what are the coordinates of a p;point on the unit circle if the angle formed by the positive x axis and the radius is 60 degrees
Answers
Using the ratios, we know that the side opposite the 30° angle (the x-axis) will be 1/2 the hypotenuse 1, which is 1/2. This means our x-coordinate is 1/2.
We also see that the side opposite the 60° angle will be the other leg, times √2. This means it will be (1/2) * √2 = √(2)/2. This is the y-coordinate.
Therefore, the coordinates of the point on the unit circle are (1/2, √(2)/2).
Related Questions
An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum values of I
Answers
Final answer:
The maximum value of the electric current I is 1 + √8, and the minimum value is -1 - √8, found by considering the amplitudes of the cosine and sine components in the given function.
Explanation:
The maximum and minimum values of an electric current, I, can be found by analyzing the function I=cos(wt)+√8sin(wt), where w is a constant and ≠0.
To find the maximum and minimum values, we need to consider the amplitude of the sine and cosine components separately. The maximum amplitude of the cosine function is 1, and for the square root of 8 times the sine function, it is √8. Therefore, the maximum possible value of the current is when both the sine and cosine functions are at their peaks. In this case, the maximum value of I would be 1 + √8.
To find the minimum value, we consider the case when the cosine function is at its minimum value, -1, and the sine function is also at its minimum, which can also be - √8. Therefore, the minimum possible value of I would be -1 - √8.
bird leaves its nest and travels 18 miles per hour downwind for x hours. On the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours. What is the distance of the entire trip?
Answers
d - 6 = distance back
time = distance ÷ speed
x = d/20
x = (d - 6)/(16)
so d/20 = (d - 6)/16. Cross multiply
20d - 120 = 16d
-120 = -4d
30 = d so the whole trip assuming the bird gets back to the starting point is 60 miles
If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest?
A. $30.72
B. $41.12
C. $46.52
D. $53.76
Answers
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$3000\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &4 \end{cases}[/tex]
[tex]\bf A=3000\left(1+\frac{0.05}{1}\right)^{1\cdot 4}\implies A=3000(1.05)^4\implies \boxed{A=3646.51875}\\\\ -------------------------------\\\\ \stackrel{\textit{compounded interest}}{3646.51875}~~-~~\stackrel{\textit{simple interest}}{3600}[/tex]
A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet. To the nearest whole unit, what is the area of the canvas, including the floor? Use 3.14 for π.
Answers
Answer:
The area of the canvas, including the floor is 1548 sq. feet.
Step-by-step explanation:
Given : A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet.
To find : What is the area of the canvas, including the floor?
Solution :
A conical tent made of canvas has a base that is 34 feet.
The diameter of the base is D=34 feet.
The radius of the base is [tex]r=\frac{34}{2}=17[/tex]
The slant height l=12
The area of the canvas, including the floor is
[tex]A=\pi r l+\pi r^2[/tex]
[tex]A=\pi r(l+r)[/tex]
[tex]A=3.14\times 17(17+12)[/tex]
[tex]A=3.14\times 17\times29[/tex]
[tex]A=1548.02[/tex]
In nearest whole unit, A=1548 sq. feet.
Therefore, The area of the canvas, including the floor is 1548 sq. feet.
find decimal notation 75 percent
Answers
Hope this helps!
How long should the metal stripping be to protect the edge of circular table top if the radius of the top is 2 feet
A) 1.26 feet
B) 4 feet
C) 122 feet
D) 6.28
E) none
Answers
find factors of 14y^2+41y+15
Answers
the picture shows a barn door what is the distance BC between two horizontal parallel bars?
Answers
tan (x) = opp / adj
In this case, tan (45°) = BC / 4
To get BC by itself, multiply both sides by 4
4 * tan (45°) = BC
The answer is D
How many solutions does 25-4x=15-3x+10-x have
Answers
-10 - 10
15 - 4x = 15 - 2x
-15 -15
-4x = - 2x
no solution
Answer: The given equation will have infinite number of solutions.
Step-by-step explanation: We are given to check the number of solutions to the following equation :
[tex]25-4x=15-3x+10-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the number of solutions, we must solve the given equation.
The solution of equation (i) is
[tex]25-4x=15-3x+10-x\\\\\Rightarrow 25-4x=25-4x\\\\\Rightarrow 4x-4x=25-25\\\\\Rightarrow 0=0,[/tex] which is always true.
Thus, the given equation will have infinite number of solutions.
A publishing company has a weekly cost equation of C=96,000+20x and a weekly revenue equation of R=26x, where x is the number of books produced and sold in a week. The company loses money when R
Answers
To find when a publisher makes or loses money, compare the cost function C=96,000+20x to the revenue function R=26x. The break-even point is at x=16,000 books produced and sold weekly. Below this, the company incurs losses.
When determining when a publishing company makes or loses money, we investigate the relationship between cost and revenue functions. The cost function given is C=96,000+20x and the revenue function is R=26x, with x representing the number of books produced and sold per week. A company loses money when costs exceed revenues, that is when C > R.
To find the quantity of books where this happens, we equate the two equations:
C = R96,000 + 20x = 26x96,000 = 26x - 20x96,000 = 6xx = 96,000 / 6x = 16,000Therefore, at the production and sale of 16,000 books, the company will break even. Producing fewer than 16,000 books would result in a loss because the cost would be higher than the revenue generated.
Line l passes through the origin and point (3,4).What is the slope of a line parallel to line l
Answers
so, that's the slope of a line passing through the origin and 3,4, and any line parallel to it, will have the same exact slope.
There are 25 squares in the pattern. What fraction of the squares have these number of edges free?
Answers
one stae leads the country in tart cherry production producing 78 out of every 100 tart cherries each year what percent of tart cherries are produced in this state
Answers
The state in question produces 78% of the country's total annual tart cherry production.
Explanation:The state in question produces 78 out of every 100 tart cherries annually, which is the same as 78 out of 100 or 78/100. When written as a fraction, this can be turned into a decimal by dividing the numerator (78) by the denominator (100). This will give 0.78. To convert this decimal into a percentage, we then multiply by 100 which leads to 78%. This means the state produces 78% of the total tart cherries grown in the country each year.
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What is 3/7 divided by 6?
Answers
1.) Divide a fraction by an integer:37 ÷ 6 = 37× 6 = 342
2.) Simplify a fraction:
342 = 1 × 314 × 3 = 1143/7 divided by 6 is equal to 1/14.
To divide 3/7 by 6, you can multiply the numerator (3) by the reciprocal of the denominator (6).
The reciprocal of 6 is 1/6.
So, (3/7) divided by 6 can be calculated as:
(3/7) × (1/6)
= (3 × 1) / (7× 6)
= 3/42
Divide numerator and denominator by 3:
= 1/14
Therefore, 3/7 divided by 6 is equal to 1/14.
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How many diameters can a circle have?
Answers
How to find the least common denominator of 10x/x-3 and 4x/x-2
Answers
Can someone show me how to do this pleases?!.
solve the equation.
- 2 = 3x/5 + 1
Answers
1. -2=1/2x
2.1/2x=-2
3. 2*(1/2x)=(2)*(-2)
4. x=-4
Hope this helps :)
-2=1/2x
1/2x=-2
2*(1/2x)=(2)*(-2)
x=-4
I hope this helped! :)
Which of the following are good ideas to use when gathering your resources? Check all that apply
A. List potential formulas.
B. Draw a diagram.
C. Guess at the solution and see if you are close.
D. Write down the facts.
E. Form an equation.
F. Organize into a table.
Answers
E. Form an equation.
F. Organize into a table.
A. List potential formulas.
And
D.
When gathering resources for problem-solving, the following ideas can be helpful:
A. List potential formulas.B. Draw a diagram.D. Write down the facts.E. Form an equation.F. Organize into a table.The given options are all effective strategies that can assist in organizing and understanding the problem, as well as formulating a solution.
Option C, guessing at the solution, might not always be reliable or effective in all scenarios and is not considered a systematic approach.
Therefore, it may not be considered a recommended idea when gathering resources for problem-solving.
