let α and β be first quadrant angles with cos ( α ) = √ 3 9 and sin ( β ) = √ 5 5 . find cos ( α − β ) . enter exact answer, or round to 4 decimals.

Answers

Answer 1

The cos(α - β) is equal to (2√15 + √390)/45, rounded to four Decimals

To find cos(α - β), we can use the trigonometric identity:

cos(α - β) = cos(α)cos(β) + sin(α)sin(β)

Given that cos(α) = √3/9 and sin(β) = √5/5, we need to find sin(α) and cos(β) to evaluate the expression.

Since α is a first quadrant angle, sin(α) is positive. We can find sin(α) using the Pythagorean identity:

sin^2(α) + cos^2(α) = 1

sin^2(α) = 1 - cos^2(α)

sin(α) = √(1 - cos^2(α))

Given that cos(α) = √3/9, we can substitute the value:

sin(α) = √(1 - (√3/9)^2)

= √(1 - 3/81)

= √(78/81)

= √78/9

Now, we can evaluate cos(β):

cos^2(β) + sin^2(β) = 1

cos^2(β) = 1 - sin^2(β)

cos(β) = √(1 - sin^2(β))

Given that sin(β) = √5/5, we can substitute the value:

cos(β) = √(1 - (√5/5)^2)

= √(1 - 5/25)

= √(20/25)

= √20/5

= 2√5/5

Now we can substitute the values of sin(α), cos(β), cos(α), and sin(β) into the expression for cos(α - β):

cos(α - β) = cos(α)cos(β) + sin(α)sin(β)

= (√3/9)(2√5/5) + (√78/9)(√5/5)

= (2√15)/45 + (√390)/45

= (2√15 + √390)/45

Therefore, cos(α - β) is equal to (2√15 + √390)/45, rounded to four decimals

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Answer 2

cos(α - β) = (√15 + √78)/45 or approximately 0.8895.

We can use the identity cos(α - β) = cos(α)cos(β) + sin(α)sin(β) to find cos(α - β).

Given that cos(α) = √3/9, we can find sin(α) using the Pythagorean identity: sin²(α) + cos²(α) = 1.

sin²(α) + (√3/9)² = 1

sin²(α) = 1 - (√3/9)²

sin(α) = √(1 - (√3/9)²) = √(1 - 3/81) = √(78/81) = √78/9

Given that sin(β) = √5/5, we can find cos(β) using the Pythagorean identity: cos²(β) + sin²(β) = 1.

cos²(β) + (√5/5)² = 1

cos²(β) = 1 - (√5/5)²

cos(β) = √(1 - (√5/5)²) = √(5/25) = 1/√5

Now we can substitute these values into the formula for cos(α - β):

cos(α - β) = cos(α)cos(β) + sin(α)sin(β)

= (√3/9)(1/√5) + (√78/9)(√5/5)

= (√3/9√5) + (√(78/5)/9)

= (√15 + √78)/45

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Related Questions

BC =
Round your answer to the nearest hundredth.
B
?
65
А
7

Answers

Answer:

14 = rounded 15

Step-by-step explanation:

What grade r u in?

And what time is where u r?

Answer: 5.52 (answer already rounded)

Step-by-step explanation:

What is the area of a square with side length:

3cm

Answers

Answer:

Since every square has the same length in sizes...

3 x 3 = 9cm

Answer: 9cm

12cm :) the reason why it’s 12 is because a square has 4 sides so 3 by 4 is 12

Is 7/5 greater than 11?

Answers

Answer:

no

Step-by-step explanation:

you take 7/5 and turn it into an improper fraction

you then have 1 2/5

1 2/5 is smaller then 11

The spinner below is divided into five equal-sized sectors. What is the probability that the spinner will stop on a number greater than 3?

Answers

Answer:

40%

Step-by-step explanation: If you have five equal-sized sectors, then the probability that the spinner will stop on 4 and 5 is 40%.

The probability that the spinner will stop on a number greater than 3 will be 0.4 or 40%.

What is probability?

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

The spinner below is divided into five equal-sized sectors.

The probability of it stopping more than 3 = probability of stops at 4 + probability of stops at 5.

⇒ 1/5 + 1/5

⇒ 2/5 = 0.4

So, 0.4 x 100 = 40%

Hence "The probability that the spinner will stop on a number greater than 3 will be 0.4 or 40%".

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Solve for value the two angles in the triangle and classify the triangle using the sides and angles

Answers

Step-by-step explanation:

x + 15 +2x + 66 = 180

3x + 81 = 180

3x = 99

x = 99/3 = 33

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

Answer:

The angles are 66, 66, and 48 degrees

The triangle is isosceles because 2 angles are equal, thus two leg lengths are equal

Step-by-step explanation:

the sum of all three angles in a triangle = 180 degrees

66 + 2x + (x+15) = 180

simplify

66 +3x + 15 = 180

reduce

81 + 3x = 180

subtract 81 from each side

81 - 81 + 3x = 180 - 81

3x = 99

divide both sides by 3

3x/3 = 99/3

x = 33

The cheerleading squad at Kensington High School had 18 members with the old coach. Now, with the new coach, there are 50% more members on the squad, how many members are on the squad now

Answers

Answer:

27 members

Step-by-step explanation:

So we have 18 members and we see a 50% increase in members.

So:

Now the squad is 150% of 18

We can set up a percent proportion

x/150=18/100

To solve, we do:

(150*18)/100 = x

27 = x

There is an easier way to do this with benchmark fractions.

We find 50% of 18 which is 9

And since it's a 50% increase, we add 9 to 18 and get 27

Let me know if you have any questions

Answer:

B) 8 + J

(It's saying my answer is too short, not too sure why)

What is the meaning of a sample in mathematics?

Answers

Answer:

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.

Step-by-step explanation:

Which equation is the result of adding theses two equations -2x+4y=17 3x-10y=-3

Answers

Answer:

x=-79/4, y=-45/8. (-79/4, -45/8).

Step-by-step explanation:

-2x+4y=17

3x-10y=-3

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

3(-2x+4y)=3(17)

2(3x-10y)=2(-3)

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

-6x+12y=51

6x-20y=-6

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

-8y=45

y=45/-8=-45/8

3x-10(-45/8)=-3

3x+450/8=-3

3x+225/4=-3

3x=-3-225/4

3x=-12/4-225/4

3x=-237/4

x=(-237/4)/3

x=(-237/4)(1/3)

x=-237/12=-79/4

hi guys..............
















please guys answer the correct answer​

Answers

Answer:

12) 1.5(m - n)/b13) 2t/(2c + d)

Step-by-step explanation:

Question 12)

Slope between the points:

A(a + b, 4m - n) and B(a - b, m + 2n)

Use slope formula:

Slope = (m + 2n - 4m + n)/(a - b - a - b) =              (-3m + 3n)/(-2b) =              (-3)(m - n)/(-2)b              1.5(m - n)/bQuestion 13)

Slope between the points:

C(3c - d, s + t) and D(c - 2d, s - t)

Use slope formula:

Slope = (s - t - s - t)/(c - 2d - 3c + d) =              (-2t)/(-2c - d) =              (-2)t/(-1)(2c + d)              2t/(2c + d)

Select the correct answer.

What are the factors of the function represented by this graph?

A. (x − 4) and (x − 8)
B. (x − 4) and (x + 8)
C. (x + 4) and (x − 8)
D. (x + 4) and (x + 8)

Answers

The factors of the function represented by the graph are (x + 4) and (x - 8)

How to determine the factors of the function represented by the graph?

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that:

The graph intersects with the x-axis at x = -4 and x = 8

So, we have

x = -4 and x = 8

Set the equations to 0

So, we have

x + 4 = 0 and x - 8 = 0

This means that the factors of the function represented by the graph are (x + 4) and (x - 8)

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A tree cast a shadow of 10 ft when the suns rays hit the ground at an angle of elevation of 28 .what is the height of the tree ? Round your answer to the nearest tenth

Answers

Answer:

crcrc4cc4crfc

Step-by-step explanation:

Answer:

You can use scale factor

Step-by-step explanation:

10. A standard stop sign measures 30.00 inches from flat to flat. What is the side length, x, of the stop

sign (to the nearest 0.01 in.)? Justify your answer.

