The expression cosine of pi over 2 times cosine of pi over 5 plus sine of pi over 2 times sine of pi over 5 can be rewritten as which of the following?
cosine of 7 times pi over 10
cosine of 3 times pi over 10
sine of 7 times pi over 10
sine of 3 times pi over 10
(The clear version of the question is in the picture below)
Answers
Answer:
(b) cos(3π/10)
Step-by-step explanation:
The given expression matches the trig identity form for the cosine of the difference of two angles:
cos(α-β) = cos(α)cos(β) +sin(α)sin(β)
__
To match the given expression exactly, we can choose ...
α = π/2
β = π/5
Then the difference is ...
α -β = π/2 -π/5 = (5/10)π -(2/10)π = 3π/10
The given expression can be shortened to ...
cos(3π/10)
__
Additional comment
Sometimes it can be difficult to remember when the signs in trig identities match, and when they differ. The fact that cosines of smaller angles have larger values can be a peg on which to hang that hat.
Related Questions
if the length of diagonal of a square is 4-√2 cm, find it's length, perimeter and area.
Answers
Step-by-step explanation:
1) the length of the side is:
[tex]\frac{4-\sqrt{2} }{\sqrt{2}}=2\sqrt{2}-1.[/tex]
2) the required perimeter is:
[tex]P=4(2\sqrt{2} -1)=8\sqrt{2} -4.[/tex]
3) the required area is:
[tex]A=(2\sqrt{2} -1)^2=9-4\sqrt{2}.[/tex]
Answer:
Side length = (2√2 - 1) units
Perimeter = (8√2 - 4) units
Area = (9 - 4√2) units²
Step-by-step explanation:
Properties of a square:
It is a quadrilateralThe opposite sides are parallelAll four sides are equal in lengthAll interior angles measure 90°The diagonal of a square creates two right triangles, with the diagonal being the hypotenuse, and the sides of the square being the 2 legs.
Let x = side length of the square
Using Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ x² + x² = (4 - √2)²
⇒ 2x² = 18 - 8√2
⇒ x² = 9 - 4√2
⇒ x = ±(2√2 - 1)
⇒ x = 2√2 - 1 only (as distance is positive)
Perimeter of a square = 4x
= 4(2√2 - 1)
= 8√2 - 4
Area of a square = x²
= (2√2 - 1)²
= 9 - 4√2
What is the smallest angle of a right triangle with sides 9, 40, and 41? Round your answer to the nearest degree, and enter the number only.
Answers
Answer: 13°
Explanation: x = tan^-1 ( 9/40) ≈ 13°
Are constant functions periodic? The reason I ask this is because a function is periodic if it has a period but in a constant function the period could be infinitely small.
Answers
Answer:
A function f:R→R is periodic if there exists some number t>0 such that
f(x)=f(x+t)
A constant function is periodic since you can take t=1,t=2, etc. (Hint: Hover over the tag "periodic-functions". What do you see?)
The fundamental period of f is the smallest of such t's. Since t cannot be 0, you are looking for the minimum of (0,∞), which does not exist.
Step-by-step explanation:
Tim bought all of the 2 3/4 lb packages for a party. How many pound of meat did tim buy?
Answers
The number is a/an...
국
Answers
sales representative can take one of 4 different routes from City B to City E and any one of 4 different routes from City E to City H. How many different routes can she take from City B to City H, going through City E?
Answers
Answer:
16
Step-by-step explanation:
4 x 4 = 16 because you have to go through city E
The weights of five different dogs are shown below. What are the minimum and maximum weights? Give your answers in kilograms (kg) Clifford 25kg
Amber 34kg
Beryl 47kg
Poppy 23kg
Toby 31kg
(please I need help right now)
Answers
Answer:
Minimum weight = 23kg
Maximum weight= 34kg
Step-by-step explanation:
Find the lowest and highest weight
Answer:
See below ↓↓
Step-by-step explanation:
Minimum weight = lowest numerical value of weight⇒ Poppy (23 kg)Maximum weight = highest numerical value of weight⇒ Beryl (47 kg)
What would the answer be?
Answers
Answer:
3 2/4
Step-by-step explanation:
1 3/4 + 1 3/4 = 6 2/4
because 3/4 +3/4 = 6/4 = 1 2/4
and 1+1+1 =3
Answer: [tex]3 \frac{1}{2}[/tex]
This is the same as writing 3 & 1/2 to mean "3 and a half".
Check out the diagram below. I've shaded the pizza slices to represent the mixed numbers being added. Notice in the bottom row I've moved one red slice over to make a full pie. Overall we have 3 full pies plus an extra half, when all is said and done.
