Review the incomplete derivation of the cosine sum identity.
A 2-column table with 5 rows. Column 1 has entries step 1, step 2, step 3, step 4, step 5. Column 2 has entries cosine (x + y), sine (StartFraction pi Over 2 EndFraction minus (x + y) ), blank, sine (StartFraction pi Over 2 EndFraction minus x) cosine (negative y) + cosine (StartFraction pi Over 2 EndFraction minus x) sine (negative y), blank.
Which expressions for Step 3 and Step 5 complete the derivation?
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) – sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) – sin(x)sin(y)
Answers
Answer:
Option (4)
Step-by-step explanation:
STEP - 1
cos(x + y)
STEP - 2
[tex]\text{sin}[\frac{\pi}{2}-(x+y)][/tex]
STEP - 3
[tex]\text{sin}[(\frac{\pi}{2}-x)-y][/tex]
STEP - 4
[tex]\text{sin}(\frac{\pi}{2}-x)\text{cos}(-y)+\text{cos}(\frac{\pi}{2}-x)\text{sin}(-y)[/tex]
STEP - 5
cos(x)cos(y) - sin(x)sin(y)
[Since, [tex]\text{sin}(\frac{\pi}{2}-x)=cos(x)[/tex] and [tex]\text{cos}(\frac{\pi}{2}-x)=\text{sin}(x)[/tex]]
[Since, cos(-x) = cos(x) and sin(-x) = -sin(x)]
Therefore, Option (4) will be the correct option.
Answer:
D
Step-by-step explanation:
Top Answer was right, don't know why it was rated poorly
Related Questions
URGENT!!
A golf ball is hit with an initial velocity of 80 feet per second. H= -16t^2 + 80t.
1) When will the ball reach 48ft?
2) When will the ball reach 110ft?
Answers
9514 1404 393
Answer:
t = 0.697 secondsnever (the maximum height is 100 ft)Step-by-step explanation:
A graphing calculator provides a nice solution to this question.
__
1) Put 48 ft in for H and solve for t:
48 = -16t^2 +80t
-3 = t^2 -5t
3.25 = t^2 -5t +6.25 = (t -2.5)^2
t = 2.5 ±√3.25
The ball will first reach 48 feet at t = 2.5 -√3.25 ≈ 0.697224 seconds.
__
2) The equation tells us the maximum height occurs at t=2.5 seconds. That height is ...
H = -16(2.5^2) +80(2.5) = 100
The maximum height is 100 feet. The ball will never reach 110 feet.
the rectangle had a length that is 6 inches less that twice it's width. If the perimeter is 54, find the dimensions of the rectangle
Answers
Answer:
11" x 16"
Step-by-step explanation:
This problem can be solved with an equation
If you translate the first words into an equation, you get:
l = 2w - 6
(where w is width and l is length)
The perimeter (p) of any rectangle is 2l + 2w, so
if p = 54
then 54 = 2l + 2w
Now, you have the following two equations:
l = 2w - 6
2l + 2w = 54
In order to solve this for w, you can replace the l in the equation with (2w - 6) because of the substitution property of equality (if a = b, then a can be replaced with b at any time), so you get:
54 = 2(2w - 6) + 2w
Now, you simplify:
54 = 2(2w - 6) + 2w
= 54 = 4w - 12 + 2w
= 54 = 6w - 12
= 66 = 6w
= w = 11
So the width is 11. In order to find the length you just need to substitute it into the equation for the perimeter:
2l + 2(11) = 54
= 2l + 22 = 54
= 2l = 32
= l = 16
In conclusion, the width is 11 and the length is 16.
Answer:
OMG HI
Step-by-step explanation:
It's been a while... how's life
A package of 5 pairs of handmade face
masks costs $32.95. What is the unit
price of one face mask?
Answers
Answer:
$6.59 per mask
Step-by-step explanation:
Take the total cost and divide by the number of masks
32.95 /5
6.59 per mask
Answer:
$6.59
Step-by-step explanation:
32.95 divided by 5= 6.59
Add dollar sign
(6x+ 3)(6x^2− 8x + 1)
can anyone please show the work on how to get the answer? Thank you :,)
Answers
Answer:
Step-by-step explanation:
36x^3 - 48x^2 + 6x + 18x^2 - 24x + 3
36x^3 - 30x^2 - 18x + 3
Why do you think the military police (MPs) confronted the men at the reservoir shack? Do you think the MPs did the right thing? Do you think Kaz and his men did the right thing? Explain.
