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3 years ago

Solve cos x + rad 2 = -cos x for over the interval [0, 2pi ]

1 answer:

6 0

$cos x + \sqrt{2} = -cosx \\ \\ 2 cos x + \sqrt{2} = 0 \\ \\ cos x = -\frac{\sqrt{2}}{2}$

The cosine function is negative in 2nd and 3rd quadrants, So you know that you will have 2 solutions. One between pi/2 and pi, the other between pi and 3pi/2.

Refer to a unit circle to find that
$cos (\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2} \\ \\ cos (\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2}$

Final Answer:
$x = \frac{3\pi}{4}, \frac{5\pi}{4}$

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Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

2 years ago

I forgot how to do this, can someone help me-

Artyom0805 [142]

Step-by-step explanation:

1) x/20 = -9

By cross multiplication,

x = -180

2) -168 = -14k

k = -168/-14

k = 12

3) -5m = -50

m = 10

4) -320 = -20n

n = 16

5) -4 = x - 5

x = 1

6) -6(-8 + n) = -54

42 - 6n = -54

-6n = -54 -52

6n = 106

n = 17.6

7) 3(x - 9) = -3

3x - 27 = -3

3x = 24

x = 8

8) 9k + 3 = -78

9k = -81

k = -9

9)4 + (n/4) = 8

By taking LCM,

16 + n/4 = 8

16 + n = 32

n = 16

10) -5r + 7 = -73

-5r = -80

r = 16

Hope it helps.

6 0

2 years ago

Convert 15/50 into a fraction

Lunna [17]

It already is a fraction though. I assume you mean to simplify it. You can simplify fraction by taking out the greatest common factor(that they share) in the denominator and numerator. In this case the denominator and numerator share the factor 5. So you if you divide the numerator and denominator by 5 you get 3/10 or the simplest form of the fraction.
The answer is $\frac{3}{10}$

8 0

3 years ago

Indica si el número es primo o compuesto?

Flura [38]

todos los numeros primos son: 2,3,5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 y 97.

y los otros numeros que no mencione son conpuestos.

3 0

3 years ago

un automovil marcha durante 3/8 del dia a una velocidad constante de 16 km/h ¿cual es el espacio recorrido?.......Doy corona al

Tanzania [10]

Answer:

LOL

Step-by-step explanation:

144 KILOMETROS....

5 0

2 years ago