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Please help me solve 9x+16=4x-19
Answers
1 2 3 4 5 6 7 8 9 10
TIME REMAINING
51:43
Which are the solutions of the quadratic equation?
x2 = 9x + 6
Answers
The solutions of the quadratic equation x^2 = 9x + 6 are (9 + sqrt(105))/2 and (9 - sqrt(105))/2.
Explanation:To find the solutions of the quadratic equation x^2 = 9x + 6, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b +- sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -9, and c = -6. Plugging in these values, we get:
x = (-(-9) +- sqrt((-9)^2 - 4(1)(-6))) / (2(1))
Simplifying further:
x = (9 +- sqrt(81 + 24)) / 2
x = (9 +- sqrt(105)) / 2
So the solutions of the quadratic equation x^2 = 9x + 6 are:
x = (9 + sqrt(105)) / 2
x = (9 - sqrt(105)) / 2
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The solutions to the quadratic equation x² = 9x + 6 are x = 3 and x = 6. This is done by rearranging the equation and then factoring into two binomials (x - 3) and (x - 6) equals 0, then set each binomial equal to zero.
Explanation:The given quadratic equation is x² = 9x + 6. To find the solutions of the quadratic equation, we first move all the terms to one side. This gives us: x² - 9x - 6 = 0. This is now a standard quadratic equation, and can be solved by either factoring or using the Quadratic Formula.
If we opt to solve via factoring, we're looking to factorize the original expression into two binomial expressions, essentially looking for two numbers which both add up to -9 and multiply to -6. These two numbers are -3 and 6. Therefore, the quadratic equation can be factored as follows: (x - 3)(x - 6) = 0. Setting each factor equal to 0 gives the possible solutions for x, in this case, x = 3 and x = 6.
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What is the value of this expression? (−8)3
Answers
=-24
Use the Rules for Signs for Multiplication
then multiply the numbers
The function y_p(t) = \ln(1 + 2 t), \ t > -\frac{1}{2}, is a particular solution to the differential equation y^{\,\prime\prime} + 3 y = g(t). find g(t)
Answers
[tex]y_{p}(t) = ln(1 + 2t) - \frac{1}{2} [/tex]
The ODE is
y'' + 3y = g(t)
Obtain the derivatives of the particular solution.
[tex]y_{p}^{'} = \frac{2}{1+2t} \\\\ y_{p}^{''} = \frac{-4}{(1+2t)^{2}} [/tex]
Because the particular solution should satisfy the ODE, therefore
[tex]g(t)=- \frac{4}{(1+2t)^{2}} +3 \, ln(1+2t)- \frac{3}{2} [/tex]
Answer: [tex]g(t) = - \frac{4}{(1+2t)^{2}} + 3 \, ln(1+2t) - \frac{3}{2} [/tex]
Then
[tex][\ln{(1+2t)}]^{\prime\prime}+3[\ln{(1+2t)}]=g(t) \\ \\ \Rightarrow\bold{g(t)= \frac{2(1+6t)}{(1+2t)^2}+3\ln{(1+2t)}}[/tex]
nearly 4 of 5 people choose vanilla as their favorite ice cream flavor. if 120 people attend an ice cream social, how many would you expect to choose vanilla?
Answers
x/182 = 4/7
---
x = 182(4/7)
---
x = 26*4
x = 104
Write 12.5% as a fraction or mixed number in simplest form
Answers
1/8 = 0.125
Your answer = 1/8
Answer: 1/8
Step-by-step explanation: A percent is a ratio that compares a number to 100. So we can write 12.5% as 12.5/100.
Next, we need to get rid of the decimal. We can multiply the numerator and denominator of a fraction by the same number without changing the value of the fraction.
So to get rid of the decimal, we can multiply the numerator and the denominator of 12.5/100 by 10 and we have 125/1000.
Now, notice that 125/1000 is not in lowest terms because we can divide the numerator and the denominator by 125 to get 1/8.
So 12.5% can be written as the fraction 1/8.
Forty percent of all registered voters in a national election are female. a random sample of 5 voters is selected. the probability that there are no females in the sample is
Answers
To calculate the probability of selecting no female voters in a sample of 5, given that 40% of the registered voters are female, we multiply the probability of selecting a male voter (60%) five times, which equals to (0.6)⁵ or 7.776% probability.