Farewell To Manzanar, Chapter 6-11. IF U GET IT RIGHT U GET BRAINLIEST, 5 STARS AND THANKS
Answers
Answer:
ywes
Step-by-step explanation:
2. One action figure sells for $3.50 How many action figures can Sergio buy for $20.00?
Answers
Answer:
5
Step-by-step explanation:
20 divided by 3.50 = 5.71428571429
Can anyone answer this ill mark you the brainliest
Answers
Answer: This is an acute triangle. Each of the angles is less than 90°
They are B=60°, C=70°, D=50°
Step-by-step explanation:
In an obtuse triangle, one of the angles is greater than 90°
In an equiangular triangle, the angles are all 60°
im confused someone help
Answers
A generator turns __?____ energy into ___?____ energy
A.Coiled wire
B.Negative wire
C.Positive wire
D.Handle that can spin
E.Light bulb
Chose two answers to place on the sentence
Help asap
Answers
B, C waaaaaaaaaaaaaaaaaaaaaa
what is the solution of 3+ x-2÷x-3<=4
Answers
Answer:
No solution
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)
Does anyone know this? If the answer is correct ill mark you as the best answer!
Which of the following does NOT represent the equation y= 2x
Answers
Answer:
G
Step-by-step explanation:
In F, the graph goes up by two and only to the side by 1. 2/1 simplifies to 2.
In H, y being the double of x would be equal to 2/1 again.
And in J, the numbers are also being doubled.
The slope for G would just be 0, which is undefined.
How is measuring an angle similar to and different from measuring a line segment?
Answers
Answer:
Line planes are flat, but angles are at an angle.
Step-by-step explanation:
cylindrical container has a height of 24 inches. Currently, the container is filled with water to a height of 18 inches. A leaky faucet drips into the container, causing the height of the water in the container to increase by 2 inches per hour. The equation below can be used to find t, the number of hours it would take to fill the container.
18 + ?t = 24
What number should be the coefficient of t?
Answers
Answer:6
Step-by-step explanation:
Answer:
6 would be the coefficient
Step-by-step explanation:
So what we are trying to do is solve for t.
18 + t = 24
-18 -18
t = 6
It would take 6 hours to fill the container.
Hope that helps and have a great day!
Andrea ordered a pizza for dinner. She ate 1/4 of the pizza. Her brother ate 35% of the pizza. Her mom ate .10 of the pizza. How much pizza is left?
Answers
Answer: 0.3, 30%, or 3/10
Step-by-step explanation:
Andrea ate 1/4 of the pizza.
1/4 = 0.25
Her brother ate 35% of the pizza.
35% = 0.35
Her mom at 0.10 of the pizza.
1 - 0.25 - 0.35 - 0.10 = 0.3 of the pizza
0.3 = 30% = 3/10
To decorate his bedroom, Jesse spent $112.65 on new furniture, $29.75 on paint, and $48.33 on accessories. About how much did he spend to decorate his bedroom?
$170
$190
$210
$230
Answers
Answer:
$190
Step-by-step explanation:
used the calculator!
Answer: B: 190 dollars
Step-by-step explanation: This is relatively simple, but lets walk through it. First, take out the cents and add them separatly,
75
65
33
You get 1.73!
Now, add the large numbers,
112
29
48
You get 189!
Add these and get 190.73! All you need to do now is round to the nearest given answer, and you get 190 dollars!
Hope this helps, if not, comment down below please!!!
John's birthday is this saturday, in buying materials for the party Vicki notices that plates come in packs of 12, cups come in packs of 10, and utensils come in packs of 8 sets. If Vicki wants to have no left overs, how many packs of utensils should she buy?
Answers
Answer:
Step-by-step explanation:
So, Vicki wants no left overs whatsoever, which means we have to get all three items to the same number. We first look at 10. We know that 10 will always have a 0 in the one's place, meaning that 8 and 12 have to be multiplied by 5, 10, 15, 20, etc., but they do not need to be multiplied by the same number.
Let's take 8 first. 8 can possibly go up to 40, 80, 120, 160, 200, etc.
Then 12. 12 can possibly go up to 60, 120, 180, 220, 280, etc.
We can see that both numbers have 120 in common, so we shall use that.
We know that we can get 10 to 120 by multiplying 10 by 12, meaning Vicki buys 12 packs of cups.
We know that we can get 12 to 120 by multiplying 12 by 10, meaning Vicki buys 10 packs of plates.
And finally, we know that we can get 8 to 120 by multiplying 8 by 15, meaning Vicki buys 15 packs of utensils.
So, since the question is asking for utensils only, we should say that Vicki buys 15 packs of utensils.
Which steps should be used to compare the fraction 2/9 and 5/8
Answers
Answer:
the last one
Step-by-step explanation:
You need make the same denominator
9 = 3*3
6 = 3*2
it follows that 3 *3 *2 is the simplest denominator
the fraction with the 6 needs to be multiplied by 3/3 and the one with 9 with 2/2
I know i already asked this but i need the answer!!!!
Which expression shows the sum 9 + 21 rewritten as a product of the GCF and a sum?
O 9(1 + 21)
O 3(3 + 7)
O 3(3 + 21)
O 9(1 + 3)
Answers
Answer:
3(3+7)
Step-by-step explanation: you factor out the greatest common multiple. 3 times 3 is 9 and 3 times 7 is 21
PLEEEEEEEEEEEEEEEASE HELP ME WITH THIS! IT IS DUE TOMORROW!!!
Answers
Answer:
can you provide more information
Step-by-step explanation:
Answer: M and I are both parallel
:)
Which of the following could be the lengths of the sides of a right triangle.
6, 8, 10
5, 5, 10
3, 4, 6
8, 15, 16
Answers
Answer:
3,4,6 6,8,10 8,15,16
Step-by-step explanation:
Pls answer this is due today
Answers
Answer:
See below.
Step-by-step explanation:
It seems that the question above said that the value of the gift card decreased by $295.
The original amount of the gift card was $400.
$400 - $295 = $105
Once the original amount of the card was decreased by $295, it still has $105 left.
Part 2 of 2
Arleen can buy the wheelbarrow because she has $105 left on the card, and the wheelbarrow costs $100.
2 + 6i
-5 + i
simplify
Answers
Answer:
7+7i
Step-by-step explanation:
you would combine like terms
Dudjehdhejdjdhdud
Ms. Carey is planning to host a neighborhood picnic. To make sure she had enough ingredients, she was making a table of
possible combinations of dried fruit to peanuts for her terrific trail mix. The ratio she used was 3 to 5. The table below shows
the original recipe's ratio of dried fruit to peanuts.
Dried Fruit
(oz)
9
Peanuts
(oz)
45
27
80
Which of the following accurately fills in the missing information to identify equivalent ratios for Ms. Carey?
A 30 ounces of peanuts and 42 ounces of dried fruit
B. 48 ounces of peanuts and 15 ounces of dried fruit C . 3 ounces of peanuts and 54 ounces of dried fruit. D. 15 ounces of peanuts and 48 ounces of dried fruit
Answers
Answer:63:9
Step-by-step explanation:63:9
Find the root(s) of f(x) = (x + 5)2(x - 9)2(x + 1).
-5 with multiplicity 3
5 with multiplicity 3
-9 with multiplicity 2
9 with multiplicity 2
-1 with multiplicity 0
-1 with multiplicity 1
N1 with multiplicity o
with multinlicity 1
Answers
Answer:
x = -5,-1, 9. -1 with multiplicity 1, 9 with multiplicity 1, and -5 with multiplicity 1.
Step-by-step explanation:
the coefficients do not change the roots of the equation but rather the local minima and maxima, and Minimum or Maximum depending on the function.
Answer:
-1 with multiplicity 1
What error did Heather make?
Heather solved this problem:
75 is 300% of what number?
O None. Her work is correct?
O She multiplied 75 and 4 incorrectly.
O She should have divided 75 by 4, and divided 100
by 4.