30.00 in

Answers

Answer:

The answer is "12.426 in".

Step-by-step explanation:

[tex]\to b+2c=30\\\\\to b = 15 \times \tan 22.5 \\\\[/tex]

      [tex]= 15 \times 0.414213562\\\\=6.21320343 \times 2 \\\\=12.4264069 \ in \\\\[/tex]

What are the 2 roots of the equation 2x^2-5x-3=0

Answers

Answer:

Hence, 3/2 and 1 are the roots of the equation.

line pass through the sets given points. which choice shows perpendicular lines?

Answers

Answer:

I have no reference to this question, there is no graph or anything to show me.

Step-by-step explanation:

Andre says that 534+ 214= 712 because 748= 712. Identify his mistake.

Answers

Step-by-step explanation:

748 ≠ 712 so 534 + 214 only = 748 not 712

He is wrong because it equals it equals 748 and 712 has nothing to do with it

Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?

Answers

2(2) + 3(3) =

4 + 9 = 13

I don't know what 90p means but basically, u have to multiply that by 3 and add it to our current total which is 13.

Then, u substract the total cost from the 20 and you should get the change.

Dilate point a in relation to the origin by a dilation factor of 5.?

Answers

Answer:

origin dilation if 5. is 5

8(8p+8)=640 solve
Answer ASAP please

Answers

Answer:

p = 9

Step-by-step explanation:

8(8p + 8) = 640

use the dist property

64p + 64 = 640

        -64      -64

64p = 576

divide by 64

p = 9

Answer:

9

Step-by-step explanation:

Find the area of the triangle.

Answers

answer: 28

explanation: a= 8(7)/2 = 28

hope this helps :)

Our teacher hasn’t explained the concept yet but class was canceled today

Answers

Answer:

What grade is this?

Step-by-step explanation:

Solve for x : 80 + x = 100 - 14

Answers

Answer:

x=6

Step-by-step explanation:

100-14=86

86-80=6

need help in this show working please​

Answers

this is what i got hope it helps

Please help due today

Answers

(-2, 4) area is 10 units

Please answer the photo.

Answers

Answer:

the answer i think is C. AB

The slope of a line passing through the point (5.-6) is 0.4.
Drag the proper numbers and signs to obtain the equation of the line in slope-intercept form.

Answers

Answer:

using formula y2-y1/x2-x1, x1= -6,x2= o, y1= 5,y2= 4

Step-by-step explanation:

4-5/0-(-6)

-1/0+6

-1/6

is your answer

Rafael and his sister bought snacks for movie night.

Rafael got 3 boxed candies and 1 bag of chips for $6.99.

His sister got 2 bags of chips and 1 boxed candy for $5.98.

Find the cost for 1 of each of these items in dollars.

Answers

Answer:

1. $2.33

2. $2.99

Step-by-step explanation:

$6.99/3  

$5.98/2

Answer:

bag of chips is 2.19

boxed candy is 1.60

Step-by-step explanation:

Desmos Calcuator

Line c has a slope of 6/5. Line d is parallel to line c. What is the slope of line d?

Answers

Answer:

6/5

Step-by-step explanation:

Parallel lines have same slopes.

Please help.
Algebra.

Answers

1. 5

2. 3

This is the answer

Answer:

question 1 should be 5 and question 2 should be 3

Step-by-step explanation:

Given: - 4x/7 > 10. Choose the solution set. {x | x < - } {x | x > - } {x | x > - } {x | x < - }

Answers

Answer:

{x | x < - 35 / 2}

Step-by-step explanation:

-4x / 7 > 10

Multiply both sides by 7

-4x /7 * 7 > 10 * 7

-4x > 70

Divide both sides by - 4

-4x / - 4 > 70 / - 4

x < - 35 / 2 (inequality sign changes)

Help ASAP I’ll give you brainlest

Answers

Answer:

5.33 OR 5 1/3

Step-by-step explanation:

3 x 2³ ÷ 2 x 4 -1 +2

3 x 8 ÷ 2 x 4 -1 + 2

24 ÷ 8 +1

24 ÷ 9

2.66 OR 2 2/3

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