4sin2xcosx+sin3x=sin<3,14+x>
Answers
The solution to 4sin2xcosx+sin3x=sin<3,14+x> is x = nπ, where n = ±{0, 0.5, 1, 1.5....}
How to solve the equation?The equation is given as:
4sin2xcosx+sin3x=sin<3,14+x>
Rewrite properly as:
4sin(2x)cos(x)+sin(3x)=sin(3.14+x)
Next, we split the equation as follows:
y = 4sin(2x)cos(x)+sin(3x)
y = sin(3.14+x)
Next, we plot the graph of both equations (see attachment)
From the attached graph, we have:
x = nπ, where n = ±{0, 0.5, 1, 1.5....}
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Related Questions
A triangle has two sides of lengths 10 and 14 what value could the length of the third side be
Answers
Answer:
17.20465053
Step-by-step explanation:
17.20465053 or
17.2 (to 1 dp)
Answer:
Third side has to be greater than 4 and less than 24.
Step-by-step explanation:
A triangle is valid if the sum of two sides is greater than the third side. That has to be the case for each of the sides. So let the sides of triangle be a, b and c.
a + b > c
a + c > b
b + c > a
Given:
a = 10
b = 14
We are looking for the third side, c.
First inequality:
a + b > c
10 + 14 > c
24 > c
This tells us that c has to be less than 24.
Second inequality:
a + c > b
c > b - a
c > 14 - 10
c > 4
This tells us that c has to be grater than 4.
Third inequality:
b + c > a
c > a - b
c > 10 - 14
c > -4
This tells us that c has to be greater than -4. But we also know that c has to be greater than 4, so we take 4 as the minimal value for c.
Final answer:
4 < c < 24
Third side has to be greater than 4 and less than 24.
ignore the answer i clicked on, i did not mean to click it
Answers
Answer:
20√2Step-by-step explanation:
The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.
Diagonal = 5 * 2 = 10
P = 2√2 * 10
P = 20√2
What is the distance between the points (4, 5) and (10, 13) on a coordinate
plane?
Answers
Answer:
10
Step-by-step explanation:
square root of 6^2 + 8^2
which of the sentence is true?
Answers
Answer:
The graph of the circle is not a function
The circle graph shows the results of a survey of registered voters the day of an election.
The error given in the graph means that the actual percentage could be 2% more or 2% less than the parent reported by the survey.
What are the minimum and maximum percentages of voters who could vote Republicans? Green?
How can you use absolute value equations to represent your answers in part (a)?
One candidate receives 44% of the vote, Which party does the candidate belong to? Explain.
Answers
The minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%
The minimum and maximum percentages of voters in Republicans? Green?The attached circle graph represents the missing information in the question.
From the graph, we have:
Republicans = 42%
Green = 2%
The actual percentage is given as: ±2%
So, we have:
Republicans = 42% ± 2% = (40%, 44%)
Green = 2% ± 2% = (0%, 4%)
Hence, the minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%
The absolute value equations of part (a)?We have:
The actual percentage is given as: ±2%
Let the number of votes be on the circle graph be x and the range be y.
So, we have:
y - x = ±2%
Express as absolute value equation
|y - x| = 2%
For Republicans, we have:
|y - 42%| = 2%
For Green, we have:
|y - 2%| = 2%
Hence, the absolute value equations are |y - 42%| = 2% and |y - 2%| = 2%
The party of candidate that receives 44% voteIn (a), we have:
Republicans = 42% ± 2% = (40%, 44%)
Hence, the party of candidate that receives 44% vote is Republican
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Jane and David had identical chocolate bars.
David ate 78 of his chocolate bar.
Jane ate more of her chocolate bar than David.
What fraction of her chocolate bar could Jane have eaten?
Answers
Answer:
Step-by-step explanation:
I'm assuming you meant "David at 78% of his chocolate bar" which means he at 78/100 of his chocolate bar. So if Jane ate more she could've eaten n/100 of her chocolate bar where [tex]78 < n \leq 100[/tex]. Greater than 78 since David at 78/100 and less than or equal to 100 since 100/100 means Jane at the entire thing at 101/100 wouldn't make any sense.
Solve the following compound inequality: (1 point)
-2(x+8) +6 > x-4 or -3x + 12 < 6(x-4)
0x<2 orx>4
Ox>2 orx<4
0x<-2 orx>4
Ox>-2 orx<44
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{First Inequality :} [/tex]
[tex]\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 2x - 10 > x - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 10 + 4 > x + 2x[/tex]
[tex]\qquad \tt \rightarrow \: - 6 > 3x[/tex]
[tex]\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x[/tex]
[tex]\qquad \tt \rightarrow \: - 2 > x[/tex]
[tex]\qquad \tt \rightarrow \: \therefore x < - 2[/tex]
[tex] \textsf{Second Inequality :} [/tex]
[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)[/tex]
[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 36 < 9x[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{36}{9} < x[/tex]
[tex]\qquad \tt \rightarrow \: 4 < x[/tex]
[tex]\qquad \tt \rightarrow \: \therefore x > 4[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 – 6x8 + x3 – 4x + 3?
Answers
All potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational rots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.
The rational root theorem suggests that for a polynomial function
f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.
In the question, we are asked to find the potential rational roots of
f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3.
Comparing the given polynomial function with the standard polynomial function f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, we can say aₙ = 15, and a₀ = 3.
By rational root theorem, we know that all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.
Therefore, we can say that p = {factors of ±3} and q = {factors of ±15},
or, p = {±1, ±3}, q = {±1, ±3, ±5, ±15}.
Now, we can write all potential roots by calculating p/q.
p/q = {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}
Therefore, all potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational roots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.
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What was k? 200 400 600
Answers
Answer:
pls yo give the full question
3. Use the following diagram to solve for x.
Answers
The value of x from the given diagram is -6
Lines and anglesLine is defined as the distance between two points. Given the line RP with the following measures
RP = 17
RQ = x + 14
QP = x + 15
Using the expression
RP = RQ + QP
Substitute
17 = x + 14 + x + 15
17 = 2x + 29
Determine the value of x
2x = 17 - 29
2x= -12
x = -6
Hence the value of x from the given diagram is -6
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Assume that A TUVE AWXY. Which of the following congruence statements
are correct? Check all that apply.
A. ZX=ZU
B. ZY ZV
C. VU = YX
D. TV = WY
E. ZWE ZV
F. ZTE ZX
Answers
Congruent triangles are exact copies of each other. The correct options are 1, 2, 3, and 4.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes the length of line segment AB, and so on for others).
The following details about the two given congruent triangles TUV and WXY can be written,
[tex]\rm m\angle T = m\angle W \: or \: \: \angle T \cong \angle W\\\\\rm m\angle U = m\angle X\: or \: \: \angle U \cong \angle X \\\\\rm m\angle V = m\angle Y \: or \: \: \angle V \cong \angle Y \\\\\rm |TU| = |WX| \: \: or \: \: TU \cong WX\\\\\rm |VU| = |YX| \: \: or \: \: VU \cong VU\\\\\rm |TV| = |WY| \: \: or \: \: TV \cong TV[/tex]
Hence, the correct options are 1, 2, 3, and 4.
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Answer: A,,B, C, D
Step-by-step explanation:
If g(x)=4x^(2)-16 were shifted 7 units to the right and 3 down, what would the new equation be?
Answers
The equation of the transformed function is h(x) = 4(x - 7)² - 19 option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
g(x) = 4x² - 16
The above function shifted 7 units to the right and 3 down.
Applying transformation:
x → (x - 7)
G(x) = 4(x - 7)² - 16
G(x) → G(x) - 3
h(x) = 4(x - 7)² - 16 - 3
h(x) = 4(x - 7)² - 19
Thus, the equation of the transformed function is h(x) = 4(x - 7)² - 19 option (C) is correct.
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100 POINTS!!!!! WILL GIVE BRAINLIEST!!!!!! PLS HELP ASAP!!!!!!!
SHOW ALL WORK!!!!!!! EXPLAIN ALL WORK ASWELL!!!!!!!!!
1.
A theater has 20 rows of seats. If there are 4 seats in the 1st row 12 in the 2nd row, 20 in the 3rd row . How many seats are there in total? Show and explain all work.
Answers
Answer:
1,600 seats in the theater
Step-by-step explanation:
well it seems like each row is being increased by 8 seats each time.
we start with 4 seats in the 1st row. 12 in the 2nd. and 20 in the 3rd. I will make a chart showing you how many seats are in each row.
4th row - 28 5th row - 36 6th row - 44 7th row - 52 8th row - 60 9th - 68 10th - 76 11th - 84 12th - 92 13th - 100 14th - 108 15th - 116 16th- 124 17th - 132 18th - 140 19th - 148 20th - 156
if we add these all together you will get 1,600
Answer:
1600 seats
Explanation:
1st row = 4 seats, 2nd row = 12 seats, 3rd row = 20 seats
This is arithmetic progression with first term (a) being 4 and common difference (d) of 8 and total term (n) of 20.
Sum of arithmetic series:
[tex]\sf S_n = \dfrac{n}{2} ( 2a + (n-1)d)[/tex]
insert values
[tex]\sf S_{20} = \dfrac{20}{2} ( 2(4) + (20-1)8)[/tex]
[tex]\sf S_{20} = 1600[/tex]
A 2-column table with 5 rows. Column 1 is labeled Number of Apples with entries 0, 1, 2, 3, 4. Column 2 is labeled Number of Slices with entries 0, 6, 12, 18, 24.
Use the table to find the constant of proportionality and the equation that represents the relationship.
Let x = number of apples and y = number of slices.
The constant of proportionality is
.
The equation for this relationship is
Answers
Answer:
The constant of proportionality is 6. This makes the relation y = 6x.
Step-by-step explanation:
Concept: As the number of apples are increasing, the number of slices are also increasing. Given that x is the number of apples and y is the number of slices. This means that y is directly proportional to x.
y ∝ x
Let the constant of proportionality be k.
y = kx
For x = 1, y = 6. So, k = 6.
For x = 2, y = 12. So, k = 6.
This follows for all the values.
Clearly, the constant of proportionality is 6.
The relationship will become y = 6x.
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The first term of an arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the last term is 81.
Answers
Answer:
n = 53
Step-by-step explanation:
the sum to n terms of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 3 and a₅ = 9 , then
3 + 4d = 9 ( subtract 3 from both sides )
4d = 6 ( divide both sides by 4 )
d = 1.5
then solving for n
3 + 1.5(n - 1) = 81 ( subtract 3 from both sides )
1.5(n - 1) = 78 ( divide both sides by 1.5 )
n - 1 = 52 ( add 1 to both sides )
n = 53
there are 53 terms in the progression
Answer:
53 terms
Step-by-step explanation:
Finding common difference :
a = 3a + 4d = 94d = 6d = 1.5Solving :
a_{n} = a + (n - 1)d81 = 3 + 1.5n - 1.579.5 = 1.5nn = 53PLEASE HELP ASAP!! Kate is trying to convert an area from meters squared to centimeters squared. She multiplied the area she had by 100 and got the wrong answer. What should she have multiplied the original area by?
1,000
1,000,000
100
10,000
Answers
Answer:
1m=100cm
1m squared=100cm×100cm
1msquared= 10000cm squared
She has to multiply 10000 to convert square centimetres to square meters. Hence option D is correct.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
We know that 1 meter is equal to 100 cm now for a 1-meter square the centimetres will be calculated as,
1m=100cm
1m squared=100cm×100cm
1msquared= 10000cm squared
Hence option D is correct.
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does this function represent a function? yes or no
Answers
Answer:b
Step-by-step explanation:
please help
It is Ms. Smith’s birthday, and her students want to surprise her with a room full of balloons. Use the Fermi process to estimate the number of balloons needed to fill Ms. Smith’s classroom. Assume the classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft. Assume the balloons are spheres with a radius of 0.35 ft. Show your work.
Answers
The number of balloons needed to fill the classroom are 46240 balloons (approx)
Concept: Fermi process is the technique that helps to formulate an answer to a problem based on a series of logical assumptions.
No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)
Given: The classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft, and the balloons are spheres with a radius of 0.35 ft.
No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)
No. of Balloons = 38*52*12/3.14*0.35*0.35*(4/3)
No. of Balloons = 23712/0.5128 = 46240 balloons (approx)
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The number of gallons of gas Connie’s car, g, uses is directly proportional with the number of miles she drives, m. Last week, she drove 469.8 miles and used 14.5 gallons of gas. Which equation would best represent the problem?
Answers
The equation which represent the problem is 14.5 = 469.8k.
What is Equation?An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.
Here, As given in question
The number of gallons of gas Connie’s car, g, uses is directly proportional with the number of miles she drives, m.
g α m
g = km ............(i)
g = 14.5 gallons of gas m = 469.8 miles
14.5 = k X 469.8
14.5 = 469.8k
Thus, the equation which represent the problem is 14.5 = 469.8k.
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Solve the following quadratic by
completing the square.
y = x2 - 6x +2
Answers
Answer:
Roots of the equation are (−3−√7) , (−3+√7)
Step-by-step explanation:
For solving a quadratic equation using completing the square method:
set the value of 'y' = 0add and subtract the square of half of the coefficient of x.solve the obtained equation for 'x'given equation:
y = x^2 - 6x +2
0 = x^2 - 6x + 2
0 = x^2 - 3^2 + 3^2 -6x +2
0 = (x-3)^2 -7
7 = (x-3)^2
±[tex]\sqrt{7}[/tex] = x-3
±[tex]\sqrt{7}[/tex] + 3 = x
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Given cos theta = √3/3 and sin theta < 0. What is the value of sin theta?
Answers
The value of the sin theta will be equal to [tex]Sin\theta =\sqrt{\dfrac{2}{3}}[/tex]
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Given that:-
Cos[tex]\theta[/tex] = √3/3 Sin[tex]\theta[/tex] <0The value of Sin will be calculated as:-
[tex]Sin^2\theta +Cos^2\theta = 1\\\\Sin^2\theta + \dfrac{\sqrt{3}}{2}=1\\\\Sin^2\theta = 1 -\dfrac{1}{3}\\\\Sin\theta = \sqrt{\dfrac{2}{3}}[/tex]
We can see that the value of sin is less than zero therefore
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Sorry I only have the answer key, lol, but for #13, can someone explain to me where they got 4.6 from?? ty and I don't need an explanation for 14; I just couldn't crop the photo
Answers
The measure of the side RS from the figure is 4.6 units
Midpoint theorem of a trapezium
The given figures are trapezoid. Given the following parameters
PQ = 4RS
We need to determine how PR is equivalent to 4.6
Since PQ = 18.4 from the diagram, hence;
18.4 = 4RS
RS = 18.4/4
RS = 4.6 units
Hence the measure of the side RS from the figure is 4.6 units
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allowing 16% discount on the MP of a television and leying 13% Vat buyer has pay RS 18984 to buy it . Find MP of that television
Answers
The marked price of the television is Rs. 20,000.
What is Marked Price?The market price is the current price at which a good or service can be purchased or sold.
