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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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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Help ASAP I’ll give you brainlest
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
Andre says that 534+ 214= 712 because 748= 712. Identify his mistake.
Step-by-step explanation:
748 ≠ 712 so 534 + 214 only = 748 not 712
Which equation is the result of adding theses two equations -2x+4y=17 3x-10y=-3
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
Find the area of the triangle.
hi guys..............
please guys answer the correct answer
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)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
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)
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.
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
Is 7/5 greater than 11?
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
Line c has a slope of 6/5. Line d is parallel to line c. What is the slope of line d?
Answer:
6/5
Step-by-step explanation:
Parallel lines have same slopes.
Given: - 4x/7 > 10. Choose the solution set. {x | x < - } {x | x > - } {x | x > - } {x | x < - }
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)
What is the area of a square with side length:
3cm
Answer:
Since every square has the same length in sizes...
3 x 3 = 9cm
Answer: 9cm
Please help.
Algebra.
1. 5
2. 3
This is the answer
Answer:
question 1 should be 5 and question 2 should be 3
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
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]
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
Answer:
crcrc4cc4crfc
Step-by-step explanation:
Answer:
You can use scale factor
Step-by-step explanation:
Please help due today
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.
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
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)
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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Our teacher hasn’t explained the concept yet but class was canceled today
Answer:
What grade is this?
Step-by-step explanation:
8(8p+8)=640 solve
Answer ASAP please
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:
Dilate point a in relation to the origin by a dilation factor of 5.?
Answer:
origin dilation if 5. is 5
need help in this show working please
BC =
Round your answer to the nearest hundredth.
B
?
65
А
7
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:
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, £?
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.
Please answer the photo.
Answer:
the answer i think is C. AB
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?
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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What is the meaning of a sample in mathematics?
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:
What are the 2 roots of the equation 2x^2-5x-3=0
Answer:
Hence, 3/2 and 1 are the roots of the equation.
Solve for x : 80 + x = 100 - 14
Answer:
x=6
Step-by-step explanation:
100-14=86
86-80=6
Solve for value the two angles in the triangle and classify the triangle using the sides and angles
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
line pass through the sets given points. which choice shows perpendicular lines?
Answer:
I have no reference to this question, there is no graph or anything to show me.
Step-by-step explanation: