Recall that
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
and by subtracting the first equation from the second, we get
cos(a - b) - cos(a + b) = 2 sin(a) sin(b)
So, we can write
sin(t) sin(3t) = 1/2 (cos(2t) - cos(4t))
and expanding the left side in the original equation gives
sin(t) sin(3t) sin(5t) = 1/2 (cos(2t) - cos(4t)) sin(5t)
… = 1/2 cos(2t) sin(5t) - 1/2 cos(4t) sin(5t)
Similarly, recall that
sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
sin(a - b) = sin(a) cos(b) - cos(a) sin(b)
===> sin(a + b) + sin(a - b) = 2 sin(a) cos(b)
Then
cos(2t) sin(5t) = 1/2 (sin(7t) + sin(3t))
and
cos(4t) sin(5t) = 1/2 (sin(9t) + sin(t))
So we have
sin(t) sin(3t) sin(5t) = 1/2 cos(2t) sin(5t) - 1/2 cos(4t) sin(5t)
… = 1/2 (1/2 (sin(7t) + sin(3t))) - 1/2 (1/2 (sin(9t) + sin(t)))
… = 1/4 sin(7t) + 1/4 sin(3t) - 1/4 sin(9t) - 1/4 sin(t)
… = 1/4 (-sin(t) + sin(3t) + sin(7t) - sin(9t))
as required.
Plz help!! Math isn’t my thing. I’ll give brainliest.
Answer:
Here is your answer
Hope it helps
Answer:
(2,-6)
Step-by-step explanation:
it is above in the photo.
f(x)= 2x^2-7+6 g(x)=4x+10 find g(f(x))
Answer:
g(f(x)) = 8x^2 + 6
Step-by-step explanation:
g(f(x)) = 4(2x^2 - 7 + 6) + 10
g(f(x)) = 8x^2 -28 + 24 + 10
g(f(x)) = 8x^2 + 6
what is the factor of 12
Answer:
1, 2, 3, 4, 6, 12
Step-by-step explanation:
Consider functions fand g.
f(x) = (x + 1)^3
g(x) = 3 x+ 1
Evaluate the function composition.
(fog)(-64) =
Answer:
-8
Step-by-step explanation:
plz watch all steps in picture
The value of the composition function (f·g)(-64) is 1750329.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=(x+1)³ and g(x)=∛x+1.
We need to find (f·g)(-64).
We know that, (f·g)(x)=f(x)×g(x)
Here, f(-64)=(-64+1)³
= -63³
= -250047
g(x)=∛(-64)+1
= -8+1
= -7
Now, (f·g)(-64)=f(-64)×g(-64)
= -250047×(-7)
= 1750329
Therefore, the value of (f·g)(-64) is 1750329.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ7
besties i need help! Select two reasonable first steps for solving the equation 2(4x-11)=10.
A. Divide each side of the equation by 2.
B. Divide each side of the equation 10.
C. Multiply each side of the equation by 2
D. Multiply each side of the equation by 1/10
E. Add 11 to each side of the equation.
F. Use the Distributive Property to simplify the right side.
G. Use the Distributive Property to simplify the left side.
Find the approximate side length of a square game board with an area of 132 in?
(Round to the nearest inch as needed)
Please explain to me how you got the answer cuz I want to learn!!
make sense of this. PLSSSS 15 POINTSSSSS
==================================================
Explanation:
The volume is 296 cm^3 and the height of the box is 8 cm
The area of the top is 296/8 = 37 cm^2. I'm using the idea that
volume of box = (area of base)*(height)
--------------------
The area of the top is 37 cm^2. Apply the square root to get sqrt(37) = 6.08276 cm which is the approximate length of each side along the top. This only works if the top is a square.
Multiply this by 4 to get 4*6.08276 = 24.33104
The perimeter along the top is roughly 24.33 cm
--------------------
The next task we have to do is convert from inches to centimeters
Multiply by 2.54 to do this.
24 & 1/4 inches = 24 + 1/4 = 24 + 0.25 = 24.25 inches
24.25 * 2.54 = 61.595 cm
The measurement 24 & 1/4 inches converts to about 61.595 cm
This means Adam has about 61.595 cm of ribbon
--------------------
To recap, we found these two facts:
The perimeter of the top is about 24.33 cmAdam has roughly 61.595 cm of ribbonSince the amount he has (61.595) exceeds the perimeter (24.33), this means he does have enough ribbon.
In fact, he has enough ribbon to do 2 boxes because 61.595/24.33 = 2.53 approximately and that rounds down to 2. We don't round to 3 even though we're closer to it.
least commom multiple of 2 and 4?
Answer:
4
BRAINLIEST, PLEASE!
Step-by-step explanation:
Multiples of 2: 2, 4, 6, 8, 10
Multiples of 4: 4, 8, 12, 16, 20
Which of the following lists is in order from smallest to largest?
0.05, 0.2, 0.48, 0.6
0.2, 0.05, 0.48, 0.6
0.05, 0.2, 0.6, 0.48
0.2, 0.48, 0.05, 0.6
Answer:
0.05, 0.2, 0.48, 0.6
Hope it helps
Answer:
A
Step-by-step explanation:
0.05 < 0.2 < 0.48 < 0.6
the sum of three consecutive even integers
Answer:look below
Step-by-step explanation:Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6=108.
Which expression is equivalent to 7.90 + 8.5 + 8.60 + 1.3?
O 16.4u + 9.9
0 -0.7u + 9.8
Submit Answer
O 16.54 + 9.8
0 -0.74 + 7.2
о
Answer:
[tex]⚪ \: \: 16.5u + 9.8[/tex]
Step-by-step explanation:
[tex]7.9u + 8.5 + 8.6u + 1.3 \\ = (7.9 + 8.6)u + 8.5 + 1.3 \\ = 16.5u + 9.8[/tex]
Solve 1/x = 1/a + 1/b find x
Answer:
[tex]x=\frac{ab}{a+b}[/tex]
Step-by-step explanation:
Combine the two fractions on the right by using the common denominator ab.
[tex]\frac{1}{x}=\frac{b}{ab}+\frac{a}{ab}\\=\frac{b+a}{ab}[/tex]
If two quantities are equal, then their reciprocals are equal.
[tex]x=\frac{ab}{b+a}[/tex]
Answer:
x = [tex]\frac{ab}{b+a}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{x}[/tex] = [tex]\frac{1}{a}[/tex] + [tex]\frac{1}{b}[/tex]
Multiply through by abx ( the LCM of denominators ) to clear the fractions
ab = bx + ax ← factor out x from each term on the left side
ab = x(b + a) ← divide both sides by (b + a)
[tex]\frac{ab}{b+a}[/tex] = x
In triangle ABC, m
a. 81°
b. 61° c. 71
d. 51°
A bag has 6 watermelon, 5 grape and 1 green apple jolly rancher. You pick one out, replace it, then pick
another. What is the probability of picking 2 watermelon jolly ranchers?
Answer:
[tex]\frac{1} {144}[/tex]
Step-by-step explanation:
The probability of picking 1 watermelon is 1 out of 12.
So [tex]\frac{1}{12}[/tex] × [tex]\frac{1}{12}[/tex] = [tex]\frac{1} {144}[/tex]
I hope this helps!
pls ❤ and mark brainliest pls!
nine and twenty hundredths in standard form
Answer:
[tex]9.2[/tex]
Step-by-step explanation:
20 hundredths is 0.2 and 9 is 9. 9+0.2=9.2.
Side note:
All you had to do is change 9 and 20 tenths into decimals.
How to find the absolute value of |2x+3|=13
Answer:
x=5 or x = -8
Step-by-step explanation:
|2x+3|=13
There are two solutions to this problem, one positive and one negative
2x+3 =13 and 2x+3 = -13
Subtract 3 from all sides
2x+3-3 = 13-3 2x+3-3 = -13-3
2x = 10 2x = -16
Divide each side by 2
2x/2=10/2 2x/2 = -16/2
x = 5 x = -8
during a cruise Mike wants to maintain his exercise schedule. He learns that on the ship’s track three laps is 5/8 of a mile. If mike wants to run 3 miles how many laps does he need to run
[tex]\frac{6}{0}[/tex]
Answer:
Not Defined
Step-by-step explanation:
Anything divided by 0 is said to be infinity or not defined.
A movie with an aspect ratio of 1.85:1 is shown as a letterboxed image on a newer 50-inch 16:9 television. Calculate the height of the image, the height of each barely visible black bar at the top and bottom of the screen, and the percent of the screen’s area that is occupied by the image. Use a variety of representations to justify your response.
The aspect ratio of a Television is the ratio of the width to the height of the television.
The height of image on the 50-inch television is 24.48 inchesThe height of each black bar is 23.52 inchesThe percentage of the screen area occupied is 96.08%The size of a TV is calculated using Pythagoras theorem. Assume the length ratio of the new 50-inch 16:9 TV is x.
The ratio is represented as:
[tex]Width : Height = 16 : 9[/tex]
Using Pythagoras theorem, we have:
[tex](16x)^2 + (9x)^2 = 50^2[/tex]
[tex]256x^2 + 81x^2 = 2500[/tex]
[tex]337x^2 = 2500[/tex]
Divide both sides by 337
[tex]x^2 = 7.42[/tex]
Take square roots of both sides
[tex]x = \sqrt{7.42[/tex]
[tex]x = 2.72[/tex]
So, the width of the image is:
[tex]Width = 16x[/tex]
[tex]Width = 16 \times 2.72[/tex]
[tex]Width = 43.52[/tex]
The height of the image is then calculated as:
[tex]Height = 9x[/tex]
[tex]Height = 9 \times 2.72[/tex]
[tex]Height = 24.48[/tex]
The height of the image is 24.48 inches
The height of each black bar is calculated as follows:
[tex]Width : Height = 1.85 : 1[/tex]
Express as fraction
[tex]\frac{Height}{Width}= \frac{1}{1.85}[/tex]
Make Height the subject
[tex]Height = \frac{1}{1.85}\times Width[/tex]
Substitute [tex]Width = 43.52[/tex]
[tex]Height = \frac{1}{1.85}\times 43.52[/tex]
[tex]Height = 23.52[/tex]
The height of each black bar is 23.52 inches
Lastly, the percentage of the screen’s area that is occupied by the image
First, we calculate the area of the bars
[tex]A_1 = Height \times Width[/tex]
Where:
[tex]Height = 23.52[/tex] and [tex]Width = 43.52[/tex]
So:
[tex]A_1 = 23.52 \times 43.52[/tex]
[tex]A_1 = 1023.59[/tex]
Next, calculate the area of the 50-inch TV
[tex]A_2 = Height \times Width[/tex]
Where
[tex]Width = 43.52[/tex] and [tex]Height = 24.48[/tex]
So:
[tex]A_2 = 24.48 \times 43.52[/tex]
[tex]A_2 = 1065.37[/tex]
So, the percentage occupied on the screen area is:
[tex]\% Screen = \frac{A_1}{A_2} \times 100\%[/tex]
[tex]\% Screen = \frac{1023.59}{1065.37} \times 100\%[/tex]
[tex]\% Screen = \frac{102359}{1065.37} \%[/tex]
[tex]\% Screen = 96.08 \%[/tex]
Hence, the percentage of the screen area occupied is 96.08%
Read more about aspect ratios at:
https://brainly.com/question/17231027
let the dimensions of a rectangle be (4*(871209)^(5)+3*49762105) ft. by (7*(871209)^(3))-(49762105) ft. determine the area of the rectangle
Answer:
Area = Approximately 9.293 x [tex]10^{48}[/tex]
help me please i forgot how to do this
Answer:
domain is where the line crosses the x-axis, and range is always all real numbers
Step-by-step explanation:
If △ABC is translated down nine unit(s) and to the right two unit(s), which
of the following would be the new coordinates of point A?
