The exact value of tan 240° is found by recognizing that 240° is in the third quadrant with a reference angle of 60°. The sine and cosine values are both negative in this quadrant. Therefore, tan 240° simplifies to √3.
To find the exact value of tan 240°, we need to consider its position on the unit circle. The angle 240° is in the third quadrant, where both sine and cosine are negative.
First, recognize that 240° is 60° beyond 180°, making its reference angle 60°.The sine and cosine of 60° are given by sin 60° = √3/2 and cos 60° = 1/2, but since 240° is in the third quadrant, these values will be negative.Thus, sin 240° = -√3/2 and cos 240° = -1/2.Tangent is the ratio of sine to cosine: tan 240° = (sin 240°) / (cos 240°) = (-√3/2) / (-1/2).Simplifying this, we get tan 240° = √3.Therefore, the exact value of tan 240° is √3.
order them from least to greatest, with the least at the top.
6\pi -6
\pi 3
\sqrt{99}
Arranging the numbers in ascending order is: √99 < 6π - 6 < π³
How to arrange the numbers in ascending order?Arranging numbers in ascending order simply means arranging them from smallest to the biggest.
Now, the given numbers are:
6π - 6
π³
√99
Let us simplify the numbers to get:
6π - 6 = 6(3.14) - 6 = 12.85
π³ = 3.14³= 31
√99 = 9.95
Thus, arranging in ascending order is:
√99 < 6π - 6 < π³
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HELP ME PLEASE THIS IS IMPORTANT
In a class experiment, Sean finds that the probability that a student plays soccer is . If the school population is 300, how many students would we expect to play soccer, based on Sean's experiment?
What is the expected value of the game if 3 hits pay $6, 2 hits pays $4, 1 hit pays $2, and 0 hits pays costs $4?
A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
pair of intersecting lines
degenerate ellipse
degenerate hyperbola
line
point
degenerate parabola
Answer:
degenerate hyperbola
pair of intersecting lines
Step-by-step explanation:
Tan α = - 4/3 lies in quad 2, and cos β = 2/3 lies in quad 1 find
a. cos(α + β)
b. sin( α+β)
c. t...
The length of a train is about 1,700 meters. If there are approximately 3.28 feet in one meter, what is the length of the train in feet?
0.002 feet
557,600 feet
5,576 feet
518 feet
To convert 1,700 meters to feet, we multiply by the conversion factor of 3.28 feet per meter, resulting in a length of 5,576 feet for the train.
Explanation:To find the length of the train in feet, we need to convert meters to feet using the conversion factor provided. Given that 1 meter is approximately 3.28 feet, we can calculate the length of the train in feet by multiplying the length of the train in meters (1,700 meters) by the conversion factor (3.28 feet per meter).
The calculation would be as follows:
1,700 meters × 3.28 feet/meter = 5,576 feet
Therefore, the length of the train is 5,576 feet.
Find the volume of the given prism. round to the nearest tenth if necessary.
a. 2,511.5 yd to the power of 3b) 1,255.7 yd to the power of 3c) 1,025.3 yd to the power of 3d) 1,450.0 yd to the power of 3
The day started at 48 degrees. by 3:00 p.m., the temperature has increased by 17 degrees. by nightfall, the temperature fell 17 degrees. what was the net change in temperature
Final answer:
The net change in temperature over the day is 0 degrees. After increasing by 17 degrees in the afternoon, the temperature fell by 17 degrees by nightfall, returning it to the starting temperature.
Explanation:
The student has asked about calculating the net change in temperature over the course of a day starting at 48 degrees. By 3:00 p.m., the temperature increased by 17 degrees, making it 65 degrees. But by nightfall, the temperature decreased by the same amount, falling back down to 48 degrees. The calculation of net change in this scenario is simple: subtract the starting temperature from the final temperature after all changes have occurred. In this case, the starting temperature was 48 degrees, it went up to 65 degrees, and then back to 48 degrees.
The net temperature change is therefore 48 degrees (final temperature) - 48 degrees (starting temperature), which equals 0 degrees. This means there was no net change in temperature over the course of the day. It is important to recognize that even though there was a temporary increase and subsequent decrease, the net effect cancels out, leaving the temperature the same as it started.
the function of y=log(x) is translated 1 unit right and 2 units down. which is the graph of the translated function
The graph of the translated function is attached
To find the graph of the function, we apply the translations
Parent function: y = log(x)
1 unit right: y = log(x - 1)
2 units down: y = log(x - 1) - 2
The graph of the function: y = log(x - 1) - 2 is attached
How to find the sum of the squares of the lengths of the legs of a triangle of a=(-6,11) b=(2,8) c=(-1,0)?
To find the sum of the squares of the lengths of the legs of a triangle, use the distance formula to calculate the length of each leg and then square these lengths, summing the squares of the two legs that do not form the hypotenuse.
Explanation:To find the sum of the squares of the lengths of the legs of a triangle with vertices A=(-6,11), B=(2,8), and C=(-1,0), we first calculate the length of each leg using the distance formula, which is √((x2-x1)² + (y2-y1)²). For AB, AC, and BC we find distances:
AB = √((-6-2)² + (11-8)²)AC = √((-6+1)² + (11-0)²)BC = √((2+1)² + (8-0)²)Then, we square each leg's length:
AB² = ((-6-2)² + (11-8)²)AC² = ((-6+1)² + (11-0)²)BC² = ((2+1)² + (8-0)²)Finally, we sum up the squares of AB and AC because they represent the legs of the triangle:
Σ(leg squares) = AB² + AC²The sum of the squares of the lengths of the legs has now been found.
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do 5, 4, 3 represent the side lengths of a triangle
Betty makes pies. To make 6 pies, she uses 127 cups of flour. How many cups of flour are needed to make 1 pie?
Find the Perimeter of the triangle. Round 2 decimal places.
Compare the exponential and logarithmic models of population growth
need help i havent done this since 2015 :// lolz
Answer:
2w+4 = 5w-6 . . . . w = 10/3
12 = 3x-3 . . . . . . . x = 5
6y = 4y+6 . . . . . . . y = 3
27 = (5/4)z +2 . . . z = 20
107 and 73
Point X is the center of regular pentagon RSTUV. What is the measure of the angle of rotation that will map S onto U?
Final answer:
The measure of the angle of rotation that will map vertex S onto vertex U in a regular pentagon is 72 degrees.
Explanation:
The student is asking about an angle of rotation in a geometric context, specifically concerning mapping one vertex of a regular pentagon onto another through rotation about the center of the shape. In a regular pentagon, the angles between adjacent vertices are all equal, as it is a symmetrical shape. Since there are five vertices in a pentagon, you can divide the full rotation of 360 degrees by the number of vertices to find the angle of rotation that will map one vertex onto the next.
To map vertex S onto vertex U in a regular pentagon, you will need to rotate the pentagon by 360 degrees divided by 5 vertices, which is 72 degrees. Therefore, a rotation of 72 degrees around the center point X of the pentagon will map S onto U.
Divide. Give the quotient and remainder.
55 Divided by 8
ABC Bookstore sells new books, n, for $12, and used books, u, for $8. The store earned $112 revenue last month. The store sold 4 more used books than new books. Using the substitution method, how many new and old books did ABC bookstore sell?
A.n = 4; u = 8
B.n = 8; u = 4
C.n = 8; u = 12
D.n = 12; u = 8
Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?
If a cube with side length 6 inches has its dimensions divided in half, what will be the volume of the new cube?
Given is the side length of a cube = 6 inches.
It says that the dimensions of this cube are divided into half, so the side length of new cube would be 3 inches.
We know the formula for volume of cube is given as follows :-
Volume of new cube = Side x Side x Side.
Volume of new cube = 3 inches x 3 inches x 3 inches.
Volume of new cube = 27 cubic inches.
Hence, 27 cubic inches is the answer.
The cylinder below has a volume of 785 ft^3. and the cone has a volume of 314 ft^3.
(please see attached picture)
Which explains which figure has the greater height?
The cylinder has a greater height because the bases are the same, but the cylinder has a greater volume.
The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 4 times the volume of the cone.
Answer:
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
Step-by-step explanation:
Just did the quiz
A student takes a 15 question
a. True
b. False quiz and guesses at every answer. what is the probability that the student gets exactly 10 questions right, given that the student got the first question right?
Wha is the greatest common factor of 1 and 27
Due tomorrow help please
Anna has leaned a ladder against the side of her house. The ladder forms a 72º angle with the ground and rests against the house at a spot that is 6 meters high. What length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
Answer:
The best approximation of AB is 2 meters.Step-by-step explanation:
Notice that this situation models a right triangle, when the height, which is a leg of the triangle, is 6 meters.
Also, we know the angle between the ladder and the ground, which is 72°.
To find the distance from A to B, which from the bottom of the ladder to the bottom of the wall, we just need to use trigonometric reasons.
[tex]tan(72\°)=\frac{opposite \ leg}{adjacent \ leg}[/tex]
Why we use tangent? Because it relates both legs where we just need to find the adjacent one.
[tex]tan(72\°)=\frac{6}{AB}\\AB=\frac{6}{tan(72\°)} \\AB \approx \frac{6}{3} \\AB \approx 2 \ m[/tex]
Therefore, the best approximation of AB is 2 meters.
What are the inputs of the function below?
Please help
Answer:
Input of the function are -8,2,4,6
Step-by-step explanation:
Input of a function are the domain .
Domain is the values of x. So inputs are the value of x in the table
Input of the table is x and output is f(x)
Input are the values that gives the output f(x)
From the table the x values are -8,2,4 and 6
Input of the function are -8,2,4,6
the solutions to a linear equation are the points in the plane that make the inequality true .
true or false ?
The statement is false. An equation's solutions are points on a line; an inequality's solutions encompass a region on the plane.
Explanation:The statement is false. The solutions to a linear equation are the points (x, y) in the plane that make the equation true, not an inequality. An equation represents a line on the coordinate plane, and every point on that line is a solution to the equation. In contrast, an inequality describes a range or region of the coordinate plane, not just a single line, and the solutions are the coordinates within that range.
For instance, the solutions to the equation y = 2x + 3 are all the points on the line where this is true. On the other hand, solutions to the inequality y > 2x + 3 would be all the points in the region above the line y = 2x + 3.
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The assertion that solutions to a linear equation are the points that make an inequality true is incorrect. It is the solutions to a linear inequality that would make the inequality true.
Explanation:The statement provided in the question is false. Solutions to a linear equation are the points on the line that make the equation true, not an inequality. If we are dealing with a linear inequality, then its solutions are the points in the plane that satisfy the inequality, often forming a region, instead of just the points on a line.
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Please help me with a simple math problem.
What is M DFE?
A. 19
B. 42
C. 78
D. 119
Given the following sets: A={ 2, 4, 6, 8, 10} B={ 3, 5, 7, 9} C={ 2, 3, 5, 7} N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Match the following Unions and intersections to the correct set.
a) {2, 3, 5, 7, 9}
b){3, 5, 7, 9}
ｃ）{2, 3, 4, 5, 6, 7, 8, 10}
ｄ）{ }
ｅ）{2, 4, 6, 8, 10}
1.
What is A U C?
2.
What is A ∩ B?
3.
What is A ∩ N?
4.
What is B ∩ N?
5.
What is B U C?