The question involves calculating the probability that none of the five randomly selected voters are female, given that 40% of registered voters are female. To find this probability, we need to use the complementary probability, which is the probability of the opposite event occurring (that is, selecting a male voter).
The probability of selecting one male voter randomly is 60% (or 0.6), as females account for 40% of the registered voters. When we select 5 voters independently, we multiply the individual probabilities together because the events are independent. Therefore, the probability of selecting no female voters in 5 trials is calculated as:
(0.6) × (0.6) × (0.6) × (0.6) × (0.6) = (0.6)⁵ = 0.07776 or 7.776%.
This is the probability that a random sample of 5 voters will contain no females.
if you had a fraction strip folded into twelfths what fractional lengths could you measure with the strip
Answers
A submarine is 671 feet below sea level. If it ascends 218 feet and then descends 1363 feet, what is its new position?
Answers
Answer:
c = 1816 feet below sea level
Step-by-step explanation:
the costume designer decides to make the sashes a little smaller, so that each of the 8 dresses can have a sash. What fraction of fabric should the costume maker use to make each sash
Answers
The fraction that the costume maker should use for each sash is 1/8 of the total fabric available, as the fabric is being evenly divided among the 8 dresses.
Explanation:
If the costume designer is making sashes for 8 dresses and aims to use each bit of fabric equally, then each sash should consist of 1/8 of the total fabric. This is because the total fabric is being divided evenly among the 8 dresses. For example, if the costume designer has 8 yards of fabric, then each sash would use 1 yard of fabric (8 divided by 8 equals 1).
In fraction terms, each sash uses 1/8 of the fabric available. So for each dress, the costume designer should use 1/8 of the total fabric to make a sash.
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Charlie is making a scale model of his kitchen. If the kitchen measures 12 feet by 11 feet, and his scale is two inches = three feet, what is the scale measure of the kitchen? Round to the nearest tenth.
A. 8 in by 7.3 in
B. 18 in by 16.5 in
C. 0.5 in by 0.4 in
D. 10 in by 9 in
Answers
Answer:
Option A. is the answer.
Step-by-step explanation:
Charlie is making a scale model of his kitchen.
The kitchen measures 12 feet by 11 feet.
We can use the unitary method to get the scale measures.
Since his scale is 3 feet = 2 inches.
So 1 feet = [tex]\frac{2}{3}[/tex] inches
and 12 feet = [tex]\frac{(2)(12)}{3} = 8[/tex] inches
Similarly 11 feet = [tex]\frac{(11)(2)}{3}=7.3[/tex] inches
Therefore, scale measures of the kitchen will be = 8 in by 7.3 in
Option A. is the correct answer.
evaluate the function
can someone please explain how I would solve this please?
Answers
y = 4 x 1/2^6
y = 4 x 1/64
y = 1/16
Before we even get there, though, consider how we define multiplication as repeated addition. When you see an expression like 3 x 5, what that essentially translates to is "add 3 to itself 5 times," so we could also write 3 x 5 as 3 + 3 + 3 + 3 + 3. Having established that, around middle school, you'll typically get your first exposure to positive exponents, which are defined at first as repeated multiplication. When you see something like [tex]3^5[/tex], we could also read that as "multiply 3 by itself 5 times," or [tex]3\times3\times3\times3\times3[/tex].
With that definition for positive exponents defined, it makes sense that we would define negative exponents in terms of the inverse of repeated multiplication: repeated division. Each time we step the exponent back by 1, we divide by the base again. For example, let's take these decreasing powers of 3 and notice what happens:
[tex]3^3 = 27\\3^2=27/3=9\\3^1=9/3=3\\3^0=3/3=1[/tex]
If we start stepping back further, we start getting to values below 1:
[tex]3^{-1}=1/3\\3^{-2}=(1/3)/3=1/3^2=1/9\\ 3^{-3}=(1/9)/3=1/3^3=1/27[/tex]
And this pattern continues, with the essential takeaway being that [tex]3^{-x}=1/3^x[/tex]
Try applying that pattern to the equation you've been given, [tex]y=4\cdot2^{-6}[/tex], and see what you get!