We use a similar strategy as in your previous question. Rewrite:
sin(5x) = sin(6x - x) = sin(6x) cos(x) - cos(6x) sin(x)
sin(7x) = sin(6x + x) = sin(6x) cos(x) + cos(6x) sin(x)
→ sin(5x) - sin(7x) = -2 cos(6x) sin(x)
sin(4x) = sin(6x - 2x) = sin(6x) cos(2x) - cos(6x) sin(2x)
sin(8x) = sin(6x + 2x) = sin(6x) cos(2x) + cos(6x) sin(2x)
→ sin(8x) - sin(4x) = 2 cos(6x) sin(2x)
cos(5x) = cos(6x - x) = cos(6x) cos(x) + sin(6x) sin(x)
cos(7x) = cos(6x + x) = cos(6x) cos(x) - sin(6x) sin(x)
→ cos(7x) - cos(5x) = -2 sin(6x) sin(x)
cos(4x) = cos(6x - 2x) = cos(6x) cos(2x) + sin(6x) sin(2x)
cos(8x) = cos(6x + 2x) = cos(6x) cos(2x) - sin(6x) sin(2x)
→ cos(4x) - cos(8x) = 2 sin(6x) sin(2x)
Then
(sin(5x) - sin(7x) - sin(4x) + sin(8x)) / (cos(4x) - cos(5x) - cos(8x) + cos(7x))
= (2 cos(6x) sin(2x) - 2 cos(6x) sin(x)) / (2 sin(6x) sin(2x) - 2 sin(6x) sin(x))
= (2 cos(6x) (sin(2x) - sin(x))) / (2 sin(6x) (sin(2x) - sin(x)))
= cos(6x) / sin(6x)
= cot(6x)
QED
(ANSWER FOR FREE BRAINPOINTS!) (FIRST TO ANSWER GETS BAINLIEST) The local park has a rectangular swimming pool that measures 40 yards in length and 15 yards in width. The community is planning to build a smaller swimming pool that is similar to the current pool. 40 yards, 15 yards, 24 yards. If the length of the new smaller pool will be 24 yards, what will be the width of the smaller pool in yards?
Answer:
9 yards
Step-by-step explanation:
Since both pools are similar, therefore the ratio of their length and width would be equal. That is:
Length of the current swimming pool : length of the new swimming pool = width of the current swimming pool : width of the new swimming pool
Thus, we can set up a proportion as shown below:
Let the width of the new swimming pool be x.
40 : 24 = 15 : x
[tex] \frac{40}{24} = \frac{15}{x} [/tex]
Cross multiply
[tex] 40*x = 15*24 [/tex]
[tex] 40x = 360 [/tex]
Divide both sides by 40
[tex] x = \frac{360}{40} [/tex]
[tex] x = 9 [/tex]
The width of the new swimming that is smaller would be 9 yards.
So everything goes to...... drazoavans1 because he/she helped me with mostly all of the questions. CONGRATS!!!
Answer:
YAY thx I appreciate it
Step-by-step explanation:
Need this answer I give you brainlist
Answer:
the 3rd one
Step-by-step explanation:
solve the system of equations below by graphing both equations with a pencil and paper, what is the solution? y= -x-1 y=x+3
Answer:
(-2, 1)
Step-by-step explanation:
Well, to actually graph it, for the first line you'd have one point at (0, -1) [0 right, 1 down] , then you go down one, right one, and place a point there, down another, right another, and repeat.
For the second you'd place a point on (0, 3) [0 right, 3 up] and then go one up, one right, and place a point. One up, one right and place a point and repeat that. the point where the two lines cross would be your answer. If you don't want to do that then the answer is (-2, 1) I believe.
Complete the steps to solve for x.
4
1
5 X-
x = 11
4
4
1
X = 11
4
x = 11
20
Is the following relation a function?
Answer:
no
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!
1728 students were asked to name their favorite color. The results are shown in this circle graph. How many students gave green as their favorite?
Green: 27.78%
Answer:
480
Step-by-step explanation: I just took the test, you can search up “what’s 27.78% of 1728” if you don’t trust me :)
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
i dont see the picture
Step-by-step explanation:
Paloma ran 3 3/4 miles around the school track
Did she?
No, but what's your actual question?
Answer:
What do you want us to do with that number
Step-by-step explanation:
Can someone help me with this? During a certain period of time about 2000 penguins had an annual growth rate of 19% why will the population of penguins be after 5 years? This is exponential growth and decay
Answer:
Future amount of penguin = 4,772.70
Step-by-step explanation:
Given:
Current amount of penguin = 2,000
Growth rate r = 19% = 0.19
Number of year n = 5
Find:
Future amount of penguin
Computation:
Future amount of penguin = Current amount of penguin[1+r]ⁿ
Future amount of penguin = 2000[1+0.19]⁵
Future amount of penguin = 4,772.70
There are 946 milliliters in a quart. There are 2 pints in a quart.
How many milliliters are in a pint?
Answer:b
Step-by-step explanation:
Answer:
Step-by-step explanation:
946mL=1q 2p=1q therfore 946mL=2p so 473mL
X2 + X-8
What is the degree
Answer:
1
Step-by-step explanation:
A window cleaner rises 36 feet up the side of a building, then descends 17 feet. What is his final position?
Answer:
19
Step-by-step:
+36 - 17 = 19
Answer: Its 19ft
You can also use Socratic to help you with any school assignments.
Charlie just bought 8 bags of 14 cookies each. He already had 9 cookies in a jar. How many cookies does Charlie have now?
Answer:
he has 121 cookies now
Step-by-step explanation:
8 times 14 plus 9
8 times 14 = 112 + 9 = 121
Answer:
121
Step-by-step explanation:
8 bags of 14 cookies means he bought 112 cookies. Since he already had 9, you add 9 to 112 and get 121 cookies in total.
Given the preimage points: find the coordinates
of the dilated image using the scale factors. *look at picture*
Question 1)
Answer:
Please see the explanation.
Step-by-step explanation:
We know that the dilation of an original object shows how much bigger or smaller the image will really get, as compared to the original shape.
Also,
if the value of scale factor > 1, the image will get bigger.if the value of scale factor < 1, the image will get smaller.The new coordinates of the image can be determined by multiplying the scale factor with the coordinates of the original object.
Given the preimage points:
A(0, 5)B(4, 9)C(-1, -8)The formula of the dilation by a scale factor of 3:
(x, y) → (3x, 3y)
As the scale factor > 1, so the image will be bigger.Therefore, the coordinates of the dilated image after the dilation by a scale factor of 3 will be:
A(x, y) → (3x, 3y) = A(0, 5) → (3(0), 3(5)) = A'(0, 15)
B(x, y) → (3x, 3y) = B(4, 9) → (3(4), 3(9)) = B'(12, 27)
C(x, y) → (3x, 3y) = C(-1, -8) → (3(-1), 3(-8)) = C'(-3, -24)
Question 2)
Answer:
Please see the explanation.
Step-by-step explanation:
Given the preimage points:
A(0, 5)B(4, 9)C(-1, -8)The formula of the dilation by a scale factor of 1/2:
(x, y) → (1/2x, 1/2y)
As the scale factor < 1, so the image will be smaller.Therefore, the coordinates of the dilated image after the dilation by a scale factor of 1/2 will be:
A(x, y) → (3x, 3y) = A(0, 5) → (1/2(0), 1/2(5)) = A'(0, 5/2)
B(x, y) → (3x, 3y) = B(4, 9) → (1/2(4), 1/2(9)) = B'(2, 9/2)
C(x, y) → (3x, 3y) = C(-1, -8) → (1/2(-1), 1/2(-8)) = C'(-1/2, -4)
Which statement is true?
Plz help
Which inequality represents the sentence below?
Two more than a number is less than 14.
2+13 14
2+1 <14
2+12 14
2+77 > 14
Answer:I would think the inequality would look like 2+x<14
Answer:
2 + n < 14
Step-by-step explanation:
One half the sum of a number and five is eleven.
Answer:
½÷n+5=11
or
0.5÷n+5=11
3-5(3a+6) in standard form 7th grade
Answer:
Step-by-step explanation:
3-5(3a+6)
3 - 15a - 30
-15a - 27
As per linear equation, the value of the given expression is (-27 - 15a).
What is a linear expression?"A linear expression is an expression in which the highest power of the variable is always 1.
Given expression is:
3 - 5(3a + 6)
= (3 - 15a -30)
= (-27 - 15a)
Therefore, the value of the given expression is (-27 - 15a).
Learn more about linear expression here: https://brainly.com/question/20592786
#SPJ2
2x + x + 12 + 96 = 180, What is x?
Answer:
X = 24
Step-by-step explanation:
2x + x + 12 + 96 = 180
combine like terms
3x + 108 = 180
subtract 108
3x = 72
divide by 3
x = 24
Hope this helps. Pls give brainliest.
Sara sold hotdogs and drinks at the soccer game.
18 hot dogs and 9 drinks sold for $45.00
20 hot dogs and 12 drinks sold for $52.00
What is the charge for an order of 4 hot dogs and 3 drinks?
Answer:
$11
Step-by-step explanation:
Set up the system of equations
18x + 9y = 45
20x + 12y = 52
Let's try to get y on one side for the first equation.
9y=45-18x
y=5-2x
Now substitute it into the second equation.
20x + 12(5-2x) = 52
20x + 60 - 24x = 52
-4x = -8
x = 2
Now solve for y using the first equation.
18(2) + 9y = 45
36 + 9y = 45
9y = 9
y = 1
Now that we know x and y we can solve for the price of 4 hot dogs and 3 drinks.
4(2) + 3(1) = z
8 + 3 = z
11 = z
That means that the price is 11 dollars.
Find the slope and y-intercept of the line in the graph.
Answer: slope = 3x , y intercept = 5
Step-by-step explanation: use the formula : y2 - y1 / x2 - x1 to find slope. y intercept is shown on graph
Jerimah rides always rides his bike and to work the total legnth
Helpppppppppppppppppppp please...................
Answer:
C and D
I am pretty sure
PLEASE HELP!!! Keith has $500 in a savings account at the beginning of summer. He wants to have at least $200 at the end of the summer. He spends $25 per week for food. How many weeks can Keith spend money on food to stay above his goal?
Answer:
20 times
Step-by-step explanation:
A girl had $6.50 while shopping at a local store. She bought 1 lb. of potatoes for $0.65 and wanted to spend the rest on tomatoes. Each pound of tomatoes costs $1.95. Which inequality models the pounds (n) of tomatoes she could buy?
Answer: 6.50-.65 > 1.95x
Step-by-step explanation:
Answer: 3 Ib
Explanation: 6.50 - 0.65 = 5.85 and 1.95 times 3 is 5.85 so she spends the rest of her money on 3 pounds of tomatoes.
good night to everyone on brainly :)
Answer:
good night :))))))))))))
Answer:
umm this question is from a wile ago hehe but anyways i got points hehehe
Step-by-step explanation:
Please Help Me It's A Homework Sheet.!!!
Answer:
45 A
Step-by-step explanation:
There are 3 grams of sodium in 1⁄2 of a liter of soda. How much sodium is in 2⁄3 of a liter of soda?
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Since 3 is 1/2 of the bottle, the whole bottle is 6. Then, 2/3 of 6 is 4!
the sum of four times a number and another number is 10. The difference of the two numbers is 35. What is the larger number? Also please explain how you got that answer
Answer:
The two numbers are 9 and -26.
The larger number is 9.
Step-by-step explanation:
Let the two unknown numbers be x and y.
The sum of a four times a number x and another number y is 10. Hence:
[tex]4x+y=10[/tex]
And the difference between the two numbers is 35. So:
[tex]x-y=35[/tex]
So, we have the system of equations:
[tex]\left\{ \begin{array} \ 4x+y=10 \\ x-y=35 \end{array}[/tex]
From the second equation, we can add y to both sides:
[tex]x=y+35[/tex]
Now, we can substitute this into the first equation:
[tex]4(y+35)+y=10[/tex]
Distribute:
[tex]4y+140+y=10[/tex]
Simplify:
[tex]5y+140=10[/tex]
Subtract 140 from both sides:
[tex]5y=-130[/tex]
Divide both sides by 5:
[tex]y=-26[/tex]
So, the value of y is -26 .
Then it follows that the value of x is:
[tex]x=y+35[/tex]
Substitute -26 for y:
[tex]x=-26+35=9[/tex]
So, our two numbers are 9 and -26.
The larger number is 9.
So, our answer is 9.
Answer:
Yup answers 9
Step-by-step explanation: just took the test