Assume cot (0) = 19. Compute the other five trig functions for the angle 8. sin (0) = cos(0) = csc (0) = sec (0) = tan (0) =

Answers

Answer 1

The required values of the trigonometric ratios are `sin(θ) = 1 / √362`, `cos(θ) = 19 / √362`, `tan(θ) = 1 / 19`, `cosec(θ) = √362` and `sec(θ) = √362 / 19`.

Given that `cot(θ) = 19`. We need to find the other trigonometric ratios i.e., `sin(θ)`, `cos(θ)`, `tan(θ)`, `sec(θ)` and `cosec(θ)`.We know that `cot(θ) = cos(θ) / sin(θ)`On substituting the value of `cot(θ)` in the above equation, we get

;`19 = cos(θ) / sin(θ)`=> `cos(θ) = 19 sin(θ)`

We know that

`sin^2(θ) + cos^2(θ) = 1`

Substituting the value of `cos(θ)` in the above equation, we get

;`sin^2(θ) + (19 sin(θ))^2 = 1`=> `sin^2(θ) + 361 sin^2(θ) = 1`=> `362 sin^2(θ) = 1`=> `sin(θ) = ±1 / √362`

Here, we consider `sin(θ)` to be positive as `θ` lies in the first quadrant.Since `sin(θ)` is positive,

`cos(θ) = 19 sin(θ)`

is also positive.Using the values of

`sin(θ)` and `cos(θ)`,

we can find the other trigonometric ratios.Using the formula

,`tan(θ) = sin(θ) / cos(θ)`=> `tan(θ) = (1 / √362) / 19(1 / √362)`=> `tan(θ) = 1 / 19`

Using the formula,

`sec(θ) = 1 / cos(θ)`=> `sec(θ) = 1 / (19 / √362)`=> `sec(θ) = √362 / 19`

Using the formula

,`cosec(θ) = 1 / sin(θ)`=> `cosec(θ) = 1 / (1 / √362)`=> `cosec(θ) = √362`

Therefore,

`sin(θ) = 1 / √362``cos(θ) = 19 / √362``tan(θ) = 1 / 19``cosec(θ) = √362``sec(θ) = √362 / 19`

Hence, the required values of the trigonometric ratios are

`sin(θ) = 1 / √362`, `cos(θ) = 19 / √362`, `tan(θ) = 1 / 19`, `cosec(θ) = √362` and `sec(θ) = √362 / 19`.

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Related Questions

Can you help me solve this!

Answers

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

What is the ratio for 2 red paper clips to 6 blue paper clips? Write it as a fraction.

Answers

Answer:

2 over 6 as a fraction simplifies as 1 over three.

Step-by-step explanation:

If you are writing as a fraction, you put 2 over 6 and simplify. Your answer is 1 over 3

Answer:

2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6 2/6

Step-by-step explanation:

its just 2/6

Someone pls help. URGENTLY NEEDED!!!!

Answers

The value of x= 4 and y= 1.

We can use the following steps to find x and y:

1. Multiply the matrices on the equation's left and right sides. This results in the equation shown below:

[4 3 L1 01] * [3 −1 4 -5 -1 7 -31] = [x + y] * [21 L6 -5 5]

2. Increase the matrix product. This results in the equation shown below:

[12 9 1 0] = [21x + 6y L 6x - 5y]

3. Put the matching terms on both sides of the equation into an equation. This results in the equations that follow:

12 = 21x + 6y 9 = 6x - 5y 1 = y

4. Resolve the equations in the system. The following steps can be used to accomplish this:

* Find y in the first equation. This results in y = 1. * Replace this

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Using the function g(x) = 175 + 85x, find
g(7).

Answers

Answer:

Step-by-step explanation:

The value of the function g(7) will be 770.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the function is g(x) = 175 + 85x. The value of the function at x =7 will be calculated as,

g(x) = 175 + 85x

g(7) = 175 + ( 85 x 7 )

g(7) = 175 + 595

g(7) = 770

Hence, the value of the function will be 770.

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Two congruent ellipses are perpendicular to each other. Squares fill the gaps between the two ellipses as shown. Show that the side of the square equals half the minor axis of the ellipse.

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The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

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D. 550 Which of the following is rational and which is irrational? a. 5.4928413....... b. 9.3722222.....

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Answer:

Step-by-step explanation:

Answer:

B is rational, A is irrational

Step-by-step explanation:

B is rational because its a repeating decimal. A is irrational becuase it cannot be expressed as the ratio of two integers.

Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? responses.

Answers

The top 25% of cars have a typical gas mileage of at least 33.5 miles per gallon.

To calculate this, you need to use the interquartile range (IQR) formula.

The IQR is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3).

IQR = Q3 - Q1

In this case, the 25th percentile (Q1) is 28.4, and the 75th percentile (Q3) is 37.9. So:

IQR = 37.9 - 28.4 = 9.5

The top 25% of cars have a gas mileage of 33.5 miles per gallon, which is Q3 + 1.5*IQR.

33.5 = Q3 + 1.5*IQR

33.5 = 37.9 + 1.5*9.5

33.5 = 37.9 + 14.25

33.5 = 52.15

Therefore, the top 25 percent of cars have a typical gas mileage of at least 33.5 miles per gallon.

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The graph shows the relationship between miles and kilometres.

a)
Convert 20 miles
to km.
b)
Convert 64 km
to miles.

Answers

By cross multiplication, we have found the following results:

a) 20 miles are equal to 32.180 kilometers.

b) 64 kilometers are equal to 39.776 miles.

How to convert a distance value into another distance unit

In this problem we must convert a given value in a unit into its equivalent quantity in another unit of same kind. We must convert miles to kilometers and viceversa by using conversion rates and cross multiplication.

First, we must convert a distance of 20 miles to kilometers by cross multiplication:

x = 20 mi × (1.609 km / 1 mi)

x = 32.180 km

Second, we must convert a distance of 64 kilometers to miles by cross multiplication:

x = 64 km × (1 mi / 1.609 km)

x = 39.776 mi

Remark

The graph is missing, but this question can resolved by using conversion rates, that is, a mile equal 1.609 kilometers.

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Answer:

here is the answer⬇️

The graph shows the relationship between miles and kilometres.a)Convert 20 milesto km.b)Convert 64 kmto

what is the product of (9+x)(9-x)

Answers

Answer:

81 - x^2

Step-by-step explanation:

this is a "special product," namely, the product of the sum and the difference of quantities 9 and x.

The product is the difference of two squares:

(9 + x)(9 - x) = 81 - x^2

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Answers

Answer:

what is this? ahdhdjxkdjjshsysusiiaiajsjjdyxc

in linear regression, what are we trying to forecast? a) Beta parameter
b) Dependent variable
c) Independent variable
d) Y-intercept of the linee

Answers

In linear regression, we are trying to forecast the dependent variable based on the independent variable.

Option C is the correct answer.

We have,

In linear regression, the dependent variable is the outcome variable or the response variable that we want to predict or explain, while the independent variable is the predictor variable or explanatory variable that helps us in predicting the dependent variable.

The beta parameter and y-intercept are coefficients of the linear regression equation that help in determining the relationship between the dependent and independent variables.

Thus,

In linear regression, we are trying to forecast the dependent variable based on the independent variable.

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Which equation can be used to solve for b?

5 cm
tan(30°) =5/b
tan(30°)=b/5
tan(30°)=10/b
tan(30°) =b/10

Answers

A
Tan 30.. means you have to look at opposite over adjacent. So you look at 30degrees and 5 is opposite and b is adjacent

what is the standard form for y+2=4/5 (x+4)

Answers

The equation in its standard form is 4x - 5y = -6

How to determine the standard form of the equation?

From the question, we have the equation to be

y+2=4/5 (x+4)

Start by multiplying both sides of the equation by 5

So, we have

5(y + 2) =4/5 (x+4) * 5

Evaluate the products

This gives

5y + 10 =4 (x+4)

Next, we open the brackets

So, we have the following representation

5y + 10 =4x + 16

Collect the like terms

4x - 5y = 10 - 16

Evaluate the like terms

This gives

4x - 5y = -6

Hence, the standard form of the equation is 4x - 5y = -6

Answers

She has to find if the tree is tall enough to fall into her house.

She is using a 12-inches ruler to find proportions. We can draw this as:

The triangle that can be drawn using as vertices the base of the tree, the top of the tree and the house is similar to the triangle formed by the rule and the the distance of 1 ft.

We can see that as the height of the ruler that indicates the top of the tree is smaller than the foot, we know that the height H of the tree is smaller than the distance D from the house to the tree, in the same proportion.

We can calculate the height of the tree using the following proportion:

$\begin{gathered} \frac{H}{D}=\frac{9\text{ in}}{1\text{ ft}} \\ \frac{H}{50\text{ ft}}=\frac{9\text{ in}}{12\text{ in}}=\frac{3}{4} \\ H=50\text{ ft}\cdot\frac{3}{4} \\ H=37.5\text{ ft} \end{gathered}$

Answer: The house is far enough, as the height of the tree is less than 50 ft (it is 37.5 ft)

Lorah is considering cutting down a tall tree in her front yard, but she is worried it might be tall

Go step by step to reduce the radical.

Answers

Answer:

$\sqrt{16}\sqrt{11}$

Step-by-step explanation:

$\sqrt{176}\implies \sqrt{16\cdot 11}\implies \sqrt{4^2\cdot 11}\implies 4\sqrt{11}$

What is the value of 2x(3+x/2) when x=−2?

Answers

Answer:

-8

Step-by-step explanation:

$2x(3+\frac{x}{2})$ $2*(-2)(3+\frac{(-2)}{2})$ $-4(3+(-1))$ $-4(2)$ $-8$

Find the measure of the missing angle

Answers

Answer:

Step-by-step explanation:

82 + 58 + ? = 180

140 + ? = 180

? = 40

Have an amazing day!

Please mark brainliest!

5+5x2=? heh i "ToTaLlY" dont know this

Answers

Answer:

Step-by-step explanation:

What other information do you need to prove GHK ≅ KLG by SAS?

A. ∠KHG ≅ ∠GLK
B. ∠HGK ≅ ∠LKG
C. ∠GHK ≅ ∠KLG
D. ∠HKG ≅ ∠LGK

Answers

Step-by-step explanation:

We know that HK and GL are congruent by Given. We can also see that GK is congruent to itself on both sides because of reflexive property. A works, because it corresponds and might fit into SAS. B doesn't, because the two angles don't correspond. C is the same as A, so it will work as well. D's angles correspond, but don't fit SAS.

This means that angle KHG and angle GLK will be congruent, as well as angles GHK and KLG (They're the same angles though).

To prove that $\triangle GHK \cong \triangle KLG$ by the SAS Congruence Theorem, the additional information we need is: D. ∠HKG ≅ ∠LGK

Recall:

If two sides and an included angle in one triangle is congruent to two sides and an included angle in another triangle, both triangles are proven by the SAS Congruence Theorem to be congruent to each other.

Given the image showing $\triangle GHK $ and $ \triangle KLG$, the following are known:

$HK \cong GL\\\\GK \cong GK$

This implies that two corresponding sides of both triangles are congruent to each other.

However, for us to prove that both triangles to be congruent, we need an additional information that tells us an included angle in one triangle is congruent to a corresponding included angle in the other.

Therefore, to prove that $\triangle GHK \cong \triangle KLG$ by the SAS Congruence Theorem, the additional information we need is: D. ∠HKG ≅ ∠LGK

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If a population has 500 individuals in it in 2010, and the per capita birth rate is 0.3 and the per capita death rate is 0.2, is the population growing or shrinking?

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The population is growing as the births are more than deaths in an year.

What is Population Growth?

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

Total population = 500Per capita birth rate = 0.3Per capita death rate = 0.2

To find: Is population growing or shrinking?

Finding:

Number of new-borns in an year = total population (per capita birth rate) = 500(0.3) = 150Number of deaths in an year = total population (per capita death rate) = 500(0.2) = 100Difference in the number of births and deaths = 150 - 100 = 50

Hence the population is growing as the births are more than deaths in an year.

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In a recent election, 63% of all registered voters participated in voting. In a survey of 275 retired voters, 162 participated in voting. Which is higher, the population proportion who participated or the sample proportion from this survey?

Answers

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) $\times$ 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Let f(x)=18/1+3^e-0.1x What is the point of maximum growth rate for the logistic function f(x)? Show all work. Round your answer to the nearest hundredth

Answers

Answer:

(0, 4.5)

Step-by-step explanation:

*The equation can be put into Desmos, to find the point, but the work to prove it is here*

f(x)=c/1+Ae^-Bx

Y=C

C=18 A=3 -B=-0.1

*Replace x with 0 in the equation, so you know 0 is the x value, and it leads you to the y value*

f(0)=18/1+3e^-o.1(0)

= 18/1+3e^0

=18/1+3(1)

=18/1+3

=18/4

=4.5

x=0 y=4.5

Maximum growth rate = (x,y) --> (0, 4.5)

Hope this helps:))!!

Let f(x)=18/1+3^e-0.1x What is the point of maximum growth rate for the logistic function f(x)? Show

if a = 6, evaluate the following expression: 36/3a

Answers

Answer:

Step-by-step explanation:

1) substitute a=6 into 36/3a:

36/3×6

2) calculate: 36/3×6 ->2

What is (gof)(x) if f(x) = 3x - 1 and g(x) = 4x² + 9?

Answers

Step-by-step explanation:

(gof)(x) is basically g(f(x))

= 4 × (3x - 1)² + 9

= 4 × (9x² - 6x + 1) + 9

= 36x² - 24x + 4 + 9

= 36x² - 24x + 13

a system consists of two components. the probability that the second component functions in a satisfactory manner during its design life is 0.7, the probability that at least one of the two components does so is 0.92, and the probability that both components do so is 0.65. given that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does also? (round your answer to three decimal places.)

Answers

Therefore, the probability that the second component functions in a satisfactory manner during its design life, given that the first component functions in a satisfactory manner throughout its design life, is 0.307.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is used in various fields, including mathematics, statistics, economics, physics, and engineering, to model and analyze uncertain situations.

Here,

Let A be the event that the first component functions in a satisfactory manner throughout its design life, and B be the event that the second component functions in a satisfactory manner during its design life. We want to find P(B|A).

By the law of total probability, we have:

P(B) = P(B|A)P(A) + P(B|A')P(A')

where A' is the event that the first component does not function in a satisfactory manner throughout its design life. Since the second component is independent of the first, we have:

P(B|A') = P(B)

So we can simplify the equation above to:

P(B) = P(B|A)P(A) + P(B)(1 - P(A))

Solving for P(B|A), we get:

P(B|A) = (P(B) - P(B)(1 - P(A))) / P(A)

= P(B) / P(A')

We have:

P(A) = 0.7 (probability that the first component functions satisfactorily)

P(B) = 0.92 (probability that at least one component functions satisfactorily)

P(A') = 1 - P(A) = 0.3 (probability that the first component does not function satisfactorily)

So we get:

P(B|A) = P(B) / P(A') = 0.92 / 0.3 = 3.067 (rounded to three decimal places)

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Jane matthew and sara each have 3 cards.The numbers on each child's card add upto 100. What numbers could they have, if each numbers is in tens?Each child has a different set of cards

Answers

Answer:

each child has a diffrent set

Step-by-step explanation:

(50 POINTS!!!!!) I NEED THE CORRECT ANSWER... FAST!

Answers

Answer:

don't know sorry forgive me

Choose the correct answer to 1,889 ÷ 36.
52 R17
51 R53
52 R15
42 R17

Answers

52 R17
It is the right answer

Sam, Larry, and Howard have contracted to paint a large room in a house. After calculating all the material costs, which are to be paid by the homeowner, they decide that $270 would be a fair price for the 16 hours it will take to prepare, paint, and clean up. Each of the men decides that $15.00 an hour is a fair wage for the job. If three-quarters of the work will be done by Larry, how much will Larry be paid for his work on the job?

Answers

Answer:

180 dollars

Step-by-step explanation:

270 for 16 hours = 16.875 dollars for each hour

15.00 an hour will be paid to larry

larry is doing 3/4 of those 16 hours

12 hours

15 x 12

larry gets 180 dollars for 12 hours of work

hope this helps x

The sum of two consecutive numbers is 25. What is the largest of the consecutive numbers? Type a numerical answer in the space provided.

Answers

In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

How can the the largest of the consecutive numbers be calculated?

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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