Lines a and b are perpendicular. If the slope of line a is 3, what is the slope of
line b?

Hi there!

To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).

First Question

What we have to do is to isolate cos first.

[tex] \displaystyle \large{ cos \theta = - \frac{1}{2} }[/tex]

Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.

Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.

Find Q2

[tex] \displaystyle \large{ \pi - \frac{ \pi}{3} = \frac{3 \pi}{3} - \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{2 \pi}{3} }[/tex]

Find Q3

[tex] \displaystyle \large{ \pi + \frac{ \pi}{3} = \frac{3 \pi}{3} + \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{4 \pi}{3} }[/tex]

Both values are apart of the interval. Hence,

[tex] \displaystyle \large \boxed{ \theta = \frac{2 \pi}{3} , \frac{4 \pi}{3} }[/tex]

Second Question

Isolate sin(4 theta).

[tex] \displaystyle \large{sin 4 \theta = - \frac{1}{ \sqrt{2} } }[/tex]

Rationalize the denominator.

[tex] \displaystyle \large{sin4 \theta = - \frac{ \sqrt{2} }{2} }[/tex]

The problem here is 4 beside theta. What we are going to do is to expand the interval.

[tex] \displaystyle \large{0 \leqslant \theta < 2 \pi}[/tex]

Multiply whole by 4.

[tex] \displaystyle \large{0 \times 4 \leqslant \theta \times 4 < 2 \pi \times 4} \\ \displaystyle \large \boxed{0 \leqslant 4 \theta < 8 \pi}[/tex]

Then find the reference angle.

We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.

sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)

Find Q3

[tex] \displaystyle \large{ \pi + \frac{ \pi}{4} = \frac{ 4 \pi}{4} + \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{5 \pi}{4} }[/tex]

Find Q4

[tex] \displaystyle \large{2 \pi - \frac{ \pi}{4} = \frac{8 \pi}{4} - \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{7 \pi}{4} }[/tex]

Both values are in [0,2π). However, we exceed our interval to < 8π.

We will be using these following:-

[tex] \displaystyle \large{ \theta + 2 \pi k = \theta \: \: \: \: \: \sf{(k \: \: is \: \: integer)}}[/tex]

Hence:-

For Q3

[tex] \displaystyle \large{ \frac{5 \pi}{4} + 2 \pi = \frac{13 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 4\pi = \frac{21 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 6\pi = \frac{29 \pi}{4} }[/tex]

We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.

For Q4

[tex] \displaystyle \large{ \frac{ 7 \pi}{4} + 2 \pi = \frac{15 \pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 4 \pi = \frac{23\pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 6 \pi = \frac{31 \pi}{4} }[/tex]

Therefore:-

[tex] \displaystyle \large{4 \theta = \frac{5 \pi}{4} , \frac{7 \pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} , \frac{29\pi}{4}, \frac{15 \pi}{4} , \frac{23\pi}{4} , \frac{31\pi}{4} }[/tex]

Then we divide all these values by 4.

[tex] \displaystyle \large \boxed{\theta = \frac{5 \pi}{16} , \frac{7 \pi}{16} , \frac{13\pi}{16} , \frac{21\pi}{16} , \frac{29\pi}{16}, \frac{15 \pi}{16} , \frac{23\pi}{16} , \frac{31\pi}{16} }[/tex]

Let me know if you have any questions!

Answer:

The function is always increasing

Step-by-step explanation:

To be increasing, the y value needs to be getting bigger as x gets bigger

This is true for all values of x

The function is increasing for all values of x

Answer:

Shade 23 boxes

Step-by-step explanation:

This is the first two rows fully (all 10 boxes) and then three more from the third row.

xxxxxxxxxx

xxxxxxxxxx

xxx . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

Answer:

2) t distribution with 58 degrees of freedom.

Step-by-step explanation:

Population standard deviations not known:

This means that the t-distribution is used to solve this question.

The sample sizes are n1 = 25 and n2 = 35.

