Answer:
the larger number is 452/7 and the smaller number is 1356/28
sin^2 x - 2sinx + 2 = sin^2 3x
Recall the triple angle identity for sine:
sin(3x) = 3 sin(x) cos²(x) - sin³(x)
… = 3 sin(x) (1 - sin²(x)) - sin³(x)
… = 3 sin(x) - 4 sin³(x)
So the equation is equivalent to
sin²(x) - 2 sin(x) + 2 = sin²(3x)
sin²(x) - 2 sin(x) + 2 = (3 sin(x) - 4 sin³(x))²
sin²(x) - 2 sin(x) + 2 = 9 sin²(x) - 24 sin⁴(x) + 16 sin⁶(x)
16 sin⁶(x) - 24 sin⁴(x) + 8 sin²(x) + 2 sin(x) - 2 = 0
or, by replacing y = sin(x),
16y ⁶ - 24y ⁴ + 8y ² + 2y - 2 = 0
By inspection, y = 1 is a root, since
16 - 24 + 8 + 2 - 2 = 0
so we get one family of solutions,
sin(x) = 1 ===> x = arcsin(1) + 2nπ = π/2 + 2nπ
Now suppose y ≠ 1. Dividing both sides of the sextic equation by y - 1 then gives
(16y ⁶ - 24y ⁴ + 8y ² + 2y - 2)/(y - 1) = 0
16y ⁵ + 16y ⁴ - 8y ³ - 8y ² + 2 = 0
Unfortunately, the remaining roots can only be obtained through numerical methods. Using a calculator, you would find
y ≈ -1.127
y ≈ -0.475 ± 0.368i
y ≈ 0.539 ± 0.127i
But if you're solving over the reals, you can ignore these solutions. Remember that sin(x) is bounded between -1 and 1, and its value goes outside this interval only when x is complex.
Write the word sentence as an inequality
6 times a number x is at most 47
Writing as a word sentence, the inequality is:
[tex]6x \leq 47[/tex]
6 times a number x is 6 multiplied by x, that is: [tex]6x[/tex].At most 47 means that it is less than, or equals, to 47, hence:[tex]6x \leq 47[/tex]
Hence, the desired inequality, from the given word sentence, is:
[tex]6x \leq 47[/tex]
A similar problem, in which a word sentence is written as an inequality, is given at https://brainly.com/question/11713066
Evaluate |bcl. given a = 5, b= -3, and c= -2.
O -6
O -5
O 5
O 6
Answer:
6
Step-by-step explanation:
(-3)(-2) is 6 because if you multiply two negatives it equals a positive, and the absolute value of 6 is 6.
Answer:
6
Step-by-step explanation:
abs(bc)=abs(-3*-2)=abs(6)=6
1) make q the subject of the formula 4(q+p)=5+7q
2) Make x the subject of the formula y=2a-bx^2
Answer:
1) [tex]q = \frac{4p}{3} -\frac{5}{3}[/tex]
2) [tex]x = \frac{\sqrt{b -y + 2a} }{b}[/tex]
Step-by-step explanation:
1) 4(q + p) = 5 + 7q
Multiply 4(q + p):
4q + 4p = 5 + 7q
4p - 5 = 7q - 4q
4p - 5 = 3q
[tex]\frac{4p}{3} - \frac{5}{3} = \frac{3q}{3}[/tex]
[tex]\frac{4p}{3} - \frac{5}{3} = q[/tex] or [tex]q = \frac{4p}{3} - \frac{5}{3}[/tex]
Help on this please will make brainliest
Answer:
help on what?
Step-by-step explanation:
Answer:
You need to post a question or a screenshot of the question so someone can help you!
What is the scale factor from Figure A to Figure B?
Answer:
1/3Step-by-step explanation:
The figure B is the scaled copy of the figure A.
The both figures are similar to each other.
The scale factor is the ratio of corresponding sides of figure B to A:
k = 3/9 = 1/3or
k = 1.2/3.6 = 1/3On figure A sides are.
