I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.
Which values are written in proper scientific notation? Check all that apply. –350 –350. 00 –3. 50 × 104 0. 000350 3. 50 × 104 3. 50 × 10–4 35. 0 × 10–5 3,500.
Values which are written in proper scientific notation are:
[tex]-3.5*10^4\\3.5*10^4\\3.5*10^-4[/tex]
What is scientific notation?
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
The given numbers are
[tex]1)-350\\2)-3.5*10^4\\3)0.000350\\4)3.5*10^4\\5)3.5*10^-4\\6)35*10^-5\\7)3500[/tex]
As we can see that every number except first, third, sixth and seventh number has been written according to the definition of scientific notation mentioned above.
Therefore, values which are written in proper scientific notation are:
[tex]-3.5*10^4\\3.5*10^4\\3.5*10^-4[/tex]
To get more about scientific notation visit:
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Determine whether y=−6x represents an exponential function
Answer:
No
Step-by-step explanation:
this is a linear function. the general shape of a exponential function is : y = ax^b + c
find the quadratic equation given that the roots are 4 and 7
Answer: {−4,7} is y=x2−3x−28 y = x 2 - 3 x - 28 .
Step-by-step explanation: so all ways do y and x first
please anyone don't delete my question I really need this
Answer:
B.
We know that angle 1 has a measure of 55 degrees
That means angle 2 is 125 degrees
This is because the two angles have to have a sum of 180
So, angle 3 is 55
Angle 4 is 125
Angle 5 is 55
Angle 6 is 125
Angle 7 is 55
Angle 8 is 125
C.
1: False - Skew lines are an example of lines that do not intersect but are not parallel
2: True - Skew lines are in 3-dimensional geometry and do not intersect. They are not parallel, though.
3: False - Perpendicular lines are lines that intersect to form a 90-degree angle
4: True - Parallel lines lie in a plane together but never intersect
5: True - Parallel lines are coplanar, meaning they coexist on one plane
The radius of a sphere is 7 cm. What is the sphere's volume? Round to the nearest tenth, and use 3. 14 for Pie
Answer:
1436.03 cm^3
Step-by-step explanation:
Equation: V = 4/3(3.14)r^3
V=4/3(3.14)(7^3)
V=4/3(1077.02)
V=1436.03
how do you graph the solution of an inequality?
Answer:
1. rearrange the equation and transform it into y=mx+b format.
2. Plot y-intercept on the graph for one the equations
3. Graph second equation by using b, or y-intercept
4. Shade above or below the graph, depending on what inequality symbol is used to represent each equation.
Step-by-step explanation:
In the answer above, hope it helps!
Have a great day :)
Please help me with this question.
Answer: 1.479
Step-by-step explanation:
1.5.5 Practice: Modeling: Best Ticket Deal
Mathematics || Sem 1
Points Possible: 20
Does anybody have this?
The best ticket deal are illustrations of linear equations
The ticket system is a better deal to the max ticket
How to determine the best ticket dealFrom the complete question, we have the following summary:
Ticket SystemCharges = $22 per person
Surcharge = $10 per transaction
Max TicketsCharges = $20 per person
Surcharge = $16 per transaction
Assume there would be only one transaction, the linear equations that represent the ticket deals are:
Ticket System: y = 22x + 10
Max Ticket: y = 20x + 16
The costs of ticket for two people in both deals are:
Ticket System: y = 22*2 + 10 = 54
Max Ticket: y = 20*2 + 16 = 56
By comparison;
54 is less than 56
This means that the ticket system is a better deal to the max ticket
Read more about linear equations at:
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Calculate the average rate of change for the function
[tex]slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= 2(x-2)^2+1\qquad \begin{cases} x_1=-2\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(-2)}{4-(-2)} \\\\\\ \cfrac{[2(4-2)^2+1]~~ - ~~[2(-2-2)^2+1]}{4+2}\implies \cfrac{[9]~~ - ~~[33]}{6}\implies \cfrac{-24}{6}\implies -4[/tex]
Subtract the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x. Subtract 2x2 - 6x - 4 from 4x2 - 4x + 3.
Answer:
2X²+2X+7
Step-by-step explanation:
(4X²-4X+3) – (2X²-6X-4) = 4X² – 4X + 3 –2X² + 6X +4
=2X² + 6X +7
Consider this equation,
cos(0) = 4/41
If 0 is an angle in quadrant IV, what is the value of sin(0)
take a peek at your Unit Circle, let's notice that in Quadrant IV the cosine is positive and the sine is negative, or namely the adjacent side is positive and the opposite side is negative, so hmmm
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{41}}\qquad \impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{41^2-4^2}=b\implies \pm\sqrt{1665}=b\implies \pm 3\sqrt{185}=b\implies \stackrel{IV~Quadrant}{-3\sqrt{185}=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill sin(\theta )=\cfrac{\stackrel{opposite}{-3\sqrt{185}}}{\underset{hypotenuse}{41}}~\hfill[/tex]
By rounding to one significant figure, estimate the answers to these questions, a) 59 + 25 b) 682 71 c) 91 x 18 58
The Answers are
Step-by-step explanation:
a) 59÷25 =2.36
b) 682/71 =9.6056
c) 91×18/58 =28.24
please mark brainliest!
