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3 years ago

Which two values of x satisfy the equation square root 3-2cos x = 2?

Mathematics

1 answer:

Andrei [34K]3 years ago

8 0

Answer: x=2π/3 and x=4π/3

Step-by-step explanation:

The equation we have is $\sqrt{3-2cosx} =2$ . All we have to do is get cosine alone to find the 2 values of x.

$3-2cosx=4\\-2cosx=1\\cosx=-\frac{1}{2}$

Now that we have our cosine left, we can use our unit circle to figure out when does cosx=-1/2. Cosine is the x value of the coordinate.

x=2π/3

x=4π/3

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The angle measures associated with which set of ordered pairs share the same reference angle? (Negative StartFraction StartRoot

Katarina [22]

Answer:

$(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)$

Step-by-step explanation:

The reference angle is the angle that the given angle makes with the x-axis.

For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.

From the given options:

$(A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)$

We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.

5 0

3 years ago

Read 2 more answers

Jasmine is part of a bowling league and wants to beat the team record of an average score of 240 out of 300 possible points per

hoa [83]

Answer:

her score in sixth game is 270

Step-by-step explanation:

The computation of the Jasmine score in her sixth game is shown below:

Let us assume her sixth game score is x

And, the first five games are 252, 227, 210, 239, 242

And, the average score is 240

So, the following formula should be used

(252 + 227 + 210 + 239 + 242 + x) ÷ 6 = 240

252 + 227 + 210 + 239 + 242 + x = 240 × 6

252 + 227 + 210 + 239 + 242 + x = 1,440

x = 270

Hence, her score in sixth game is 270

6 0

3 years ago

Using Substitution solve: y=x+5<br> 4x+y=20

Vladimir [108]

Answer:

Step-by-step explanation:

So first, plugin y to your equation, it should look like this: 4x+x+5+20. Now, we can solve this. Next, we have two x's so we can combine them. The equation will now look like this: 5x+5=20. Now, we have an extra 5 laying around that we need to get rid of, so we can subtract that 5 to both sides of the equation and we get this: 5x-5=20-5 which ends up being 5x=15. Now, we just divide both ides by 5 and since 15 divided by 5 is 3, we get: x=3

4 0

3 years ago

We test for a hypothesized difference between two population means: H0: μ1 = μ2. The population standard deviations are unknown

Lina20 [59]

Answer:

The degrees of freedom associated with the critical value is 25.

Step-by-step explanation:

The number of values in the final calculation of a statistic that are free to vary is referred to as the degrees of freedom. That is, it is the number of independent ways by which a dynamic system can move, without disrupting any constraint imposed on it.

The degrees of freedom for the t-distribution is obtained by substituting the values of n1 and n2 in the degrees of freedom formula.

Degrees of freedom, df = n1+n2−2

= 15+12−2=27−2=25

Therefore, the degrees of freedom associated with the critical value is 25.

4 0

3 years ago

Examine the following system of inequalities.

lubasha [3.4K]

Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

$y > -x+4$ ----> inequality A

The solution of the inequality A is the shaded area above the dotted line $y=-x+4$

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

$y \leq -(1/2)^{x} +6$ -----> inequality B

The solution of the inequality B is the shaded area above the solid line $y=-(1/2)^{x} +6$

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

7 0

3 years ago