Answer:
A'(2, -5)
Step-by-step explanation:
we only need to focus on point a (0,4). The translation is moved 9 units down and 2 units to the right, so point (x,y) would become (x+2, y-9). plug 0 and 4 in for x and y respectively, and you get (0+2, 4-9) = (2, -5)
Can someone explain this?
If S is directly proportional to t squared and s= 8 when t= 4 find the value of s when t= 3
Answer:9/2
Step-by-step explanation:
Answer:
1.5
Step-by-step explanation:
k=8÷16=0.5
s=0.5×3=1.5
Find the rational approximation of √15.
9514 1404 393
Answer:
1921/496
Step-by-step explanation:
There are many rational approximations to √15, some better than others.
A linear approximation is often used:
√15 ≈ 3 +(15-3^2)/(4^2-3^2) = 3 6/7 = 27/7
That can be refined by one iteration of the Babylonian method of determining the root:
√15 ≈ (27/7 +15/(27/7))/2 = (3 6/7 +3 8/9)/2 = 3 55/63 = 244/63
This value is equivalent to the root rounded to 4 decimal places.
__
Another iteration of the Babylonian method gives the approximation ...
√15 ≈ 119071/30744, equivalent to the root rounded to 9 decimal places.
__
The approximation 1921/496 is the best approximation that has a denominator under 1000.
_____
Additional comment
Successive rational convergents of the continued fraction approximation of √15 can be found as ...
a'/b' = (3a +15b)/(a +3b)
This method adds approximately one more good decimal place per iteration.
__
Successive rational approximations can be found using the Babylonian method (Newton's method iteration) as ...
a'/b' = (a² +15b²)/(2ab)
This method has "quadratic" convergence. It approximately doubles the number of good decimal places with each iteration.
You can use 3/1, 4/1, or 27/7 to begin either of these iterations.
please help
answer choices are:
A. (3, -3)
B. (1,-6)
C. (8,-6)
D. (-1, 3)
Answer:
C ( 8,-6)
Because you move the points according to the rule.
a + 1 = 3000
a = ?
This is my first question, I know the answer. I just wanna test the platform.
Answer:
2999
Step-by-step explanation:
a + 1 = 3000
=> Subtracting 1 from both sides,
=> a + 1 - 1 = 3000 - 1
=> a = 2999
Which is 6 logx + 5log(x - 8) written as a single logarithm?
Answer:
log ([tex]x^{6}[/tex][tex](x-8)^{5}[/tex]
Step-by-step explanation:
Using the rules of logarithms
log [tex]x^{n}[/tex] ⇔ nlog x
log x + log y = log(xy)
Given
6 log x + 5log(x - 8)
= log[tex]x^{6}[/tex] + log[tex](x-8)^{5}[/tex]
= log ([tex]x^{6}[/tex][tex](x-8)^{5}[/tex] )
Answer:
d) on edge
Step-by-step explanation:
have a nice day :)
a gift house allowed 20% discount on the marked price of a doll, 13% VAT was levied on it. If the doll was sold as Rs 1808. What was its marked price?
Answer:
Profit = 20% = 360 Rs
So, Cost Price = 360 / 20 * 100 = 1800 Rs
And Sales Price = 1800 + 360 = 2160 Rs
Discount = 25% of marked price
So Sales Price = (100 - 25) % = 75 % of mark price.
=> 2160 = 75% of marked price.
=> marked price = 2160/75 * 100 = 2880 rs
Hope it helps you.
what is -2 1/3 - (-5)=
Answer:
[tex] \frac{8}{3} [/tex]
Step-by-step explanation:
[tex] - 2 \frac{1}{3} - ( - 5)[/tex]
convert mixed fraction into improper fraction.
[tex] - \frac{7}{3} + ( - 5)[/tex]
calculate the sum of the fraction:
[tex] \frac{8}{3} [/tex]