9,3.6On figure B sides are.
3,1.2Scale factor[tex]\sf\longmapsto k=\dfrac{3}{9}=\dfrac{1.2}{3.6}=\dfrac{1}{3}[/tex]
At a pet store the ratio of cats to dogs sold was 6 : 5. If there were 12 cats that were sold, how many dogs were sold?
Which statement is TRUE?
Answer:
it is a or d
Step-by-step explanation:
Plot each pair of points in the Cartesian plane and solve for the distance between them. Write your answer on a separate one whole graph paper. ( 15 points) 1. A(0,8) and B(5,5) 2. C(3, 1) and D(0,-2) 3. EC -6,3) and F(-6,-2)
Answer:
hame naghi ahta
Step-by-step explanation:
Alex's school had 20 hours for 400 students. Abbey's school has 225 students riding 15 uses. Whose school has the greater ratio of students/buses?
Answer:
20/400 or 20 to 400
Step-by-step explanation:
Fill in the function table: y = -2(x - 1)
please help
we first substitute the x
y= -2(-2-1)
=6
and then use a calculator to do the sum
which gives us 6
y= -2(-1-1)
= 4
y= -2(0-1)
=2
y= -2(1-1)
=0
y= -2(2-1)
=-2
me need a lot of help
The graph shows the amount of money you and a friend are saving for a camping trip.
You: 4 weeks 60 dollars. 8 weeks 120 dollars.
Friend: 2 weeks 40 dollars. 5 weeks 100 dollars
B) Find the slope of each line.
C) How much more money does your friend save each week than you?
D) The camping trip costs $165. How long well it take you to save enough money
What is 241m as a fraction of 5.4km
Answer:
i think 223/499
Step-by-step explanation:
There are 20 black, 15 white, 12 green, 12 red, 9 blue, and 2 yellow candies in a box. How many candies should you take (without looking at them) to be sure that you have at least 3 candies the same color?
Answer:
All of them lol.
Step-by-step explanation:
If you take all of them, you have a 100% chance at getting at LEAST 3 candies of the same color.
what is 4-1/4 help please
Answer:
3 3/4
Step-by-step explanation:
Because 1 = 4/4
then 4 = 12/4
then you take away 1/4
And get 11/4
Then you Turn that into a mixed number
And get 3 3/4
Decimal form is 3.75
Answer:
15/4 alternate answers - 3 3/4 or 3.75
that's what I got
DOES ANYONE KNOW THIS ONE?
Answer:
no sorry
Step-by-step explanation:
I NEED THE RIGHT ANSWER ASAP NO LINKS!!!
Answer:
the answer is 21.8
Substitute the value of the variable into the equation and simplify.
please help me solve for X
Answer:
-7
Step-by-step explanation:
Find the value of x.
Answer:
-5
Step-by-step explanation:
hope it works out for you
CAN SOMEONE PLEASE HELP WITH QUESTIONS 3 THROUGH 11?? YOU DON’T EVEN HAVE TO DO ALL OF THEM JUST THE ONES U FEEL LIKE DOING (ILL MARK AS BRAINLIEST!!)
Answer:
3. 3/2
4. -1/3
5. -3.5
6. -6and 2/3
7. -18and 13/24
8. 1/18
9.-2.6
10.-1.83
11. 14.963
Step-by-step explanation:
HOPE THIS HELPS, if not see me in the comments
BRANILIEST PLZZZ
A water tank in Stewart's
home had a small, steady
leak.
Loss of 1 3/5 mL in 10 min.
a. Use a complex fraction to
represent the change in the
volume of water in 1 minute.
___ milliliters
10 minutes
b. Simplify the complex fraction to find the change in the volume of water in the tank in 1 minute.
The change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
Since a water tank in Stewart's home had a small, steady leak loss of 1 3/5 mL in 10 min, to find the change in the volume of water in 1 minute, the following calculation must be performed:
The total leak must be calculated and divided by the 10 minutes duration. 3/5 = 0.6 1 + 0.6 = 1.6 1.6 / 10 = 0.16
Therefore, the change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
Learn more in https://brainly.com/question/19747831
solve the pattern:
15, 17, 32, 49, 81 __ __ ← those are the blank spaces.
Answer:
130 and 211
Step-by-step explanation:
15+17= 32
17+32=49
32+49=81
49+81=130
81+130=211
Answer:
130 and 211
Step-by-step explanation:
15,17,32,49,81 _ _
15+2=17+15=32+17=49+32=81
that mean 81+ 49=130
and 81+130= 211
Hence, the answer is 130 and 211.
How many tons are equal to 54,000 pounds?
Answer:
I think About 27 short ton
What is the equation of the line that passes through the points (4, 15) and (0, 3)?
Answer:
Y=3x+3
Step-by-step explanation:
Gradient = :[tex]\frac{y2-y1}{x2-x1}[/tex] = :[tex]\frac{3-15}{0-4}[/tex] = :[tex]\frac{-12}{-4}[/tex] = 3
Y= mx + c
y = 3x + c
Insert x and y values for first point(4,15)
15 = 3 (4) + c
15 = 12 + c
3 = c
Y=3x +3
Answer:
The equation of the line is y=3x+3
Step-by-step explanation:
y=mx+b is the y intercept form of the equation of this line.
m=slope, and we find the slope by the equation m=y2-y1/x2-x1. Plugging our number into that formula, we get m=3 - 15/ 0 - 4, or -12/-4, which simplifies to 3.
Now we can add our slope into the formula.
y=3x+b
Next, we solve for the y intercept, or b. You can use whatever point to get the answer, but I will use 4 ,15).
y=mx+b is the equation, or substituting the numbers, gets you 15=3×4+b. now solve for b: b=15-(3)(4). b=3.
now, with slope and y intercept plugged in, the final equation is. y=3x+3
Find the unit rate:
150 words read in 8 minutes
Step-by-step explanation:
the unit rate: 150/8 × 60 minutes =
1,125 words/hour
Answer:
18,75 word read/minutes
or :
1,125 word read/hour
Step-by-step explanation:
The unit rate :
= 150 words read : 8 minutes
= 150/1 words read : 8/1 minutes
= 150/1 × 1/8 word read/minutes
= 150/8 word read/minutes
= 18 6/8 word read/minutes
= 18 3/4 word read/minutes
= 18,75 word read/minutes
= 1,125 word read/hour
What is the area of a parallelogram with a base of 20 centimeters and a height of 9 centimeters?
Answer:
Area = 108
Step-by-step explanation:
A = base * height
A = 20 * 9 = ?
A = 20 * 9 = 108
Triangle ABC is shown. What value of x will prove that Triangle ABC is a right triangle?
In the given triangle ABC in the figure, the value obtained for x will be equal to 6.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given information in the question,
Use the equation of Pythagoras' theorem,
h² = p² + b²
(2x - 2)² = x² + (x - 2)²
4x² - 2(2x)(2) + 4 = x² + x² + 4 + 4x
4x² - 8x + 4 = 2x² + 4x + 4
4x² - 2x² - 8x - 4x + 4 - 4 = 0
2x² - 12x = 0
2x² - 12x = 0
2x(x - 6) = 0
So,
2x = 0
⇒ x = 0, it is not possible.
Or,
x - 6 = 0
x = 6
To know more about Triangle:
https://brainly.com/question/2773823
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The given question is incomplete, the complete question might be in the attachment.
what is 1+1-923422354x2x26757635
Answer: [tex]-4.9417197e+16[/tex]
Step-by-step explanation:
Drag each label to the correct location.
Use what you’ve learned about proportional relationships to classify these equations as direct variation, inverse variation, or neither.
PLEASE HELPPP
Answer:
Step-by-step explanation:
