How many points did the player with the fewer points score?

Find all solutions of the equation in the interval [0,2π) sec(theta) +2=0

Komok [63]

I will first reveal the most obvious secret of trig: Most of the problems are 30/60/90 or 45/45/90 triangles of some sort.

$\sec \theta + 2 = 0$

$\dfrac{1 }{ \cos \theta} = -2$

$\cos \theta = - \frac 1 2$

The rule to remember is $\cos x = \cos a$ has solutions

$x = \pm a + 2 \pi k \quad$ integer $k$

Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is $120^\circ$ .

$\cos \theta = - \frac 1 2$

$\cos \theta = \cos \frac {2\pi} 3$

$\theta = \pm \frac {2\pi} 3 + 2 \pi k \quad$ integer $k$

In the range we want, that's $k=0$ with the plus sign and $k=1$ with the minus, so

$\theta = \frac {2\pi} 3$ or $-\frac {2\pi} 3 + 2 \pi = \frac{4 \pi} 3$

$\theta = \frac {2\pi} 3$ or $\frac{4 \pi} 3$

6 0

3 years ago

Sorry, here's another one on inequalities

Yuki888 [10]

Answer:

y > 4x + 1

Step-by-step explanation:

Equation of the dotted line:

Slope = (-3-1)/(0-1) = 4

Y intercept is +1

y = 4x + 1

Shaded region:

y > 4x + 1

6 0

3 years ago

According to the American Lung Association, 7% of the population has lung disease. Of those having lung disease, 90% are smokers

postnew [5]

Answer:

Probability that a smoker has lung disease = 0.2132

Step-by-step explanation:

Let L = event that % of population having lung disease, P(L) = 0.07

So,% of population not having lung disease, P(L') = 1 - P(L) = 1 - 0.07 = 0.93

S = event that person is smoker

% of population that are smokers given they are having lung disease, P(S/L) = 0.90

% of population that are smokers given they are not having lung disease, P(S/L') = 0.25

We know that, conditional probability formula is given by;

P(S/L) = $\frac{P(S\bigcap L)}{P(L)}$

$P(S\bigcap L)$ = P(S/L) * P(L)

= 0.90 * 0.07 = 0.063

So, $P(S\bigcap L)$ = 0.063 .

Now, probability that a smoker has lung disease is given by = P(L/S)

P(L/S) = $\frac{P(S\bigcap L)}{P(S)}$

P(S) = P(S/L) * P(L) + P(S/L') * P(L')

= 0.90 * 0.07 + 0.25 * 0.93 = 0.2955

Therefore, P(L/S) = $\frac{0.063}{0.2955}$ = 0.2132

Hence, probability that a smoker has lung disease is 0.2132 .

7 0

3 years ago

Find the length of BC. <br> A.) 14<br> B.) 9<br> C.) 2<br> D.) 3

Vera_Pavlovna [14]

Answer:

A) 14

Step-by-step explanation:

BC is congruent to DC in saying this you can plug the equations to each other and solve for y and then put its back into the equation for BC to get the length.

3y+5=5y-1

subtract 3y from both sides --> 5=2y-1

add 1 to both sides --> 6=2y

now get y alone, divide by 2 by both side --> y=3

plug y in back to 5y-1 --> 5x3-1

15-1

BC = 14

7 0

3 years ago

What is f(5) the table that represents a function

Dominik [7]

Answer: The table represents a function. What is f(5)?

–8

–1

1

8

Step-by-step explanation:

3 0

3 years ago