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loris [4]
2 years ago
5

Find all solutions of the equation in the interval [0, 2pi) cosx (2 sinx+1)=0

Mathematics
1 answer:
Vinil7 [7]2 years ago
6 0

Answer:

x = pi/2 and 11pi/6

Step-by-step explanation:

Given the trigonometry expression

cosx (2 sinx+1)=0

This can be written in two forms as;

cosx  = 0 and 2sinx + 1 =  0

If cos x  = 0

x = arccos0

x = 90degrees

x = pi/2

Similarly

2sinx  + 1 = 0

2sinx = -1

sinx = -1/2

sinx  =-0.5

x = aarcsin(-0.5)

x = -30

Since sin is negative in the third and 4th quadrant

x = 270 + 30

x = 330degrees

x = 330pi/180

x = 11pi/6

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An advertising campaign is canceled before launch with probability 0.10, in which case the marketing company is fired with proba
Feliz [49]

Answer:

0.2231 (22.31%)

Step-by-step explanation:

defining the event F = the marketing company is fired, then the probability of being fired is:

P(F)= probability that the advertising campaign is cancelled before lunch * probability that marking department is fired given that the advertising campaign was cancelled before lunch + probability that the advertising campaign is launched but cancelled early  * probability that marking department is fired given that the advertising campaign is launched but cancelled early        ....   (for all the 4 posible scenarios where the marketing department is fired)

thus

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then the probability that the marketing department is fired is  0.2231 (22.31%)

7 0
2 years ago
The function Q(x)=2x^2-kx+18. For what value of k does Q(x) have one distinct real solution? (NEEDS TO BE DONE WITHIN 2 HOURS!)
Aliun [14]

Answer:

k = 12

Step-by-step explanation:

Given:

The equation Q(x)=2x^2-kx+18

To find:

Value of k = ? for which the given equation has one distinct real solution.

Solution:

The given equation is a quadratic equation.

There are always two solutions of a quadratic equation.

For the equation: ax^{2} +bx+c=0 to have one distinct solution:

b^2 - 4ac = 0

Here,

a = 2,

b = -k and

c = 18

Putting the values, we get:

(-k)^2 - 4\times 2\times 18 = 0\\\Rightarrow k^2 = 18\times 8\\\Rightarrow k^2 =144\\\Rightarrow k = 12

The equation becomes:

Q(x)=2x^2-12x+18

And the one root is:

2(x^2-6x+9 ) = 0\\\Rightarrow 2(x-3)^2=0\\\Rightarrow x = 3

4 0
2 years ago
A person who weighs 100 pounds on earth weighs 16.6 lb on the moon. What is the independent variable? Explain why
Leviafan [203]
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5 0
3 years ago
Use the rule for order of operations to simplify the expression as much as possible.
ratelena [41]

Answer:

The answer to your question is 3

Step-by-step explanation:

Expression

                        3⁴ + 9² / 3³ - 9²

1.- Do the division

                        3⁴ + (9² / 3³) - 9²

Use law of exponents

                        3⁴ + (3⁴ / 3³) - 9²

                        3⁴ + 3⁴⁻³ - 9²

Simplify

                        3⁴ + 3 - 9²

2.- Convert 9² to base 3

                        3⁴ + 3 - 3⁴

3.- Simplify (associative property)

                        ( 3⁴ - 3⁴ ) + 3

4.- Result

                              3

                       

                       

7 0
3 years ago
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