Here, let the marked price of the television be Rs. x
Discount = 16% on MP
VAT = 13% additional on MP
Total paid amount = Rs. 18984
Now, according to question;
MP X (1 - Discount) X (1 + VAT) = 18984
x (1 - 0.16)(1+0.13) = 18984
x = 18984/(0.84 X 1.13)
x = 18984 / 0.9492
x = 20,000
Thus, the marked price of the television is Rs. 20,000.
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A roll of paper towels is wound around a hollow cardboard tube. the
cardboard tube in the middle of the roll has an outside radius of 2.4 cm. the
thickness of the paper is 0.3 mm. the sequence of distances of the loops of
paper away from the center of the roll (in centimeters) is the following:
21, 22, az, a4 a5, ... = 2.40, 2.43, 2.46, 2.49, 2.52, ..
what is the radius of the 85th loop of paper, starting from the center of the
tube?
a. 4.95 cm
b. 4.86 cm
c. 4.92 cm
d. 4.89 cm
Answers
The correct Option is Option C: The radius of the cardboard tube of 85th loop of paper is 4.92cm
The arithmetic sequence is the sequence where every term is increased or decreased by a fixed number from the previous number.
Here the outer radius of the tube is 2.4 cm
the thickness of the paper is 0.3mm= 0.03cm
i.e. in every loop the increase in the radius of the loop is 0.03cm
then the radius in every sequence will be 2.40, 2.43, 2.46, 2.49, 2.52, .....
so here it is clear that it is an arithmetic sequence with a common difference of 0.03.
nth term of the sequence, aₙ = a₁ + (n - 1)d where a₁ is the first term, n is the index of the loop, and d is a common difference.
here a₁ =2.40
d=0.03
n=85
the radius of tube of the 85th loop will be= r= 2.40+(85-1)0.03= 2.40+ 2.52= 4.92
Therefore The radius of the cardboard tube of the 85th loop of paper is 4.92cm
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Someone pls help I don’t really understand graphing
Answers
y=Mx+c (M is slope and c is y-intercept)
First find slope and use any two points on the line I prefer picking (-3,0) and (0,2)
= y2-y1/x2-x1 = 2-0/0-(-3) = 2/3
Y=2/3x+c (now last step we find c by replacing any of the giving points)
2=2/3(0)+c
C= 2
Final answer :
Y=2/3x+2
Roni wants to write an equation to represent a proportional relationship that has a constant of proportionality equal to StartFraction 7 over 25 EndFraction. She writes the equation y = x + StartFraction 7 over 25 EndFraction. What error is Roni making?
She should have written y = negative x + StartFraction 7 over 25 EndFraction so that x and y have a constant sum.
She should have written x y = StartFraction 7 over 25 EndFraction so that x and y have a constant product.
She should have written y = StartFraction 7 over 25 EndFraction x so that x and y have a constant quotient.
She should have written y = StartFraction 7 over 25 EndFraction so that y has a constant value.
Answers
Answer:
y = 7/25x
Step-by-step explanation:
For a proportional relationship, we have
y ∞ x.
Let k = constant of proportionality = 7/25
Removing the proportionality sign, we have
y = k x
Therefore, the answer is
y = 7/25x
Instead of y= x + 7/25
So, the error is that x should be multiplied by 7/25 and not added.
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What are the x-coordinates of the solutions to this system of equations?
x² + y² = 16
y = x + 4
Answers
The x-coordinates are -4 and 0.
What is the mean absolute deviation of Patrick’s scores? Show your work
Answers
Which graph represents the solution of x² + y² < 25 and y² <6x?
Answers
The graph is shown below
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, the equation x² + y² < 25 represents equation of circle.
So, the graph will be of the form circle.
and, y² <6x is the equation to represent parabola
So, the graph will represent a parabola.
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A man 1.8 m tall observes the angle of elevation of a tree to be 26 degrees, if he is standing bf 16 m from the tree find the height of the tree
Answers
The height of the tree is the man's height plus x.
[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]
So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]
