Find all solutions to the equation sin2x+sinx-2cosx-1=0 in the interval [0, 2pi)
Answers
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}
Related Questions
Consider this system of linear equations:
22x − y = -23 (equation 1)
11x + 12y = 1 (equation 2)
Answers
1. You have the folllowing system of equations given in the problem above:
22x − y = -23 (equation 1)
11x + 12y = 1 (equation 2)
2. If you multiply the equation 2 by -2, and then sum the equation 1+equation 2, you obtain:
-25y=-25
y=1
3. Then, you must substitute y=1 into the equation 1, then you have:
x=-1
4. As you can see, when you solve it, the solutions are:
x=-1
y=1
22x − y = -23
-
(11x + 12y = 1) *2
22x − y = -23
-
22x + 24y = 2
0 -25y = -25
y = 1
22x - 1 = -23
x = 1
Simple interest is calculated on the principal in an account using the formula I=prt. How much simple interest does $3,500.00 earn in 6 months at an annual interest rate of 2.5%?
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A house on a floor plan is 10.5 inches long and 6.5 inches wide. If the scale used is 0.5 inch = 2 ft, how long is the actual house?
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1. You have the following information given in the problem above:
- The house on the plan is 10.5 inches long and 6.5 inches wide.
- The scale used is 0.5 inch=2 ft
2. Therefore, you have:
0.5 inch-------2 feet
10.5 inches--x
x=10.5x2/0.5
x=42 feet
Therefore, the answer is: 42 feet long.
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. A. 44.4 cm, 11.1 cm B. 44.4 cm, 3.2 cm C. 11.1 cm, 4.9 cm D. 24 cm, 4.9 cm
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TIMED, need the answer ASAP, will give brainiest
Answers
Suppose it costs $15 to roll a pair of dice. you get paid 2 dollars times the sum of the numbers that appear on the dice. what is the expected payoff of the game? is it a fair game?
Answers
We can conclude that, the money recieved by the player will be 2(x + y) and game is a fair game.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is it costs $15 to roll a pair of dice and you get paid 2 dollars times the sum of the numbers that appear on the dice.
Assume that you get x and y value on dice 1 and dice 2 respectively. Then the equation representing the money recieved by a individual will be -
2(x + y)
The game will be fair if -
2(x + y) > 15
Now, for the sum of (x + y) = 7, the player will not have any profit. However, from (x + y) = 8, the players will start making profits. So, we can say it is a fair game, if your luck is not bad so far.
Therefore, we can conclude that, the money recieved by the player will be 2(x + y) and game is a fair game.
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Given the system of inequalities below: -3x - y < 12 and 2x + 3y ≥ 9
Answers
y(less than or equal to)-2/3x+9
A bakery has 49 donuts and 28 muffins for sale. What is the ratio of muffins to donuts? Please answer ASAP 99 Points :V
Answers
In a ratio, the first thing or item mentioned is first in the ratio. Let the muffins stand for x, and the donuts stand for y. It asks for the ratio of muffins to donuts.
x:y
Plug in the numbers.
28:49
Both numbers are divisible by 7.
28/7= 4 49/7=7
4:7 <=== simplified ratio
I hope this helps!
~kaikers
Donuts: 49
Muffins to donuts: 28/49
Answer = 28/49 = 4/8 = 1/2
~Hope this helped~
A silo is constructed using a cylinder with a hemisphere on top. The circumference of the hemisphere and the circumference of the cylinder are equal. The diameter of the circular base of the cylinder is 10 feet. The cylinder is 40 feet tall. One of the circular bases on the cylinder is in contact with the ground. What is the area of the surface of the silo that will be exposed to rain, wind, and sun?
Answers
The area of the surface of the silo that will be exposed to rain, wind, and sun is 450π square feet.
Explanation:Solution:
To find the area of the surface of the silo that will be exposed to rain, wind, and sun, we need to find the combined surface area of the hemisphere and the cylinder.
The radius of the circular base of the cylinder is half of its diameter, which is 10/2 = 5 feet.The height of the cylinder is 40 feet.The circumference of both the hemisphere and the cylinder is equal, so the circumference of the circular base of the cylinder is 2πr, where r is the radius of the base.The surface area of the hemisphere is equal to half of the surface area of a sphere with the same radius, which is 2πr²/2 = πr².The surface area of the circular base of the cylinder is πr².The surface area of the curved surface of the cylinder is the circumference of the base multiplied by the height of the cylinder, which is 2πr * 40.Now, let's calculate:
Surface area of the hemisphere = π(5)^2 = 25π square feetSurface area of the circular base of the cylinder = π(5)^2 = 25π square feetSurface area of the curved surface of the cylinder = 2π(5) * 40 = 400π square feetTo find the total surface area, we add up the surface areas of the hemisphere, the circular base, and the curved surface:
Total surface area = Surface area of hemisphere + Surface area of circular base + Surface area of curved surface = 25π + 25π + 400π = 450π square feet.
Therefore, the area of the surface of the silo that will be exposed to rain, wind, and sun is 450π square feet.
If it costs $7.50 to park, how much will the stadium make from parking 10,600 vehicles?
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When the polynomial is written in standard form, what are the values of the leading coefficient and the constant? 5x + 2 - 3x^2
Answers
Constant = 2
When you order them in standard form, you need to put them in ascending order of the exponents. Therefore the -3x^2 would come first, which makes the number attached (-3) the lead coefficient.
Also, since the number (2) without an x attached would be last (due to the power of x technically being 0), than that is the constant.
Solve the system of equations using the substitution method.
{2x+8y=4 x=−3y+5
Enter your answers in the boxes.
Answers
I believe the answer is (14,-3)
have a great day & good luck!
The trapezoids are similar. the area of the smaller trapezoid is 131 m2. find the area of the larger trapezoid to the nearest whole number. (1 point)
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
T.A. =
Answers
Please, see the attached file.
Thanks.
Answer:
Step-by-step explanation:
Which is the first step in drawing a line graph?
A. Plot a point for each piece of data.
B. Draw x- and y-axes on graph paper.
C. Create a scale that covers the data range.
D. Draw a line of best fit to show a trend.
Answers
Answer:
B) Draw x- & y-axes on graph paper.
Step-by-step explanation:
You need a graph before you can create your line.
The area of a rectangle is represented by the expression 6x^3y^5. Which of the following could be the dimensions of the rectangle?
2xy^2 and 3x^2y^3
2xy^2 and 4x^2y^3
2x^3y and 3y^4
2x^3y and 3xy^4
Answers
Answer:a&c
Step-by-step explanation:
Can somone help me with this 1 problem? In the figure shown, △RST is an isosceles triangle with RS≅RT. Which is the measure of ∠T?
A.21°
B.40°
C.70°
D.110°
Answers
Based on your information, T and S are congruent. So we know that the measure of angle T is 3x+7. But we need to solve for x. Let's add all the angle values together and set it to 180 because the angles of a triangle sum to 180.
1) 2(3x+7) + 2x - 2 = 180
2) 6x + 14 + 2x - 2 = 180
3) 8x + 12 = 180
4) 8x = 168
5) x = 21
6) m<T = 3x + 7 = 3(21) + 7 = 63 + 7 = 70
I got C, but it is always helpful to double check work. Hope this helps!
In an isosceles triangle, base angles are congruent, meaning ∠R would equal ∠T. However, no angle measures are provided, making it impossible to determine the measure of ∠T with the given information.
Explanation:The given figure is an isosceles triangle, triangle RST, where RS is congruent to RT. In an isosceles triangle, the base angles are congruent, meaning that they have the same measure. Therefore, if we know the measure of one of the base angles, we know the measure of the other. The problem, however, does not provide the measures for any of the angles. This makes determining the measure of ∠T impossible with the given information. We would need to know either the measure of angle R or S or the measure of the angle at the vertex, angle T, to find the measure of ∠T. Without additional information, we cannot definitively choose between options A, B, C, or D.
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12q^2-17q-7
A. (3q+1)(4q-7)
B. (3q-1)(4q+7)
C. (3q+7)(4q-1)
D. (3q-7)(4q+1)
Answers
Andy currently runs a total of 12 miles each week. He plans to increase the number of miles he runs each week by 1.5 miles untill he is running a total of 26 miles each week. How many weeks will it take Andy to reach his goal?
Answers
26 = 1.5n + 12
14 = 1.5n
It will take 9.333 weeks for andy to reach 26 miles, so at 10 weeks he will be running more than 26.
You bought 12 one-gallon bottles of apple and orange juice for a school dance. the apple juice was on sale for $1.00 per one-gallon bottle. the orange juice was $1.75 per one-gallon bottle. you spend $15.00. how many bottles of each type of juice did you buy?
Answers
x: bottles of apple juice
y: bottles of orange juice
We write the system of equations:
x + y = 12
1x + 1.75y = 15
Solving the system of equations we have:
x = 8
y = 4
Answer:
you did buy:
8 bottles of apple juice
4 bottles of orange juice
The Freshman class has 27 more boys than girls. If there are 283 freshman, how many are girls?
Answers
283 = x + (x + 27)
Here, we are adding the number of girls with 27 more people than this amount of girls. This will allow us to add the number of girls, x, with the number of boys, x + 27, to get a total of 283.
This equation can be simplified if we add the like terms together: the x's.
So,
283 = 2x + 27.
Since this is a multi-step equation, we must use the reversed order of operations; undo addition first.
283 - 27 = 2x + 27 - 27
256 = 2x + 0
256 = 2x
Now, we must undo multiplication by dividing.
256/2 = 2x/2
128 = 1x
So, x, the number of girls, is equal to 128.
Hope this helps you! :)
#2 The lunch choices last Friday were mushroom or pepperoni pizza. The cafeteria made 57 mushroom pizzas and 38 pepperoni pizzas. What percentage of the pizzas were mushroom pizzas?
Answers
To find this, you add up 57 and 38 to find the total number of pizzas, then divide 57 (number of mushroom pizzas) by 95 (the total). This will give you 0.6, which you miltiply to get a percent. Thus getting 60% as the final answer.
I hope this helps!
To find the percentage of pizzas that were mushroom pizzas, you must divide the number of mushroom pizzas by the total number of pizzas. To find the total number of pizzas, we must add the number of mushroom and pepperoni pizzas together.
57 + 38 = 95
Next, we can complete our division.
57/95 = 0.6
Finally, we should multiply by 100. This is because to convert a decimal to a percentage, we must move the decimal point two places to the right so that this value is out of 100 total percent.
0.6 * 100 = 60%
Therefore, 60% of the total pizzas are mushroom.
Hope this helps!
The equation of a circle is x2+y2-6y+1=0 what are the coordintes of the center and the length of the radius
Answers
The coordinates of the centre will be ( 0,3) and the length of the radius is equal to 2√2.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the out trace.
The general form of the equation of the circle is given as:-
( x - h )² + ( y - k )² = r²
We have an equation:-
x² + y² - 6y + 1 = 0
x² + y² - 6y + 9 - 9 + 1 = 0
( x - 0 )² + ( y - 3 )² = 8
By comparing the equation from the standard form we will get the centre ( 0,3) and the radius r = 2√2.
Therefore the coordinates of the centre will be ( 0,3) and the length of the radius is equal to 2√2.
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Need this geometry answer quick!
(I think its answer c but not sure)
Answers
angle B =50
angle C = 130
simplify. x-2/(x^2+4x-12)
Answers
x-2/(x^2+4x-12)
factoring out the denominator we get:
x^2+4x-12
=x^2-2x+6x-12
=x(x-2)+6(x-2)
=(x+6)(x-2)
thus our expression will be:
(x-2)/[(x+6)(x-2)]
simplifying the above we get:
1/(x+6)
Answer: 1/(x+6)
A trait has two alleles, and their frequencies are represented by p and q. if p = 0.90, what is q?
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Therefore, we have the following equation:
p + q = 1
Substituting values we have:
0.90 + q = 1
Clearing the value of q we have:
q = 1 - 0.90
q = 0.10
Answer:
The value of q is given by:
q = 0.10
A cone and a pyramid have the same height and same volume. If the radius of the base of the cone is r, what is the side length of the square base of the pyramid?
Answers
Vc=πr²h/3
Vp=(lwh)/3
make it equal to each other and cancel out the 3.
πr²h = lwh
heights will cancel out
πr²=lw
l=(πr²)/w
To find the side length of the square base of a pyramid with the same volume and height as a cone with radius r, one can use the volume formulas V = (1/3)πr²h for a cone and V = (1/3)a²h for a pyramid. Setting them equal and solving for a yields a = r√π, indicating that the pyramid's base side length is the cone's radius times the square root of π.
The student is asking for the relationship between the dimensions of a cone and a pyramid that have the same volume and height. Specifically, if we have a cone with a radius r, and we want to find the side length of a square base of a pyramid that also has the same volume and height as the cone.
The volume of a cone is given by the formula [tex]V = (\frac{1}{3}) \pi r^2h[/tex], where radius of the cone's base is denoted by 'r' and the height is denoted by 'h'. For a pyramid with a square base, the volume formula is [tex]V = (\frac{1}{3} )a^2h[/tex], where a is the side length of the square base and h is again the height.
Given that both volumes are equal, we can set the formulas equal to each other and solve for a: [tex](\frac{1}{3} )\pi r^2h = (\frac{1}{3} )a^2h[/tex]. The heights cancel out, and we can simplify the equation to solve for the side length a: a = r√π. Therefore, the side length of the square base of the pyramid is the radius of the cone's base times the square root of π.
HELP ASAP WILL GIVE BRAINLIEST
Answers
I mean it could also be viewed as if they intersect at every point so I'm sorry if its wrong (the M is slightly above the N so it should be parallel)
Its perpendicular if it only intersected at one point- 1 solution
If it intersects at every point- infinitely many solutions
The lines are parallel because they are side by side and have the same distance continuously between them. Please give me brainliest because I need one more to turn Virtuoso
Help! Thanks in advance!
Screenshotted question!
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Simplify: 8x - 4(2x - 5) - 2
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[tex]8x - 8x + 20 - 2 \\ = 18[/tex]
Hope this helps. - M