The number of degrees of freedom is the sum of the sample sizes subtracted by the number of samples, in this case 2. So

25 + 35 - 2 = 58 df.

Thus the correct answer is given by option 2.

To solve this question, the normal distribution and the central limit theorem are used.

Doing this, there is an 0.0129 = 1.29% probability that the mean installation time for 31 computers is less than 43 minutes.

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First, these concepts are presented, then we identify mean, standard deviation and sample size, and then, we find the desired probability.

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

------------------------------------

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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Mean of 45, standard deviation of 5:

This means that [tex]\mu = 45, \sigma = 5[/tex]

Sample size of 31:

This means that [tex]n = 31, s = \frac{5}{\sqrt{31}}[/tex]

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Probability the sample mean is less than 43:

This is the p-value of Z when X = 43, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{43 - 45}{\frac{5}{\sqrt{31}}}[/tex]

[tex]Z = -2.23[/tex]

[tex]Z = -2.23[/tex] has a p-value of 0.0129.

Thus, 0.0129 = 1.29% probability that the mean installation time for 31 computers is less than 43 minutes.

A similar question is given at: https://brainly.com/question/15020228

Answer:

OD) 16 cubic centimeters

Answer:

total number of boys in skool is 216

And

ratio of girls to boys is a 3:4

Step-by-step explanation:

let total no. of boys be X

ACCORDING TO QUESTION

ratio of boys to girls = 4:3

total number of girls = 162

now

4/3=X/162

or, 4×162= 3x

or, 4×162/3= X

hence

X = 216

therefore total number of boys is 216

and

ratio of girls to boys is =162/216

=3/4

=3:4

Answer:

40 per minute.

Step-by-step explanation:

360/9=40

Answer:

Hello

Step-by-step explanation:

[tex]Formula: \\\\\boxed{\Large a^3\pm b^3=(a \pm b)(a^2 \mp ab+b^2)}\\\\8x^3+1=(2x)^3+1^3=(2x+1)(4x^2-2x+1)\\\\8x^3-1=(2x)^3-1^3=(2x-1)(4x^2+2x+1)\\[/tex]

The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The expression is given below.

8x³ + 1 and 8x³ - 1³

(2x)³ + 1³ and (2x)³ - 1³

We know that the formula is given as,

a³ + b³ = (a + b) (a² – ab + b²)

a³ – b³ = (a – b) (a² + ab + b²)

Then the expression is written as,

(2x)³ + 1³ = (2x + 1) [(2x)² – 2x + 1²]

(2x)³ + 1³ = (2x + 1) (4x² – 2x + 1)

(2x)³ – 1³ = (2x – 1) [(2x)² + 2x + 1²]

(2x)³ – 1³ = (2x – 1) (4x² + 2x + 1)

The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.

More about the polynomial link is given below.

https://brainly.com/question/17822016

#SPJ2

Answer:

A. 0; 1

Step-by-step explanation:

Required

Mean and standard deviation of a standardized normal distribution

A standardized normal distribution is represented as:

[tex](\mu,\sigma) = (0,1)[/tex]

This implies that:

[tex]\mu = 0[/tex] -- mean

[tex]\sigma = 1[/tex] --- standard deviation

Hence, (a) is true

Step-by-step explanation:

Let the husband's income be x

Wife's income be x + 9000

X + X + 9000 = 81000

2X + 9000 – 9000 = 81000 – 9000

2X= 72000

X = 36000

Husband, 36000,

Wife, 9000+36000, 45000

The 2 triangles are congruent

Answer:

Does the answer help you?

Answer:

1/52

Step-by-step explanation:

Answer:

Option C

We need to make the negative exponent positive.

