tan α=2.4, Find: sin α and cot α

Answers

Answer 1

Answer:

cot α = 1/tan α = 1/2.4 = 0.42

Step-by-step explanation:

cot α=0.42

sin α = 0.92

we know that  cot α = 1/tan α

thus,

cot α = 1/tan α = 1/2.4 = 0.42

we know that

sin(x)=tan(x)1+tan2(x)√

[tex]\ sin(\alpha )=tan(\alpha )/\sqrt{ 1+tan^2(\alpha )} \\sin(\alpha )= 2.4/\sqrt{1+2.4^2} = 2.4/\sqrt{1+5.76}\\sin(\alpha )= 2.4/\sqrt{6.76} = 2.4/2.6 = 12/13 = 0.92[/tex]

sin α = 0.92


Related Questions

NEED HELP..... Select the polynomial that is a perfect square trinomial. 36x^2 − 4x + 16 16x^2 − 8x + 36 25x^2 + 9x + 4 4x^2 + 20x + 25

Answers

Answer: Choice D.  4x^2 + 20x + 25

===============================================

Explanation:

Perfect square trinomials are in the form (a+b)^2 = a^2+2ab+b^2

So the first and last terms must be perfect squares. The middle term is twice that of the square roots of each first and last term.

Choice D fits the description because 4x^2 = (2x)^2 is the first term, so a = 2x and 25 = 5^2 is the last term meaning b = 5. Note how 2ab = 2*2x*5 = 20x is the middle term.

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

(a+b)^2 = a^2+2ab+b^2

(2x+5)^2 = (2x)^2+2*2x*5+5^2

(2x+5)^2 = 4x^2 + 20x + 25

Answer:

(2x+5)² or (2x+5)(2x+5)

Step-by-step explanation:

4x²+ 20x + 25

(2x       ) (2x      )     first step 2x*2x=4x²

(2x  +  5   )(2x  +   5  )  the constant sign is plus so it can be ( minus × minus=plus OR plus×plus=plus) look at the middle value it is positive so the two signs are positive or plus sign.

(2x+5)²

Which transformation can be used to map one triangle onto the other select two options

Answers

Answer:

Reflection only and rotation then translation.

Step-by-step explanation:

im not sure

Answer:

look at the picture below

Step-by-step explanation:

Solve 2(x - 5) = 48 - 4(x + 1)​

Answers

2(x - 5) = 48 - 4(x + 1)
2x - 10 = 48 - 4x - 4
6x = 54
x = 9

Answer:

x = 9

Step-by-step explanation:

first remove the brackets

2x - 5 = 48 - 4x + 1

then take numbers to the opposite sides

2x + 4x = 48 + 5 + 1

I have used addition because since your taking-5 to the other side it becomes+5 and -4 becomes +4

now solve

2x + 4x= 6x

48+5+1= 54

6x = 54

now solve for x

divide both sides by 6x

x = 9


BRAINLIEST!!! Plz help ASAP
M(5, 7) is the midpoint of side RS.The coordinates of S are (6, 9). What are the coordinates of R?Please answer with full explanation and no non sense answers will reports. Will give brainiest to those who answered correctly with full explanation. Thank you.

Answers

Answer: R = (4, 5)

Step-by-step explanation: Midpoint is simply the center of a line. So, the equation for it is ((x1+x2)/2, (y1+y2)/2). Hence for this,

x coordinate- (6+x)/2=5

                        x=4

y coordinates- (9+y)/2=7

                         y=5

And therefore R is (4, 5)

Complete the recursive formula of the geometric sequence 7, -14, 28, -56, ....

Answers

Answer:

[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex]

Step-by-step explanation:

A geometric recursive formula has the form

[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]

where r is the common ratio

Here r = - 14 ÷ 7 = - 2, thus

[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex] with a₁ = 7

Which function has a range of y < 3? y=3(2)x y = 3(3)x y = -(2)x+ 3 y = (2)x-3

Answers

Answer:

Third option is the correct answer

[tex]y = -(2)x+ 3[/tex]

Step-by-step explanation:

Given functions are:

[tex]y=3(2)x\\ y = 3(3)x\\ y = -(2)x+ 3\\ y = (2)x-3[/tex]

To find:

The function which has a range [tex]y <3[/tex] ?

Solution:

First of all, let us learn about the terms Domain and Range for a function:

[tex]y = f(x)[/tex]

Domain is the value of [tex]x[/tex] which is given as input to the function and gives a valid value of output as [tex]y[/tex] (i.e. function is defined).

Range of a function is the value [tex]y[/tex] that comes as output when given a valid value of [tex]x[/tex] as input.

Now, let us consider the given options above.

Third option is the correct answer.

[tex]y = -(2)x+ 3[/tex]

As we can see, [tex](2)x[/tex] is subtracted from 3 so [tex]y[/tex] will have a value which is lesser than 3.

i.e. range will be [tex]y <3[/tex].

No other function has such condition present in it.

[tex]y = -(2)x+ 3[/tex] is the correct answer.

Hi how do I solve this simultaneous equation

Answers

Answer:

M (-3, -5/2)

N (3, -1)

Step-by-step explanation:

Solve the first equation for x.

4y = x − 7

x = 4y + 7

Substitute into the second equation.

x² + xy = 4 + 2y²

(4y + 7)² + (4y + 7)y = 4 + 2y²

Simplify.

16y² + 56y + 49 + 4y² + 7y = 4 + 2y²

18y² + 63y + 45 = 0

2y² + 7y + 5 = 0

Factor.

(y + 1) (2y + 5) = 0

y = -1 or -5/2

Plug back into the first equation to find x.

x = 4(-1) + 7 = 3

x = 4(-5/2) + 7 = -3

M (-3, -5/2)

N (3, -1)

Matthew has 170 tiles he can use for this project. Identify the largest patio design that he can make. Show or explain your reasoning.

Answers

Answer:

Design 12

Step-by-step explanation:

See the attached for missing part of the question

As we see each design comprises of entrance and exit - each one tile and:

Design 1 has 1 row and 3 columns,Design 2 has 2 rows and 4 columns,Design 3 has 3 rows and 5 columns.

So design x has x rows and two more columns according the pattern we observe.

The number of tiles of design x is:

x by (x + 2) and 2 more tiles

We can put it as equation to get 170 tiles and solve for x:

x(x+2) + 2 = 170x² + 2x - 168 = 0x² - 12x + 14x - 168 = 0x(x - 12) + 14(x - 12) = 0(x + 14)(x - 12) = 0x = - 14 (discarded as negative root)x = 12 (the solution)

So this is a design 12

It has 12 rows, 14 columns, 1 entrance and 1 exit tiles, the total number is

12*14 + 2 = 170 tiles

solve for x 3(x+2) + 4(x-5)=10

Answers

Answer:

x= 3.43

Step-by-step explanation:

First, use the distributive property and multiply 3 by x and 3 by 2:

3x + 6

next use the distributive property again and multiply 4 by x and -5:

4x - 20

Combine Like terms: 3x + 6 + 4x - 20

3x + 4x = 7x

6 - 20 = -14

Now Add 14 to both sides: 7x - 14 = 10

10 + 14 = 24

Now divide 7 by both sides: 7x = 24

24 / 7 = 3.428571429 = 3.43

Answer:

x=24/7 or 3 3/7

Step-by-step explanation:

3(x+2) + 4(x-5)=10   parenthesis first

3x+6+4x-20=10

7x-14=10               addition on both sides

7x-14+14=10+14

7x=24

x=24/7

check the answer:

3(x+2) + 4(x-5)=10

3(24/7+2)+4(24/7-5)=10

72/7+6+96/7-20=10

168/7-14=10

24-14=10

10=10 correct

What characteristics do similar triangles share? a They have the same sides and angles. b They have the same sides but different angles. c They have the same ratios for the sides. d They are the exact same.

