After traveling a distance of 2π/3 on the unit circle in the counter-clockwise direction from (1,0), the ant stops at the coordinates (-1/2, √3/2), which are found using the unit circle's parametric equations.
Explanation:The question asks about finding the coordinates of a point on the unit circle after traveling a certain distance in the counter-clockwise direction. The distance given is 2π/3, which, when considering the circumference of the unit circle (2π), represents an arc that is a third of the full circle. The unit circle is centered at the origin (0,0) and has a radius of 1, with points on it defined by cos(θ) and sin(θ) for any angle θ measured in radians from the positive x-axis.
Traveling 2π/3 radians from (1,0) in the counter-clockwise direction lands us at an angle of 2π/3 radians from the positive x-axis. The coordinates of the point on the unit circle at this angle can be found using the circle's parametric equations x = cos(θ) and y = sin(θ). Substituting θ with 2π/3, we obtain:
x = cos(2π/3) = -1/2y = sin(2π/3) = √3/2Therefore, the coordinates of the point where the ant stops are (-1/2, √3/2).
A farmer harvested 35 acres of corn and 20 acres of beans. Animals ate 1/8 of the corn he originally planted. how many acres of corn did the farmer plant?
Lilia parked her 18 model cars in equal rows. 3time6. Write another way lilia could arrange her cars in equal rows
Which best describes angelica solution
The error that Angelica made is an error substituting the values into the Pythagorean theorem. The equation should be c² + 6² = 10²
How to use Pythagoras Theorem?
From the brainly link attached below, we can see the steps Angelica used in calculating the distance between the two points shown on the graph below.
The steps she took are;
Step 1: Use the point C(–4, –5) to make a right triangle with the 90 degree vertex at C.
Step 2: Determine the lengths of the legs: AC = 6 and BC = 10.
Step 3: Substitute the values into the Pythagorean theorem: 10² = 6² + c²
Step 4: Evaluate
From the graph and looking at the steps she took, we can say that the error that Angelica made is an error substituting the values into the Pythagorean theorem. The equation should be c² + 6² = 10²
Read more about Pythagoras Theorem at; https://brainly.com/question/9917504
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99 POINTS TOP RECORD I NEED PRO'S FOR THIS!
HELP ASAP
!! ;D
(-10.3)(2)x = 4(-10.3)(2)
cross out the same terms on both sides and you end up with x =4
collection of dimes and quarters has a total of $19.55. If there are three times as many quarters as dimes, find the number of each?
Graph the following sequence of transformations for
While going on a field trip, a busload of 54 students will have to be split up into three groups. two thirds will go to lunch first, and one third will go visit the exhibits. how many will go to lunch first?
is the square root of 10 greater than,less than or equal to 5
During a certain week, a post office sold Rs.280 worth of 14-paisas stamps. How many of these stamps did they sell?
The post office sold 2000.
To find out how many 14-paisa stamps the post office sold to make Rs.280, we need to follow a step-by-step solution.
Convert the total amount from rupees to paisas:Since the stamp's value is given in paisas.There are 100 paisas in 1 rupee.Rs.280 = 280 x 100 = 28000 paisas.The value of one stamp is 14 paisas.To find the number of stamps sold, we divide the total amount in paisas by the value of one stamp:28000 paisas ÷ 14 paisas per stamp = 2000 stamps.
A deep-sea diver is in search of coral reefs. He finds a beautiful one at an elevation of -120 4/7 feet. While taking pictures of the reef, he catches sight of a manta ray. He swims up 25 3/7 feet to check it out. What is the diver's new elevation?
The position of the diver's new elevation will be negative 666 / 7.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A remote ocean jumper is looking for coral reefs. He tracks down a wonderful one at a rise of - 120 ⁴/₇ feet. While taking photos of the reef, he sees a manta beam. He swims up 25 ³/₇ feet to look at it.
Convert the mixed fraction number into a fraction number. Then we have
- 120 ⁴/₇ = - 844 / 7
25 ³/₇ = 178 / 7
The position of the diver's new elevation will be given as,
⇒ - 844 / 7 + 178 / 7
⇒ (- 844 + 178) / 7
⇒ - 666/7
The position of the diver's new elevation will be negative 666 / 7.
More about the Algebra link is given below.
https://brainly.com/question/953809
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jose rodriguez's checking account had a starting balance of 1,234.56. he wrote a check for 115.12 for plumbing supplies and check for 225.00 for a loan payment. Yesterday he deposited 96.75 in his checking account. what jose's current balance?
five quarts of latex enamel paint will cover about 100 square feet of wall surface. how many quart are needed to cover 71 square feet of kitchen wall and 69 square feet of bathroom wall ?
What is the ordered pair for point K? A. (–4,–5)
B. (4,–5)
C. (5,–4)
D. (–4,5)
Answer:
B
if you read the graph it is 4,-5
CD player: $120, 20% markup (show work)
simplify the expression 4y - 1 - 3y + 2
Another order calls for 26 widgets. The widgets comes in boxes of 5. How many full boxes of 5 do you pull? How many single items do you still need?
divide 26 by 5
26 /5 = 5.2
so 5 full boxes
5*5 = 25
26-25 = 1
so 5 full boxes and 1 single widget
For an order of 26 widgets with each box containing 5 widgets, you would pull 5 full boxes and still need 1 more single widget.
Explanation:To solve this problem, we need to find out how many full boxes of 5 widgets we can make from 26 widgets and how many single widgets we will have left. Whole number quantities, such as the number of widgets and boxes, are important here. First, we divide 26 by 5 to find out the number of full boxes. This gives us 5 full boxes with a remainder of 1, which means we have one widget left. So, we pull 5 full boxes and still need 1 more single widget.
Learn more about Dividing Whole Numbers here:https://brainly.com/question/10221961
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which decimal represents the fraction of candles in this group that have flames
What is the prime factorization of 72?
From 1980 to 1990, Lior’s weight increased by 25%. If his weight was k kilograms in 1990, what was it in 1980?
Ththe weight of Lior in 1990 in terms of k is [tex]\frac{4}{5} k[/tex]
Let the weight of Lior in 1980 be "w"
If Lior's weight increased by 25%, his new weight was "k". This can be expressed as:
w + (25% of w) = k
w + (0.255w) = k
w + 0.15w = k
1.25w = k
Divide both sides by 1.25
[tex]\frac{1.25w}{1.25} =\frac{k}{1.25} \\w=\frac{k}{1.25} \\w=\frac{100k}{125} \\w=\frac{4}{5}k[/tex]
This shows that the weight of Lior in 1990 in terms of k is [tex]\frac{4}{5} k[/tex]
Learn more here: https://brainly.com/question/7287613
how do i find 3/4 of 460
Can I get some points? Please ask me a very simple question like 1 plus 1 or sum and I will answer and get pts? please? Youll get 10 points lol if you have a lot can I get like 70 or sum
Answer:the answer is two double check i could be wrong
Step-by-step explanation:1 x 1 x 1 + 1 / 1 = 2
Jade spend $37.60 on groceries. 4/5 of that total was spent on vegetables. How much was spent on other items
divide the total spent by 5 to get what 1/5 is
37.60 / 5 = 7.52
they spent $7.52 on other items
Ann had 75 fliers to post around town. Last week,
she posted 2/5 of them. This week, she posted 2/3 of the remaining fliers. How many fliers has she still not posted?
i need help due tommorrow !
9/11÷13/33
what step can you take to check that your results is correct
A. multiply your results by 13/33
B. multiply your results by11/9
C. multiply your results by 9/11
D. multiply your results by 13/33
Matty jogs 9 km/hr. Identify the correct conversion factor setup required to compute Matty's speed in m/s.
Answer:
2.5 m/s
Step-by-step explanation:
we have given that Matty jogs 9 km/hr
we have to convert 9 km/hr to m/s
we know, 1 km= 1000 m
and 1 hr= 60 minutes and 1 minute= 60 seconds
which implies that 1 hr=60 x 60 = 3600 seconds
now, to convert km/hr into minute/second we have to multiply it by 1000/3600 or 5/18
i.e. 9×1000/3600= 5/2=2.5 m/s
A single microvillus is a rod-like structure that is 1.0 μm in height. it has a hemispherical top approximately 0.1 μm in diameter. calculate the surface area of the cylinder that forms the "sides" of the microvillus rod. use 3.14 for π.
Final answer:
The surface area of the cylinder forming the sides of a microvillus rod with a diameter of 0.1 µm and a height of 1.0 µm is 0.314 µm².
Explanation:
To calculate the surface area of the cylinder that forms the "sides" of the microvillus rod, we will use the formula for the surface area of a cylinder without the top or bottom, which is circumference multiplied by height
(A = 2πrh).
Since the diameter (d) of the microvillus is given as 0.1 µm, we first find the radius (r) by dividing the diameter by 2.
Therefore, r = 0.1 µm / 2 = 0.05 µm.
The height (h) is given as 1.0 µm.
Inserting these values into our formula, we get:
A = 2 × 3.14 × 0.05 µm × 1.0 µm = 0.314 µm².
Hence, the surface area of the sides of the microvillus rod is 0.314 µm².
A really bad carton of 18 eggs contains 9 spoiled eggs. an unsuspecting chef picks 6 eggs at random for his "mega-omelet surprise." find the probability that the number of unspoiled eggs among the 6 selected is
Final answer:
To find the probability that the number of unspoiled eggs among the 6 selected is X, we can use the hypergeometric probability formula. This formula is used when the sample drawn is without replacement from a finite population.
Explanation:
To find the probability that the number of unspoiled eggs among the 6 selected is X, we can use the hypergeometric probability formula. This formula is used when the sample drawn is without replacement from a finite population. In this case, we have 18 total eggs in the carton, with 9 spoiled eggs. So the probability that X unspoiled eggs are selected out of the 6 can be calculated as:
P(X) = (C(X,6) * C(9,6)) / C(18,6)
Where C(n,r) represents the combination of n things taken r at a time.
Solve each equation 4y-x=16
find the gradient of the line between each pair of points A(2,2) and B(6,6)
A person invests $4000 at 2% interest compounded annually for 4 years and then invests the balance (the $4000 plus the interest earned) in an account at 8% interest for 7 years. Find the value of the investment after 11 years.
(Hint: You need to break this up into two steps/calculations. Be sure to round your balance at the end of the first 4 years to the nearest penny so you can use it in the second set of calculations.)