Unit circle : a circle with radius of one. Unit circle is centered at the origin.
Use the formula cot x = base / perpendicular, where x is the angle. Substituting x,y and t to the formula, we get cot (t) = x / y.
To find the trigonometric function values for a point on the unit circle corresponding to a real number t involves using the x and y coordinates, which are derived from the cosine and sine functions at that angle t.
The student's question involves finding the values of trigonometric functions for a point p(x, y) on the unit circle that corresponds to a real number t. This typically involves understanding the relationship between the coordinates of a point on the unit circle and the trigonometric functions sin, cos, and tan. In this context, x(t) and y(t) are understood as the x and y coordinates of a point on the unit circle at a certain angle t. The point p(x, y) would be given by the cosine and sine functions: x(t) = cos(t) and y(t) = sin(t). In more advanced contexts, these functions can take different forms like x(t) = A cos(wt + p) where A, w, and p are constants. The solution to trigonometric equations may involve differential equations or complex numbers in such cases.
A bag contains 8 blue marbles, 5 green marbles and 7 red marbles. If Alicia removes two marbles without replacing them, what is the probability that he will choose red, then green?
To find the probability of choosing a red marble, then a green marble without replacement, multiply the probabilities of the individual events which is 7/76.
Explanation:To find the probability that Alicia will choose red, then green marbles, we need to calculate the probability of drawing a red marble and then a green marble without replacement.
Given that there are 8 blue marbles, 5 green marbles, and 7 red marbles in the bag, the probability of drawing a red marble first is 7/20.
After removing the red marble, there are 19 marbles left in the bag, including 5 green marbles. Therefore, the probability of drawing a green marble second is 5/19.
To find the combined probability, we multiply the probabilities of the individual events:
P(Red, then Green) = P(Red) * P(Green | Red) = (7/20) * (5/19) = 35/380 = 7/76.
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Two angles that are complementary __________ form a right angle. 2. angles with a common side and a common vertex ______ form a linear pair. 3. two angles that are supplementary are _______ complementary.
Solve.
−1/2x ≥ −8 then Graph the solution
Roger can run one mile in 10 minutes. jeff can run one mile in 8 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up to roger? how far will each have run?
Which function represents the graph of f(s)=-4[x] after it is translated 3 units down?
Given the midpoint and one of the endpoints,find the other endpoint of the segment
what is 2 1/2x−3/4(2x+5)=3/8
Deon caught a 4 3/4 pound fish how much it weigh in ounces
Bryan used the six steps to solve this problem. On one of the steps, he decided that he would use multiplication and addition to compare the companies and find the best rate. Which step did Bryan use to help him decide?
What is the distance between points A and B?
___ units
we know that
the distance's formula between two points is equal to
[tex]d=\left|xB-xA\right|[/tex]
substitute
[tex]d=\left|1-(-5)\right|[/tex]
[tex]d=6\ units[/tex]
therefore
the answer is
[tex]6\ units[/tex]
The distance between two point [tex]A{\text{ and }}B[/tex] is [tex]\boxed{{\mathbf{6 units}}}[/tex].
Further explanation:
The distance between two points is the modulus of difference of the given two points.
The distance between two points can be found by the distance formula as,
[tex]\left| {B - A} \right|[/tex]
Here, [tex]A{\text{ and }}B[/tex] are the points on the number line.
The distance cannot be negative therefore modulus is applied in the formula.
Step by step explanation:
Step 1:
First we determine the points from the given number line.
It can be observed from the given number line that there are two points one is on the left side of the origin and the second is right side of the origin.
The point [tex]A[/tex] is [tex]- 5[/tex] and the point [tex]B[/tex] is 1.
Step 2:
Now use the distance formula to obtain the distance between the two points [tex]A{\text{ and }}B[/tex].
Here, the value of A is [tex]-5[/tex] and B is 1.
Substitute the value of [tex]A{\text{ and }}B[/tex] to obtain the distance as,
[tex]\begin{aligned}d&= \left| {B - A} \right| \\&= \left| {1 - \left( { - 5} \right)} \right|\\&= 6{\text{ units}}\\\end{aligned}[/tex]
Therefore, the distance between two point [tex]A{\text{ and }}B[/tex] is [tex]6{\text{ units}}[/tex].
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Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Number line
Keywords: Integers, distance, point, number line, units, measurement, origin, negative numbers, positive numbers, right side, left side, difference.
he coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4).
What is the perimeter of the polygon to the nearest tenth of a unit?
Answer:
16.9
Step-by-step explanation:
The distance formula can be used to find the lengths of individual segments. It tells you ...
d = √((Δx)² +(Δy)²)
where Δx and Δy are the differences between x- and y-coordinates of the segment end points.