If sodium 24 has a half life of 15 hours if there are 800g of na-24 initially how long will it take for 750g of na-25 to decay so that only 50g remains
Answers
It would take about 60 hours to decay so that only 50g of the sodium remains
How to calculate half life?The half life is 15 hours and there are 800 g initially. Let N(t) represent the amount of sodium after t hours. Hence:
[tex]N(t)=800(\frac{1}{2} )^\frac{t}{15} \\\\For\ 50g\ to \ remain:\\\\50 = 800(\frac{1}{2} )^\frac{t}{15}\\\\t=60\ hours[/tex]
It would take about 60 hours to decay so that only 50g of the sodium remains
Find out more on half life at: https://brainly.com/question/2320811
The hanger image below represents a balanced equation, write an equation to represent the image.
Answers
Unit 6 lesson 10 surface area and volume unit test
Answers
Answer:
You have to ask a question
Step-by-step explanation:
The triangles on the grid below represent a translation.
4
3
0
2
1
b
8
54-32-14
1 2
3
b
8
To form the image, the pre-image moved
five units right and three units up.
two units right and three units up.
Mark this and return
Save and Exit
Next
Answers
Answer:
Five units right and three units up.
If you notice there's a ' on the green triangle (a',b',c')
That means that the blue triangle was translated to get to the green triangle
Evaluate
A)–16
B)–4
C)16
D)[tex]-\frac{1}{32}[/tex]
Answers
Answer:
Answer is {C}
Step-by-step explanation:
Solve the system by graphing.
What is the solution of y=-x+4 and y=3/5x+4
Answers
Answer:
x=0 and y=4 thats where the points meet
Step-by-step explanation:
solution of x and y:
both equations equal to y so you can put them together
3/5x+4=-x+4
separate the variables and numbers...
1.6x=0
x=0
y=4
if ur using a graph, use the y intercept (0,4) for your first point
then, using y=-x+4, make -x a fraction -1/1
by using rise/run go down one unit from (0,4) since its negative 1
then one unit to the right from where you are
you should be able to connect the points for the first equation
find the second equation on your own now:)
Select the correct answer. The total cost of a flower bouquet depends on the types of flowers in the arrangement. A bouquet containing 6 roses, 3 lilies, and 2 carnations costs $26.75. A bouquet containing 3 roses, 4 lilies, and 5 carnations costs $25.50. A bouquet containing 1 of each flower costs $6.75. Which system of equations represents this situation, where rrepresents the number of roses, /represents the number of lilies, and c represents the number of carnations?
Answers
Answer: Roses 2.70 Lillies 2.45 Carnations 1.60
Step-by-step explanation:
I dont know if its wrong its mostly correct but hope it helps
22. Four years ago, age of X was 3 times Y. Six years from now X will be twice Y. Ages of X and Y
now are:
A.
034 and 14
B.
034 and 13
C.
033 and 14
D.
035 and 14
Answers
Answer:
a 34 and 14
Step-by-step explanation:
let present age be x and y
equation 1
x-4=3(y-4)
x=3y-8
equation 2
x+6=2(y+6)
x=2y+6
then
2y+6=3y-6
y=14
x=34
Researchers gave 40 index cards to a waitress at an Italian restaurant in New Jersey. Before delivering the bill to each customer, the waitress selected one of the index cards without reading it and wrote on the bill the same message that was printed on the card. Twenty of the cards had the message "The weather is supposed to be really good tomorrow. I hope you enjoy the day!" Another 20 cards contained the message "The weather is supposed to be not so good tomorrow. I hope you enjoy the day anyway!" After the customers left, the waitress recorded the amount of the tip (percentage of bill) before taxes. The tips for those receiving the good‑weather message are as follows.
20.8 18.7 19.9 20.6 21.9 23.4 22.8 24.9 22.2 20.3
24.9 22.3 27.0 20.5 22.2 24.0 21.2 22.1 22.0 22.7
The tips for the 20 customers who received the bad weather message are as follows.
18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 14.0
17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 18.2 19.4
Click to download the data in your preferred format.
CSV Excel JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt!
Back‑to‑back stemplots of the tips are shown.
Good Weather Tips Bad Weather Tips
13 6
14 0
15
16 1 8
17 0 5
7 18 0 0 2 4 5 8 8
9 19 0 1 2 4
8 6 5 3 20 0 2
9 2 21
8 7 3 2 2 1 0 22
4 23 2
9 9 0 24
25
26
0 27
Because the distributions are reasonably symmetric with no extreme outliers, the procedures will work well.
Is there good evidence that the two different messages produce different percentage tips?
Bruce Rind and David B. Strohmetz, "Effect of beliefs about future weather conditions on restaurant tipping," Journal of Applied Social Psychology, 31 (2001), pp. 2160–2164.
Carry out a two‑sample test. What is the test statistic? Give your answer to three decimal places.
=
What is the -value? Give your answer to three decimal places.
-value:
Answers
The test statistic and p-value of the given data are 6.274 and 0.0001 respectively.