Mark bought a jewelry box in the shape of a cube. The jewelry box has edge lengths of 6 inches. What is the surface area of the jewelry box?
Answer:
6*6*6=216
Step-by-step explanation:
To find length you use length*width*height
Since it is a cube are the side are equal to 6
To solve you can do 6*6*6 or 6^3 to get you to your answer which is 216
Find the quotient. Write the answer in the simplest form (reduce)
36) 3/8 ÷ 3 /4 =
37) 3 /4 ÷ 12 =
These tables represent a quadratic function with a vertex at (0, -1). What is the average rate of change for the interval from x = 9 to x = 10?
A. -19
B. -2
C. -101
D. -82
Answer:
B.–2Step-by-step explanation:
HOPE IT'S HELP THANK YOU FOR THE REST OF YOUR LIFE
Convert 8/20
to a decimal.
If you place a 32-foot ladder against the top of a 23-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
Answer:
22.2 feet
Step-by-step explanation:
Treat the ladder, building, and the ground between the bottom of the ladder and the building as the legs of a right triangle.
Then, you can use the Pythagorean Theorem.
X^2 + Y^2 = Z^2
The ladder is the "diagonal" side, so it is the hypotenuse, Z.
It doesn't particularly matter whether the building is X or Y; the end result will be the same.
Therefore:
(23)^2 + Y^2 = (32)^2
Y^2 = (1024 - 529) = 495
Y = 22.249; rounded to the nearest tenth, 22.2 feet
I hope this helped! :)
3RD ATTEMPT!!! REAL ANSWERS ONLY!!!
Draw u + v + w.
Answer:
See pic below
Step-by-step explanation:
Use a method of graphic vector addition.
See the picture below.
The average distance of the planet Neptune from the Sun is 3,000,000 % times the average distance of the Earth from the Sun.
What is this as a decimal?
Answer:
3 x 10⁴ or 30,000
Step-by-step explanation:
Percentage to decimal conversion.
=> % / 100 = decimal
=> 3 x 10⁶ / 10²
=> 3 x 10⁴ or 30,000
Speed 65 kph; Time 4.5 hours; Distance ? ___ km
Answer:
292.5 km
Step-by-step explanation:
You have to first do 65 x 4 = 260
Then 65/2 = 32.5
260 + 32.5 = 292.5
Answer = 292.5 km
Answer:
292.5 km
Step-by-step explanation:
65 x 4 = 260
65/2 = 32.5
260 + 32.5 = 292.5
Ans = 292.5 km
15 divided by 6 = 2 with a ? Of 3
15 divided 6 is 2.5. So you have an extra '0.5' to the 2
Hope that helps!
Suppose a researcher is conducting a public-opinion poll for a politician during an election. The politician cares about getting an accurate response but isn't inclined to pay more than she needs to so long as the margin of error is less than 4%. How big of a sample size should the researcher aim to get
One farmer has 119 sheep and another has 73. After they each sell the same number of sheep, one is left with three times as many sheep as the other. How many sheep did each sell?
Answer:
119×3= 357
73×3= 219
357-219 =138
138÷3 =46.
please double check your answer if you're confused
what is the answer to the problem
Answer:
[tex] \sqrt{63} = 7.9[/tex]
So between 7 and 8
The age of the father is 42 and the age of the son is 9. At what age, will the father be twice old as the son?
(Solve by equation system.)
Answer:
24
Step-by-step explanation:
42 + x = 2 (9 +x) (solve for x)
42 + x = 18 + 2x
42 -18 = 2x -x
24 = x
42 + 24 = 66
9 + 24 = 33
When the man turns 66, his son will be 33, or half his age.
What is the value of p?
Answer:
p = 12 °
Step-by-step explanation:
p + ( p + 6 ) = p + 41
2p + p = 41 - 6
3p = 35
3p/3 = 35/3
p = 11.6
p = 12 °
Use the distance formula to classify each triangle as Scalene, Isosceles, or Equilateral.
△ABC with vertices A (-2,-2), B (4,3), C (3,4)
Please show how to solve
Answer:
3 because we'll I don't know
Mr Asiedu earns an annual salary of GH6000.00. His total allowances is GH2000.00.How much tax does he pay if the rate of tax is 15%
Answer:
GH 1200
Step-by-step explanation:
Salary = GH6000
Allowances= GH2000
Taxable income = (Salary + Allowances)
Taxable income = GH6000 + GH2000
=GH8000
Tax rate = 15%
Tax = GH8000 X 15/100
= GH 1,200
given that (-2,-2) is on the graph of f(x), find the corrisponding point for the function f(x)+5
Answer:
(-2, 3)
Step-by-step explanation:
The +5 represents shifting 5 units up, so we can add 5 to the y coordinate.
This gives us (-2, -2+5)=(-2, 3)
7124 divided by 26, please help I’ll give brainliest and pleas with the long division
Answer:
274Step-by-step calculations:
7124 ÷ 26 = 274
~Refer to attachment for work~
Learn more:
Learn the steps for long division: https://brainly.com/question/9470426Learn the definition of long division: https://brainly.com/question/1974422Answer: 274
Step-by-step explanation: Instead of saying 26 divided by 7 equals 3.714, you could just use the division symbol, which is a slash, as we did above.