Since the value is squared, the sign of the difference doesn't matter. It can be easier to write it as always positive, so in some cases it may be Δx = x₂-x₁ and in other cases it might be Δx = x₁-x₂, for example.
If the segments are labeled A, B, C, D, E in order, the distances are ...
AB = √(5²+1²) = √26 ≈ 5.099
BC = √(1²+3²) = √10 ≈ 3.162
CD = Δx = 3
DE = √(3²+2²) = √13 ≈ 3.606
EA = Δy = 2
Then the perimeter is ...
P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867
P ≈ 16.9
On an algebra test , the highest grade was 42 points higher than the lowest grade . The sum of the two grades was 138 . Find the lowest grade .
The lowest grade is 48.
What is substitution method?The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.
Let the lowest grade be x and highest grade be y.
According to the given question.
[tex]y = 42 + x[/tex]
Also,
[tex]x + y= 138[/tex]
For finding the points of lowest grade and highest grade substitute
y = 42 + x in x + y = 38.
[tex]x + ( 42 + x ) = 138[/tex]
⇒ [tex]2x + 42 = 138[/tex]
⇒ [tex]x + 21 = 69[/tex]
⇒[tex]x = 69 -21[/tex]
⇒[tex]x = 48[/tex]
Therefore,
[tex]y = 48 + 42 =90[/tex]
Hence, the lowest grade is 48.
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9. Darcy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. Apples cost $0.24 each and oranges cost $0.80 each. She has $12 to spend and would like to purchase at least 20 pieces of fruit total.
a) Write a system of linear inequalities to represent
this situation, then graph.
b) Using your graph, give two possible combinations
of apples and oranges Darcy can buy.
Help please pre calculus
put 7.6*10^-1 into the equation to get:
10log(1/7.6*10^-4) = 31.19
Sonia has three bracelets. she wears them all at the same time but if a different order each day. how many different combinations does sonia have to choose from
Given the functions f(x) = 2x2 - 8x, g(x) = x2 - 6x + 1, and h(x) = -2x2, rank them from least to greatest based on their axis of symmetry. (2 points)
g(x), f(x), h(x)
f(x), g(x), h(x)
h(x), f(x), g(x)
h(x), g(x), f(x)
Answer:
h(x), f(x) , g(x)
Step-by-step explanation:
[tex]f(x) = 2x^2 - 8x[/tex]
Axis of symmetry at [tex]x=\frac{-b}{2a}[/tex], a=2, b=-8
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-8)}{2(2)}=2[/tex]
[tex]g(x) = x^2 - 6x + 1[/tex], a= 1, b=-6
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-6)}{2(1)}=3[/tex]
[tex]h(x) = -2x^2[/tex], a=-2, b=0
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(0)}{2(-2)}=0[/tex]
Now rank the function based on their axis of symmetry
h(x), f(x) , g(x)
Miguel is going for a walk. he takes 3 hours to walk 7.5 miles. what is his speed?
divide total distance by time
7.5 miles / 3 hours = 2.5 miles per hour is his speed
Braic equation. two airplanes leave chicago at the same time and fly in opposite directions. if one travels at 490 miles per hour and the other at 470 miles per hour, how long will it take for them to be 4,800 miles apart
Harry and his friends share some watermelon equally. Each person gets of a watermelon. Which of the following shows a possible way that the watermelon is served?
2 watermelons divided among 7 people.
7 watermelons divided among 2 people.
of a watermelon divided among 2 people.
of a watermelon divided among 7 people.
Use synthetic division to evaluate the function at the indicated values
h(x)=x^6-4x^4+5x^2+1
h(2)
h(-1)
please show your work
Final answer:
[tex]\[ h(2) = 55, \quad h(-1) = 3 \][/tex]
Explanation:
To evaluate [tex]\(h(x)\)[/tex] at the given values using synthetic division, we start with the coefficients of the polynomial [tex]\(x^6 - 4x^4 + 5x^2 + 1\).[/tex]
1. For [tex]\(h(2)\):[/tex]
- Write down the coefficients: 1, 0, -4, 0, 5, 0, 1.
- Using synthetic division with 2 as the divisor, perform the operations to obtain the result 55.
2. For [tex]\(h(-1)\):[/tex]
- Repeat the process with -1 as the divisor, using the coefficients: 1, 0, -4, 0, 5, 0, 1.
- After the calculations, the result is 3.
In both cases, the final values represent the result of evaluating the function [tex]\(h(x)\)[/tex] at x = 2 and [tex]\(x = -1\)[/tex] respectively.
Given a = {1, 2, 3, 4, 5, 6, 7, 8, 9} and b = {2, 4, 6, 8} what is AUB?
exTrA cREdiT BOnuS pOiNTS
How to solve equations with 2 variables step by step?
Two step algebraic equations are relatively quick and easy -- after all, they should only take two steps. To solve a two step algebraic equation, all you have to do is isolate the variable by using either addition, subtraction, multiplication, or division. If you want to know how to solve two step algebraic equations in a variety of ways, just follow these steps.
1. Write the problem. The first step to solving a two step algebraic equation is just to write the problem so you can start to visualize the solution. Let's say we're working with the following problem: -4x + 7 = 15.
2. Decide whether to use addition or subtraction to isolate the variable term. The next step is to find a way to keep "-4x" on one side and to keep the constants (whole numbers) on the other side. To do this, you'll have to do the "Additive Inverse," finding the opposite of +7, which is -7. Subtract 7 from both sides of the equation so that the "+7" on the same side as the variable term is canceled out. Just write "-7" below the 7 on one side and below the 15 on the other so the equation remains balanced. Remember the Golden Rule of Algebra. Whatever you do to one side of an equation must be done to the other side to maintain the balance. That is why 7 is subtracted from the 15 as well. We only need to subtract 7 once per side, which is why the 7 is not subtracted from the -4x as well.
3. Add or subtract the constant on both sides of the equation. This will complete the process of isolating the variable term. Subtracting 7 from +7 on the left side of the equation will leave no constant term (or 0) on the left side of the equation. Subtracting 7 from +15, on the right side of the equation, will leave you with 8. Therefore, the new equation is -4x = 8. -4x + 7 = 15 =-4x = 84. Eliminate the coefficient of the variable through division or multiplication. The coefficient is the number attached to the variable. In this example, the coefficient is -4. To remove the -4 in -4x, you'll have to divide both sides of the equation by -4. Right now, the x is being multiplied by the -4, so the opposite of this operation is division and you'll have to do it on both sides. Again, whatever you do to the equation must be done to both sides. That is why you see ÷ -4 twice.5.Solve for the variable. To do this, divide the left side of the equation, -4x, by -4, to get x. Divide the right side of the equation, 8, by -4, to get -2. Therefore, x = -2. You've taken two steps -- subtraction and division -- to solve this equation.To solve two-variable equations, identify unknowns, find related equations, substitute known values, and solve for one variable before finding the other. Use substitution or elimination methods in case of a system of equations.
To solve equations with 2 variables, follow these steps:
Identify the unknowns: Determine what you need to find.Find a set of equations that relate the unknowns.Substitute known values into the equations, ensuring unit consistency.Combine equations and isolate one variable to solve for it.Use the solved variable to find the other unknown in one of the original equations.If necessary, make and note assumptions that simplify the equations—but be aware of their implications.Regarding a 2x2 system (two equations with two unknowns), you can either use substitution—solving one equation for one variable and then substituting into the other—or elimination—adding or subtracting equations to cancel one of the variables. If an equation has more than one unknown, additional equations are necessary to solve the system.
For instance, consider a pair of equations:
1) x + y = 10
2) x - y = 6
By adding these two equations, y is eliminated, and we can solve for x quickly. Then, we can substitute the value of x into either equation to solve for y.
In Indianapolis, the Market Tower has 2/3 as many stories as the Chase Tower. If the Market Tower has 32 stories, how many stories does the Chase Tower have?
The distance on a map is 4 1/8 inches. find the actual distance if the scale on the map is 20 inches= 40 miles.
Factoring quadratic trinomials in the form (ax 2 + bx +
c. where a = ≠ 1
Solve 5c + 4 = −26.
6
−6
−4.4
3
Answer:
-6 :))))))))))))))))))
Step-by-step explanation:
The scale on a map indicates that 1 inch corresponds to an actual distance of 95 miles. two cities are 4.5 inches apart on the map. what is the actual distance between the two cities?
Oranges are on sale for $1.59 per pound. Write a funtion as a standard equation and in a funtion notation.
BRAINLIESTTTTTTTT!!!!!!!!!!!!!!!!!!
Simplify the expression 111,000 × 0.072 using scientific notation and express your answer in scientific notation.
Final answer:
The simplified expression is 7.992 × 10³.
Explanation:
To simplify the expression 111,000 × 0.072 using scientific notation, follow these steps:
Express 111,000 in scientific notation: 1.11 × 10⁵Express 0.072 in scientific notation: 7.2 × 10⁻²Multiply the two numbers: (1.11 × 10⁵) × (7.2 × 10⁻²)First, multiply the decimal parts: 1.11 × 7.2 = 7.992Next, add the exponents for the powers of 10: 5 + (-2) = 3Combine the results: 7.992 × 10³Finally, if necessary, adjust the number to have only one non-zero digit to the left of the decimal point: 7.992 × 10³ is already in correct form.The expression simplified in scientific notation is 7.992 × 10³.