Test StatisticThe test statistic can be calculated using the formula below
[tex]t = \frac{x-\mu}{\sigma / \sqrt{n} }[/tex]
Solving for the mean and standard deviation, we can substitute the values into the above equation which will be
[tex]t = \frac{x-\mu}{\sigma / \sqrt{n} } = 6.274[/tex]
P-ValueUsing the data from the test statistic, we can calculate the p-value of the data
[tex]p-value = p(z < 6.274)= 0.0001 = 0.00[/tex]
From the calculation above, the test statistic and p-value of the given data are
6.2740.0001Learn more on test statistic and p-value here;
https://brainly.com/question/4621112
Find the area
(Please would mark Brainily
Answers
Answer:
195.5 m²
Step-by-step explanation:
A = bh/2
A = (23)(17)/2
A = 391/2
A ≈ 195.5 m²
complete the ordered pair so that it is a solution of 2/3x + y -1 = 0
Answers
Answer:
Step-by-step explanation:
No solution; 3x+y-1 =/ 0
five years ago, Nina was twice as old as Sam. In five years she will be 1.5 times as old as Sam. How old are Nina and Sam now?
Answers
The age of Nina and sam are 15years and 10 years respectively now
System of equationsThey consists of equations and unknown variables
Let their current age be x and y
If five years ago, Nina was twice as old as Sam then;
x - 5 = 2(y-5)
If in five years she will be 1.5 times as old as Sam, then;
x = 1.5y
Substitute
1.5y - 5 = 2y -10
-0.5y = -5
y =5/0.5
y = 10
Since x = 1.5y
x = 15years
Hence the age of Nina and sam are 15years and 10 years respectively now
Learn more on equation here: https://brainly.com/question/2972832
#SPJ2
A souvenir shop has a number of different souvenirs. The table below shows the number of souvenirs and their price. Which histogram matches the table?
please help fast its important
Answers
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
To find out what values each bar in the graph represents, we use the lines and the y axis. Follow the line, and your value will be determined.
Hope this helps. If you have any further questions, let me know!
- profparis
if i helped you, i would appreciate a brainliest :D
Jed rode his scooter to school at 20 miles per hour and then jogged back at 8 miles per hour. If the round trip took him 7 hours, how many miles was it to school?
Answers
Answer:
196 Miles
Step-by-step explanation:
Jed Rode=20 miles per hour
jog back 8 miles per hour
28×7 = 196
Answer: 196 miles
Step-by-step explanation: 7(20+8) You have to distribute the 7 to each number(20 & 8). Then add the answers you get from the 7x20 and 7x8.
7x20=140
7x8= 56
56+140=196
A rectangular playground measures 5/8 mile long and 1/4 mile wide. What is the area, in square miles, of the playground?
Answers
Answer:
5/32 square miles or 0.15625 square miles
Step-by-step explanation:
1/4 miles × 5/8 miles
=5/32 square miles or 0.15625 square miles
Larry, a chemistry student, needs 10% acetic acid solution for a chemistry experiment. He realizes he only has 5% and 20% acetic acid solutions available. He decides to make the 10% solution by combining the 5% and 20% solutions. How many liters of the 5% solution must he add to 8 liters of the 20% solution to get a solution that is 10% acetic acid?
a) 16.5
b) 32
c) 16
d) 8.5
e) 24
Answers
Show the problem on a number line:
4(-2) =
Answers
Answer:
-8
Step-by-step explanation:
This is the same as 4 x -2.
The parenthesis just means to multiply the number to the left by whatver is in the paranthesis when it is touching like that.
Just answer
1 + 23 =
i give you 100 pts
I quit
Answers
hmm a tough one ima go with 24
28. Pay attention to the height data (cm) of the following 10 students! 155, 153, 153, 160 157, 155. 160, 155, 150, 155 The data mode is Your :
A. 150
B. 153
C. 155
D. 157
Answers
Answer:
c.155
Step-by-step explanation:
because it appears there the most :)
help!
Can you please give me the area of this. I would really like it.
Answers
Answer:
The answer is 340 ft²
To find the total area we make two squares and a big rectangle.
1st square
3x5=15
2nd square
5x5=25
Rectangle
20x15=300
Total Area
15+25+300 = 340ft²
How can we use the distributive property to find an expression equivalent to
10(5 – 2x)? Place the steps in order.
Answers
Answer: multiply 10 to both terms and subrtact products
Step-by-step explanation:
10(5 - 2x)
multipy 10 to both terms
50 20x
subtract products
50 - 20x
Answer:
1. subtract 2×from get 3.×= 682+ 4672
pls like and follow me you byeSelect the correct answer.
Tatum plans to buy some personalized sticky notes for her home office. The graph shows a proportional relationship between the number of packs of sticky notes she can buy and the total price. If Tatum has $30.50 to spend on sticky notes, how many packs can she buy? Assume that she can buy only whole packs.
A. 1
B.2
C.3
D.4
ANSWER FAST I NEED THIS NOWW