All categories

2 years ago

Which of the following is a solution to 2sin^(2)x+sinx-1=0

Mathematics

1 answer:

lukranit [14]2 years ago

6 0

Hello,

$2*sin^2(x)+sin(x)-1=0\\\Delta=1+4*2*1=9=3^2\\sin^2(x)=\frac{-1-3}{4} =-1\ (impossible)\\or\\sin^2(x)=\frac{-1+3}{4} =\dfrac{1}{2}\\sin(x)=\dfrac{\sqrt{2} }{2} \Longrightarrow (x=45^o\ or\ x=135^o)\\or\\sin(x)=-\dfrac{\sqrt{2} }{2} \Longrightarrow (x=315^o\ or\ x=225^o)\\$

Answer A : 45°

You might be interested in

The table shows three unique functions.

Dovator [93]

Answer:

<h2>All three functions have a y-intercept.</h2>

Step-by-step explanation:

The table is attached, there you can observe functions f(x), g(x) and h(x).

Remember, when x = 0, it represents a y-intercept. So, we can deduct that all three functions have y-intercept, (0,1) for f(x), (0, -1/2) for g(x) and (0,-5) for h(x).

Also, x-values represent domain values, however, in this case, we can't say that all three function have the same domain values, because we don't know the domain defintion for each of them to determine such thing.

Additionally, in the table you can observe that f(x) has the greatest maxium, so the second choice is also false. And neither function has x-intercept.

Therefore, the only right answer is the third choice.

5 0

3 years ago

Find the perimeter of the figure.

Alika [10]

1+1=2

2+3=5

5+3=8

8+5=13 inches

3 0

2 years ago

The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 273 meters, find the dimensions

AleksandrR [38]

The length of the rectangle = 16 meters

The width of the rectangle = 10.5 meters

Step-by-step explanation:

Given that,

The Area of the rectangle is 273.

Step 1 :

Let, the width of the rectangle be 'x'

The length of the rectangle is 2x - 5

Step 2 :

Area of the rectangle = length $\times$ width

273 = (2x - 5) x

273 = 2x^2 - 5x

Step 3 :

The equation formed is 2x^2 - 5x -273 = 0

a= coefficient of x^2 = 2

b= coefficient of x = -5

c = constant = -273

Find the roots of the equation, to find the width.

Step 4 :

Find the roots using factorizing method,

ac = 2 $\times$ -273 = -546 and b= -5

Factorizing -546 as -26 $\times$ 21

The product of -26 $\times$ 21 = -546

The sum of -26 + 21 = -5

Step 5 :

The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2

The values of x are x= -13 and x= 10.5

Since the width cannot be a negative value, neglect x= -13

Step 6 :

Therefore,

The width of the rectangle = 10.5 meters

The length of the rectangle = 2x-5

= 2(10.5) - 5

= 21 - 5

length = 16 meters

5 0

3 years ago

A park creates new habitats for 182 monkeys. Each habitat will house 8 or fewer monkeys. What did you do with the remainder? exp

Anuta_ua [19.1K]

32 because 1plus 31 equals 32

7 0

3 years ago

Read 2 more answers

Given the trinomial x^2+bx+c where both the first and second signs are positive, the signs of the factors will be: A. both negat

Lunna [17]

The answer here is C. The sign of the factors are both positive. We can use the FOIL method as reference in determining the sign of the factors. The 3rd term C is positive; therefore our only option is either both negative or both positive. Looking the middle term, which is positive, we know that the middle term is the sum of the outer and inner in FOIL method, which means, signs of the factors must be both positive

7 0

3 years ago