The rule is: [tex]A^{-B} =\frac{1}{A^{B} }[/tex]

Here, A=x, B= 12

[tex]so,[/tex] [tex]x^{-12}[/tex]

[tex]=\frac{1}{x^{12} }[/tex]

OAmalOHopeO

Answer:

60

Step-by-step explanation:

Use similar triangles or the ratios from the right triangle altitude theorem.

x/36 = (64 + 36)/x

x² = 3600

x = 60

Answer:

184.8

Step-by-step explanation:

y =kx

k=y/x

k=42/5=8.4

y=8.4*22

Answer:

I think its C:37

Step-by-step explanation:

And if im wrong sorry :/

Hi there!  

»»————-　★　————-««

I believe your answer is:  

330

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

We are rounding the number 326 to the nearest tens.

The '2' is in the tens place, and the '6' is to the right of the digit.

Since the '6' is greater than or equal to 5, then we would round up.

326 ≈ 330

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

120

Step-by-step explanation:

There are 10 possible toppings to choose from, you choose 7.

Using combinatorics, it's 10!/(7! 3!), or 120.

The formula is (total amount to choose from )! divided by (amount you choose)!(amount you don't choose)!

Or search up combination formula

A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

The formula for combination.

= [tex]^nC_r[/tex]

= n! / r! (n -r)!

The number of possible 7-toppings for the pizza is 120.

A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

The total number of toppings = 10.

n = 10

The number of required toppings = 7.

r = 7

The formula for combination.

= [tex]^nC_r[/tex]

= n! / r! (n -r)!

The possible number of possible 7-toppings pizzas.

= [tex]^{10}C_7[/tex]

= (10 x 9 x 8) / (3 x 2)

= 120

Thus,

n = 10 and r = 7

[tex]^{10}C_7[/tex] = 120

The number of possible 7-toppings for the pizza is 120.

Learn more about combination here:

https://brainly.com/question/14355408

#SPJ2

Answer:

es1433

Step-by-step explanation:

Answer:

x=  $6,284.15

Step-by-step explanation:

7300 = x(1 + .025/12)^72

x = [tex]\frac{7300}{(1 + \frac{.025}{12} )^{72} }[/tex]

x=  $6,284.15  

Answer:

-3

Step-by-step explanation:

Slope is equal to (-5-7)/(2-(-2)=-12/4=-3

Answer:

8 months 11 days 1 year

Answer:

Hello,

Step-by-step explanation:

[tex]\displaystyleV=2*\pi*\int\limits^4_2 {(\dfrac{1}{x}-\dfrac{1}{x^3} )*x } \, dx \\=2*\pi*\int\limits^4_2 {(1-\dfrac{1}{x^2} ) } \, dx \\=2*\pi* [x+\dfrac{1}{x}]^4_2\\\\\boxed{V=\dfrac{7\pi}{2}}\\[/tex]

Answer:

Step-by-step explanation:

-24

-55

84

20

-60

9514 1404 393

Answer:

  x = π

Step-by-step explanation:

You want f(g(x)) = g(f(x)):

  3 +cos(2x) = 2(3 +cos(x))

  cos(2x) -2cos(x) = 3 . . . . . . . rearrange

  2cos(x)²-1 -2cos(x) = 3 . . . . . use an identity for cos(2x)

  2(c² -c -2) = 0 . . . . . . . . . . . . substitute c = cos(x)

  (c -2)(c +1) = 0 . . . . . . . . . . . factor

  c = 2 (not possible)

  c = -1 = cos(x) . . . . . true for x = π

The value of x that makes f(g(x)) = g(f(x)) is x = π.

_____

Additional comment

The substitution c=cos(x) just makes the equation easier to write and the form of it easier to see. There is really no other reason for making any sort of substitution. In the end, the equation is quadratic in cos(x), so is solved by any of the usual methods of solving quadratics.

(2^-1)^2/2×2^0

2^(-1×2)/2^1

2^-2/2^1

2^(-2-1)

2^(-3)

(1/2)^3

Properties used (m^n)^a = m^na

(m)^-n = (1/m)^n

m^0 = 1

m^n/m^a = m^(n-a)

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Answer:

a

Step-by-step explanation:

3x tables

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Answer:

a

Step-by-step explanation:

Has pattern 3x tables. Answer is 15 A.