sin(x - 20)° = cos(5x - 10)°
Expand 5x - 10 in terms of x - 20:
5x - 10 = 5x - 100 + 90
… = 5 (x - 20) + 90
and recall that for all θ, cos(θ + 90)° = - sin(θ)°, so
sin(x - 20)° = cos(5 (x - 20) + 90)°
sin(x - 20)° = - sin(5 (x - 20))°
Replace (x - 20)° = y ° to make this a bit easier to read:
sin(y °) = - sin(5y )°
Expand the right side in terms of powers of sin:
sin(5θ) = 5 sin(θ) - 20 sin³(θ) + 16 sin⁵(θ)
so the equation becomes
sin(y °) = -5 sin(y °) + 20 sin³(y °) - 16 sin⁵(y °)
16 sin⁵(y °) - 20 sin³(y °) + 6 sin(y °) = 0
Replace z = sin(y °) to get a polynomial equation:
16z ⁵ - 20z ³ + 6z = 0
Factorize the left side:
2z (8z ⁴ - 10z ² + 3) = 0
2z (2z ² - 1) (4z ² - 3) = 0
Solve for z :
• 2z = 0 → z = 0
• 2z ² - 1 = 0 → z ² = 1/2 → z = ± 1/√2
• 4z ² - 3 = 0 → z ² = 3/4 → z = ± √3/2
Solve for y in each case above:
• z = sin(y °) = 0 → y = 0 + 360n or y = 180 + 360n
(where n is any integer)
These solutions can be combined into one family, y = 180n.
• z = sin(y °) = -1/√2 → y = 225 + 360n or y = 315 + 360n
• z = sin(y °) = 1/√2 → y = 45 + 360n or y = 135 + 360n
These solutions can also be combined, y = 45 + 90n.
• z = sin(y °) = -√3/2 → y = 240 + 360n or y = 300 + 360n
• z = sin(y °) = √3/2 → y = 60 + 360n or y = 120 + 360n
These can be combined as y = 60 + 180n or y = 120 + 180n.
Solve for x in each case:
• y = x - 20 = 180n → x = 20 + 180n
• y = x - 20 = 45 + 90n → x = 65 + 90n
• y = x - 20 = 60 + 180n → x = 80 + 180n
• y = x - 20 = 120 + 180n → x = 140 + 180n
Combine the like terms to create an equivalent expression,
Зу +6 – у
HELPPPPPP NOWWWW
100 points
Answer: 2y+6
Step-by-step explanation:
Answer:
x and y
Step-by-step explanation:
Stella works for a company that makes aluminum cans. A large soup can have a radius of 8 centimeters and a height of 20 centimeters. How much aluminum is used to make the can?
Out of all of the topics covered so far in the course (whole numbers, fraction notation: multiplication, division, and mixed numerals), which did you enjoy the most? Which do you enjoy the least? Why?
Answer: I would say I've liked multiplication the most and division the least! I have always gotten multiplication because.. I don't really know. It's just easy for me. I can't really explain. For multiplication though.. I have never gotten it. It is the exact opposite. I've never understand how you have to skip a digit because you can't divide it to the other number.
Step-by-step explanation:
Hope this helps! This is my opinion.
I made this don't copy my answer
if f(x) and g(x) are inverse function, find f(g(x)).
Answer:
The answer is x.
Step-by-step explanation:
Inverse functions undo each other, so if f(x) spits out a number, g(x) reverses that and gives you x again.
What is the lateral surface area of this net
Help!!!
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Answer:
720 square feet
Step-by-step explanation:
The lateral area is the area of the central rectangle of the net. It is 12+12+12 = 36 feet long and 20 ft wide.
The lateral area is (36 ft)(20 ft) = 720 ft².
1. x²+2xy+y²
2. x²-8x+16
3. 16a⁴_24a²b²+9b
Answer:
1.(x+y)²
2. (x-4)²
3. (4a²-3b²)²
if i have 71% of something done but i need 100% done in 25 days how many percent should i complete everyday
Answer:
.75% a day
Step-by-step explanation:
Solve the quadratic equation by using either a numeric or a graphic approach.
