2sin²(x)-5cos(x)+1=0

Answers

Answer 1

Answer: Remember the basic trig identity

$\sin^2 x + \cos^2 x = 1$

We can move the cosine term to the right side to get

$\sin^2 x = 1 - \cos^2 x$

We can then replace $\sin^2 x$ in the original equation and basically factor the resulting equation like a quadratic:

$2(1 - \cos^2 x) - 5 \cos x + 1 = 0$
$(2 - 2 \cos^2 x) - 5 \cos x + 1 = 0$
${-2} \cos^2 x - 5 \cos x + 3 = 0$
$2 \cos^2 x + 5 \cos x - 3 = 0$
$(2 \cos x - 1)(\cos x + 3) = 0$

Then, we can see that $\cos x$ either equals $(1)/(2)$ or $-3$ . But since the range of cosine is only from $[-1, 1]$ , cosine can't equal $-3$ at all! So, you just have to solve for x when $\cos x = (1)/(2)$ , which is when

$x = \{ (\pi)/(3), (5\pi)/(3) \} + 2 \pi k | k \in \mathbb{Z}$
(The last part of the solution says that k can be any integer.)

If you only want solutions in the range $[0, 2\pi)$ , then your answer is just

$x = (\pi)/(3), (5\pi)/(3)$

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The Nguyen family spent $48 on entrance fees to the county fair. Each ticket for an adult cost $12. Each ticket for a child cost $5. Each senior citizen paid $2. There were six people in the group. There were 2 fewer tickets purchased for senior citizens than adult tickets. How many adult tickets were purchased?

Answers

i wanna say 3 but not sure

From the set {20, 38, 47}, use substitution to determine which value of x makes the inequality true. x - 9 > 29
a. 47

b.none of these

c.38

d.20

Answers

one way is to solve (it's easier)

x-9>29
add 9
x+9-9>29+9
x+0>38
x>38
just pick the numbers bigger than 38 as answer

47 is only number (38>38 is false)

answer is A

The minimum monthly payment for Alicia's credit card is 2% of her balance or $10, whichever is higher. If Alicia's balance at the end of her last billing cycle was $470, what is her minimum monthly payment?

Answers

Answer:

Alicia's minimum monthly payment is $10.

Step-by-step explanation:

Given is :

Alicia's balance at the end of her last billing cycle was $470. So, its 2 % becomes:

$(2)/(100) *470$ = $9.40

As it is stated that the minimum monthly payment for Alicia's credit card is 2% of her balance or $10, whichever is higher.

Therefore, $10 is higher amount than $9.40

So, the correct answer is: Alicia's minimum monthly payment is $10.

The scatter plot shows a hiker's elevation above sea level during a hike from the base to the top of a mountain. The equation of a trend line for the hiker's elevation is y equals=9.069.06xplus+651651, where x represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of the trend line to estimate the hiker's elevation after 175 minutes.

Answers

Answer:

2236.5

Step-by-step explanation:

The regression equation for predicting hiker's elevation is

y=9.06x+651.

Here x is the number of minutes.

We wish to estimate hiker's elevation after 175 minutes. For this purpose we put x=175 in the predicted regression equation.

y=9.06(175)+651

y=1585.5+651

y=2236.5

Thus, the hiker's elevation after 175 minutes is 2236.5 feet.

the line defined by the equation y=-(4/7)x+5 is prependicular to the line defined by which equation ? (1) y=(4/7)x+3 (2) y=-(4/7)x+3 (3) y=-(7/4)x+3 (4) (7/4)x+3

Answers

y=mx+b
m=slope

perpendicular lines have slopes that multiply to -1

the line we have is y=-4/7x+5
therefor
if the slope we are looking for is m
(-4/7)m=-1
times -7/4 both sides
m=7/4
we are looking for
y=7/4x+b

last one is answer

A number increased by 5 and then divided by 7 is 12.

Answers

Answer:

Step-by-step explanation:

hope it helped !! :))

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