O She used the part, 75, to write the percent ratio. The
part-to-whole percent ratio is 300/100
Answers
Answer:
Its is D i took the test you welcome also give me 5stars plsss and like as well thank you
Step-by-step explanation:
She used the part, 75, to write the percent ratio. The part-to-whole percent ratio is StartFraction 300 Over 100 EndFraction
need this asap please !:)
at a local strawberry farm customers fill a bucket with strawberries. the function f(x)=4x models the cost for the strawberries, where x is the number of pounds of strawberries in
the bucket. a bucket can hold up to 10 pounds of strawberries. which is an appropriate domain of the function?
*answer choices in picture!*
Answers
answer - o<x<10
thank me later
A sequence can be generated by using an=an−1+9, where a1=−5 and n is a whole number greater than 1. What are the first four terms in the sequence?
A.−5, 4, 13, 22
B.9, 4, −1, −6
C.−5, −45, −405, −3645
D. 9, −45, 225, −1125
Answers
Answer:
B.9, 4, −1, −6
Step-by-step explanation:
A sequence can be generated by using an=an−1+9, where a1=−5 and n is a whole number greater than 1. What are the first four terms in the sequence?
A.−5, 4, 13, 22
B.9, 4, −1, −6
C.−5, −45, −405, −3645
D. 9, −45, 225, −1125
From the above question,
A sequence can be generated by using an=a(n−1)+9, where a1=−5
The formula = an = a1 + (n - 1)d
a1 = First term
d = common difference = 9
We are to find the first 5 terms
First term = a1 =
an=an−1+9, where a1=−5
The formula =
a1 = -5 (1 - 1) + 9
= -5(0) 9
= -9
Second term = a2 =
an=an−1+9, where a1=−5
The formula = an = a1 (n - 1) + d
a2 = -5(2 - 1) + 9
= -5(1)+ 9
= -5 + 9
= 4
Third term = a3 =
an=an−1+9, where a1=−5
The formula = an = a1(n - 1) + d
a3 = -5(3 - 1)9
= -5(2) + 9
= -10+ 9
= -1
Fourth term = a2 =
an=an−1+9, where a1=−5
The formula = an = a1(n - 1) + d
a4 = -5(4 - 1)9
= -5(3) +9
= -15 +9
= -6
Solve for x: 5 − (x + 5) > −2(x + 4)
x > −8
x −18
x < −18
PLS PLS PLS HURRY I GIVE BRAINLIEST
Answers
Answer:
The answer is
[tex] \huge x > - 8[/tex]
Step-by-step explanation:
[tex]5 − (x + 5) > −2(x + 4)[/tex]
First of all expand the terms in the bracket
That's
[tex]5 - x - 5 > - 2x - 8 \\ - x > - 2x - 8[/tex]
Add 2x to both sides
[tex] - x + 2x > 2x - 2x - 8 \\ x > - 8[/tex]
We have the final answer as
[tex]x > - 8 [/tex]
Hope this helps you
Answer:
x > -8
Step-by-step explanation:
5 − (x + 5) > −2(x + 4)
Simplify both sides first:
5 - x - 5 > -2x - 8
-x > -2x -8
Now isolate the variable:
-x > -2x -8
+2x +2x
x > -8
What is the slope of the line that passes through the points (-2, -1)
and (2, -3)? Write your answer in simplest form.
Answers
Plug this into the formula y2 - y1 / x2 - x1
-2 = x1, x2 = 2, y1 = -1, y2 = -3
-3 - (-1) / 2 - (-2)
-2 / 4
-1/2
The slope is -1/2.
The sports store made $564 from selling pool rafts this week (Monday-Friday). Of that amount, it made $132.56 on Monday and $107.38 on Tuesday. IT made an equal amount of money on Wednesday, Thursday, and Friday. How much money did the store make from selling pool rafts on Friday?
Answers
Answer:
Amount made from selling pool rafts on Friday is equal to $108.02
Step-by-step explanation:
Total amount made from selling pool rafts = $564
Amount made from selling pool rafts on Monday = $132.56
Amount made from selling pool rafts on Tuesday = $107.38
Let amount made on each of the days - Wednesday, Thursday, and Friday be equal to $x.
Therefore,
[tex]132.56+107.38+x+x+x=564\\239.94+3x=564\\3x=564-239.94\\3x=324.06\\x=\frac{324.06}{3}\\ x=$108.02[/tex]
So,
amount made from selling pool rafts on Friday is equal to $108.02