Answer:
C
Step-by-step explanation:
x²-14x-49=0
x²-14x+49=49+49
(x-7)²=98
(x-7)²=49×2
x-7=±7√2
x=7+7√2=7(1+√2)≈7(1+1.414)≈7(2.414)≈16.898≈16.9
or
x=7-7√2=7(1-√2)≈7(1-1.414)≈-7×0.414≈-2.898≈2.9
Pueden ayudarme pliiis
Un niño lanza una piedra hacia abajo con velocidad inicial vy = -2 m/s, desde una
altura de 25 m.
a. ¿cuánto tiempo demora la piedra en llegar al suelo?
b. Determina la velocidad para ese tiempo.
c. Realiza las gráficas de posición, velocidad y aceleración para el desplazamiento
de la piedra mientras está en movimiento.
Answer:\b
Step-by-step explanation:
Which function is shown in the graph below?
y= 22-2 + 3
y = 2X+2+3
y = 2X-3+2 Y=2^x+3+2
Answer:
B 2^x+2 +3
Step-by-step explanation:
hope this helps :)
The function that matches the graph and the given points (7, 0) and (-8, 5) is: y = 2X + 2 + 3. (option b)
This function seems to have a typo, as it simplifies to y = 23, which is a constant value and does not depend on the variable x. This means the graph would be a horizontal line at y = 23 and would not pass through the points (7, 0) and (-8, 5).
y = 2X + 2 + 3
This function can be simplified to y = 2X + 5. Evaluating the points (7, 0) and (-8, 5) in this function:
For (7, 0):
y = 2 * 7 + 5
y = 14 + 5
y = 19
For (-8, 5):
y = 2 * (-8) + 5
y = -16 + 5
y = -11
y = 2X - 3 + 2 Y = 2ˣ + 3 + 2:
It seems there is a typo in this option with "Y" being capitalized. Assuming it is meant to be y, we have two separate functions:
a. y = 2X - 3 + 2
b. y = 2ˣ + 3 + 2
a. For y = 2X - 3 + 2:
Evaluating the points (7, 0) and (-8, 5):
For (7, 0):
y = 2 * 7 - 3 + 2
y = 14 - 3 + 2
y = 13
For (-8, 5):
y = 2 * (-8) - 3 + 2
y = -16 - 3 + 2
y = -17
b. For y = 2ˣ + 3 + 2:
Evaluating the points (7, 0) and (-8, 5):
For (7, 0):
y = 2⁷ + 3 + 2
y = 128 + 3 + 2
y = 133
For (-8, 5):
y = 2⁻⁸ + 3 + 2
y ≈ 0.004 + 3 + 2
y ≈ 5.004
To know more about function here
https://brainly.com/question/28193995
#SPJ2
I need help on how to do this
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Answer:
see attached
Step-by-step explanation:
a) A system of equations has no solutions when the graphs of those equations do not intersect. If the equations are equations of a line, then the lines must be parallel in order for them not to intersect.
Any parallel line will do.
__
b) There is one solution when the graphs intersect in exactly one point.
Any line that crosses the one shown will do.
__
c) There are infinite solutions when the graphs describe the same curve.
A line overlapping the one shown is the one you want.
Sarah and Nathan each picked a bucket of strawberries. Sarah picked 4 pounds, and Nathan picked 3 pounds. How much more did Sarah pick than Nathan?
1 pounds
2 pounds
pound
1 pound
Answer:1 pound
Step-by-step explanation:
Directly you see from Qestion Sarah picked 4 pounds and Nathan 3...for difference 4-3=1
Answer:
A: 1 pound
Step-by-step explanation:
4lbs -- 3lbs = 1lbs
A rental car company charges a fixed fee of $30 plus $0.05 per mile. The Boggs family paid $49.75 for their car rental. How many miles did they drive? Write an equation and solve.
Answer: 395
Step-by-step explanation:
Need help question #4. Show steps please
Answer:
C.
