point = ( 4 , 3 )

sub them into the formula,

3 = -13 (4) + c

3 = -52 + c

3 + 52 = c

55 = c

c = 55

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3 years ago

Andrea spent 5/9 of her money buying a guitar if she had €296 left how much had she had first

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3 years ago

A graph displays point A (5, 3, 4) and point B (−4, 2, 6). Calculate the approximate distance each point is from the origin. Rou

SIZIF [17.4K]

Distance from the origin to the points ≈ 0.41.

<h3>What is the distance between two points ( p,q) and (x,y)?</h3>

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]

Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;

Let OB is the distance from the origin to the point B

Let OA is the distance from the origin to the point A

Using the formula for calculating the distance between two points;

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(4-0)²+(3-0)²+(5-0)²

OA = √(16)+(9)+(25)

OA = √50

OA = 7.071

Similarly;

OB = √(6-0)²+(2-0)²+(-4-0)²

OB = √(6)²+(2)²+(-4)²

OB = √36+4+16

OB = √56

OB = 7.4833

Distance from the origin to the points = 7.4833 - 7.071= 0.4123

Distance from the origin to the points ≈ 0.41

Learn more about distance between two points here:

brainly.com/question/16410393

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2 years ago

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