Answers

Answer:

b. they have the same sides but different angles

Step-by-step explanation:

this answer makes the most sense

Answer:

C they have the same ratios for the sides

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.

The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system. FYI it’s not b

Answers

Answer:

c.

Step-by-step explanation:

From the last row in the matrix z = 1.

From the second row:

y + 5z = -4

y = -4 -5(1) = -9.

From the first row:

x + -1 = -3

x = - 3 + 1

x = -2.

How can I fin the remainder to 8,595 ÷ 24?

Answers

Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

24 goes into 85, 3 times with 13 left overBring down the 9 and 24 goes into 139, 5 times with 19 left overThen bring down the 5 and 24 goes inside 195, 8 times with 3 left over

So your remainder would be 3

Hope this helps

Point P' (1, 5) is the image of P (-3,1) under a translation. Determine the translation. Use non-negative numbers.

Answers

Answer:

T: 4 units right, 4 units up

Step-by-step explanation:

From x = -3 to x = 1, you need to add 4 to x, so the translation in x is 4 units right.

From y = 1 to y = 5, you need to add 4, so the translation in y is 4 units up.

T: 4 units right, 4 units up

The translation vector is (4, 4).

Vectorially speaking, a translation between two distinct point on cartesian plane is described by the following formula:

[tex]P'(x,y) = P(x,y) + T(x,y)[/tex] (1)

Where:

[tex]P(x,y)[/tex] - Original point.[tex]P'(x,y)[/tex] - Translated point.[tex]T(x,y)[/tex] - Translation vector.

If we know that [tex]P(x,y) = (-3, 1)[/tex] and [tex]P'(x,y) = (1,5)[/tex], then the translation vector is:

[tex]T(x,y) = P'(x,y) - P(x,y)[/tex]

[tex]T(x,y) = (1,5) - (-3, 1)[/tex]

[tex]T(x,y) = (4,4)[/tex]

The translation vector is (4, 4).

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-14 = x - 12 pls answer this if I can and check answer

Answers

Answer:

x = -2

Step-by-step explanation:

-14 = x - 12

-14 + 12 = x

-2 = x

check:

-14 = -2 - 12

A survey of athletes at a high school is conducted, and the following facts are discovered: 28% of the athletes are football players, 25% are basketball players, and 24% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player

Answers

Answer: 0.29 or 29%

Step-by-step explanation:

Given :

Probability that the athletes are football players : P(football ) = 0.28

Probability that the athletes are basketball players : P(basketball) = 0.25

Probability that the athletes play both football and basketball: P( both football and basketball ) = 0.24

Now, using formula

P(either  football or basketball)= P(football )+ P(basketball+ P( both football and basketball )

⇒P(either  football or basketball)= 0.28+0.25-0.24 = 0.29

Hence, the probability that they are either a football player or a basketball player = 0.29 .

30 times the square of a nonzero number is equal to eight times the number what is the number

Answers

Answer: 4/15

Step-by-step explanation:

Answer:

[tex]\frac{4}{15}[/tex]

Step-by-step explanation:

Number sentence: [tex]30x^{2}[/tex] = [tex]8x[/tex]

You can start by applying algebra to the left side of the equation by dividing each side by x. This should be how it looks now: 30x = 8

Now divide each side by 30 to keep reducing it: [tex]x = \frac{8}{30}[/tex]

Now that we have [tex]\frac{8}{30}[/tex], we can reduce that by dividing the top and bottom by 2:

[tex]\frac{8}{30} = \frac{4}{15}[/tex].

Therefore, the number is [tex]\frac{4}{15}[/tex].

ABC is an eqilateral triangle with sides 10cm find the length of the prependicular from A to BC

Answers

All sides are equal in an equilateral triangle and the perpendicular bisects the side too.

so BC will be bisected and the segments be 5 each.

you can use Pythagoras theorem to find the altitude length, hypotenuse will be one side of the triangle.

[tex] 5^2+h^2=10^2[/tex]

$h^2=100-25=75$

$h=\sqrt{75}=5\sqrt3$

Need help with mark brainlist.

Nam worked on a job for 10 days. On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. If he worked 69 hours in all, how many hours did he work during the last 2 days together?

Answers

Answer: 17 hours

Step-by-step explanation:

Given that On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. That is he worked additional 4 hours for the two days.

Let the total hours for the 8 days = E

The mean = E/8 = 0.125E

For the two last days, he worked

( 0.125E + 2 ) × 2 = 0.25E + 4

If he worked 69 hours in all, then

E + 0.25E + 4 = 69

Collect the like terms

1.25E = 69 - 4

1.25E = 65

E = 65/1.25

E = 52.

Now find the mean of the first 8 days

Mean = 52 / 8 = 6.5 hours

Nam works during the last 2 days together for:

(6.5 + 2)×2

8.5 × 2 = 17 hours

A son is 8 years old. His father is 5 times as old. How old was the father when his son was born?

Answers

Answer:

he was 32

Step-by-step explanation:

8x5 is 40 because he was born 8 years ago you subtract 8 from 40 to get 32

The Father is 32. I know this because 8 x 5 is 40 so he is 40 years old rn. When he was born he was 32 because 40 - 8 is 32. HOPE THIS HELPS!

2 liters is equivalent to how many ounces

Answers

Answer:

hey hon! 2 liters is equal to 67.628 fluid ounces :) hope you have a nice day.

Choose the best definition for the following phrase: combining like terms (1 point)
A letter that holds the place for some unknown value in mathematics
A process where you must look for terms that have identical variable parts and then combine their coefficients
A process where if two things are equal, one can be put in the place of the other and nothing will change
Terms that have identical variable parts

Answers

Answer:

D. Terms that have identical variable parts

Step-by-step explanation:

Like terms refers to terms that have identical variable parts.

For example:

Given the expression

2xy + z + x + 3y - 5z + 4y - xy + 3x

The like terms in the expression are:

2xy - xy= xy

z - 5z= -4z

x + 3x= 4x

3y + 4y=7y

The new expression will be

xy - 4z + 4x + 7y

WILL MARK BRAINLIEST Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x.

Answers

Answer:

third option

Step-by-step explanation:

∠ E = 180° - (65 + 53)° = 180° - 118° = 62°, then

∠ A = ∠ F = 53° and ∠ C = ∠ E = 62° , thus

Δ ABC ~ Δ FDE by the AA postulate

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{BC}{DE}[/tex] = [tex]\frac{AB}{FD}[/tex] , substitute values

[tex]\frac{x}{z}[/tex] = [tex]\frac{w}{r}[/tex] ( multiply both sides by z )

x = z × [tex]\frac{w}{r}[/tex]

The expression to solve for x would be x = r × w/z Therefore, the correct option is 3.

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Since,

∠ E = 180° - (65 + 53)°

= 180° - 118° = 62°,

then

∠ A = ∠ F = 53° and ∠ C = ∠ E = 62° ,

Thus, Δ ABC ~ Δ FDE are congruent by the AA postulate.

Since the triangles are similar then the ratios of corresponding sides are equal so,

BC / DF = AB / ED

Substitute;

x / r = w/ z ( multiply both sides by z )

x = r × w/z

Therefore, the correct option is 3.

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what is the value of x ?

Answers

Answer:

28 degrees

Step-by-step explanation:

there is a square in the corner which means it is a right angle, 90 degrees.

90-62=28

Answer:

28 deggrees

Step-by-step explanation

A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. A deer is 10 miles per hour faster than a bison.

Answers

3520/5280 = 2/3 of a mile per minute.

2/3 x 60 minutes per hour = 40 miles per hour.

40-30 = 10

Bison runs 40 miles per hour

The bison runs 10 miles an hour faster than the deer

Answer:

American bison is faster than the white-tailed deer by 10 more miles per hour.

Step-by-step explanation:

In 1 hour there are 60 minutes.

=> 3520 feet = 1 minute

=> 60 minutes = 3520 x 60

=> 211200 feet = 60 minutes

So, 211200 feet can be converted in miles.

=> 1 mile = 5280 feet

=> 211200 feet = x miles

=> x = 211200 / 5280

=> x = 40 miles per hour.

So, a white-tailed deer can run up to 30 miles per hour.

     an American bison can run up to 40 miles per hour.

American bison runs 10 more miles per hour than a white-tailed deer.

Please answer this question now

Answers

Answer:

420 cubic inches is the answer

Answer:

420 cubic inches

Step-by-step explanation:

Volume of rectangular pyramid

= 1/3*lbh

= 1/3 * 10*9*14

= 10*3*14

= 420 cubic inches

Given: AB tangent at D, AD = OD = 4 Find: Area of the shaded region

Answers

Answer:

1.72

Step-by-step explanation:

AB tangent at D, AD = OD = 4

so triangle OAD is right angle with side of 4 and 4.

area of OAD = 1/2 * 4 * 4 = 8

Angle AOD = DAO = 45 deg.

so circular sector OCD area = area of circle O * 45/360

= pi * 4 * 4 * 45/360

= 2pi

Shade area ACD = trigangle OAD - circular sector OCD

= 8 - 2pi

= 1.72

The lengths of two sides of an isosceles triangle are 5 and 9. The length of the third side could be

Answers

2 need to be equal so it would probably be 9

The length of the side can be both 5 and 9.

What is an Isosceles Triangle?

An Isosceles Triangle is a triangle that has two equal sides.

The length of the sides of an isosceles triangle is given as 5 and 9

To determine the third side, the property of Triangle Inequality will be used

According to the property, the sum of any pair of a triangle’s sides is always greater than the third side.

If the third side is 5 then

5+5 > 9

10 >9

true

if the third side is 9 then

5+9 > 9

14>9

Therefore, the length of the side can be both 5 and 9.

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PLZ HELP ME!!!! I NEED THE ANSWER QUICK SO IM GIVING BRAINLIEST TO THE FASTEST AND BEST ANSWER.

Answers

Answer:

f(x) = 8(1/2)^x.

Step-by-step explanation:

According to the graph, there is a point at (0, 8) and (1, 4).

That means that when x = 0, y = 8.

8 = a(b)^0

1a = 8

a = 8

That means that a = 8, and when x = 1, y = 4.

4 = 8(b)^1

4 = 8b

8b = 4

b = 4/8

b = 1/2

So, f(x) = 8(1/2)^x.

Hope this helps!

PLZ HELP I WILL MARK YOU AS BRAINLIEST
The ages of two groups of karate students are shown in the following dot plots: The mean absolute deviation (MAD) for group A is 2.07 and the MAD for group B is 5.51. Which of the following observations can be made using these data? Group A has greater variability in the data. Group A has less variability in the data. Group B has a lower range. Group B has a lower mean.

Answers

Answer:

Group A has less variability in the data.

Step-by-step explanation:

Examining the data for both groups virtually as represented on the dot plot, we can easily tell that the data in group A are less spread compared to group B data.

Group A has a range value of 10 (14 - 4), while group B has a range value of 19 (26 - 7).

Therefore, "Group A has less variability in the data."

Para la función f(x) = x + 6, ¿ cuál es
resultado de la función si x=2 ?

Answers

Answer:

f(x) = 8

Step-by-step explanation:

Como x = 2, simplemente lo sustituiría por x en la función y sumaría.

f(x) = 2+6

f(x) = 8

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