Step-by-step explanation:
We are given the integral:
[tex]\displaystyle \int_1^2\frac{x^7-4x^3+6}{x^2}\, dx[/tex]
And we want to select its equivalent form.
We can simply divide the fraction. Therefore:
[tex]=\displaystyle \int_{1}^2\frac{x^7}{x^2}-\frac{4x^3}{x^2}+\frac{6}{x^2}\, dx[/tex]
Simplify:
[tex]\displaystyle =\int_1^2 x^5-4x+6x^{-2}\, dx[/tex]
Our answer is C.
i have been struggling with this question for 30mins. if you answer it can you please show work? thank you
Answer:
a)22
Step-by-step explanation:
Simplify 45/63 show work plz
Daniel has 250 songs on his MP3 player.
Ninety-five of the songs are by the same singer.
What percent of Daniel's songs are by that one
singer??
A. 26%
B. 38%
C. 62%
D. 83%
Consider the expression
10x2 + 5x – 25.
What is the GCF (greatest common factor)?
Answer:
5
Step-by-step explanation:
Answer:
Its def 5, My calculations are never wrong
Which statement best describes the values of x and y in the table?
If you don’t know I don’t answer (NO LINKS )
Uhh I might just answer this so the guy who did so much can get brainliest
Can someone help me with this please ?
Answer:
The corner is 90 degrees so I believe you add them so 60+90+30 is 180!!!
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Jonathan sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
140 visitors purchased no costume.
166 visitors purchased exactly one costume.
32 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase one or more costumes as a percent to the nearest whole number.
Answer: it should be A/1
PLEASE HELP ME!!! PLEASE
Answer:
it should be (8,-7)
Step-by-step explanation:
Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 3 (*sqaure root sign*) t (20 − t), [0, 20]
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Answer:
maximum: 15∛5 ≈ 25.6496392002minimum: 0Step-by-step explanation:
The minimum will be found at the ends of the interval, where f(t) = 0.
The maximum is found in the middle of the interval, where f'(t) = 0.
[tex]f(t)=\sqrt[3]{t}(20-t)\\\\f'(t)=\dfrac{20-t}{3\sqrt[3]{t^2}}-\sqrt[3]{t}=\sqrt[3]{t}\left(\dfrac{4(5-t)}{3t}\right)[/tex]
This derivative is zero when the numerator is zero, at t=5. The function is a maximum at that point. The value there is ...
f(5) = (∛5)(20-5) = 15∛5
The absolute maximum on the interval is 15∛5 at t=5.
Please somebody help me and solve this problem
Answer:
this is the equation for the graph y=(x+3)(x-2)
e)
2 Before you calculate these answers, first estimate the
a) 30 870 ÷49
b) 221 340 ÷17
c) 100 719÷ 279
d) 75 640 ÷310
Step-by-step explanation:
1.) 630
2.) 13020
3.) 361
4.) 244
The table shows the width and length of different pictures that Nethan has enlarged for the school yearbook:
WILL GIVE BRAINLIEST
Enlarged Pictures
Width (inch) Length (inch)
4 5
8 10
12 15
Based on the table, what is the length of a picture that has a width of 20 inches?
Answer:
from 2nd and 3rd figures
width of 2nd figure + width of 3rd figure
8 + 12 = 20inch
so, length of a picture that has a width of 20 inches will be , length of 2nd figure + length of 3rd figure
=10 + 15
=25 inch
Step-by-step explanation:
Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $49. At another store she can borrow the tile saw for free if she buys tiles there for $1.29 per tile. How many tiles must she buy for the cost to be the same at both stores?
Margo must buy
tiles for the cost to be the same at both stores.
Answer:
Also need help
Define the following terms.
Mode:
Median
Mean:
Range:
M.A.D:
1.Q.R:
Answer:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.
1Q: 1st Quarter
R: Range
Step-by-step explanation:
I’ll give points and brainalist for correct answer / explanation
Answer:
i think you forgot to attach the image lol
Step-by-step explanation: