What are the coordinates of the point that corresponds to -7x/4 on the unit circle

Answers

Answer 1

This is a problem of intersection. So, we have two equations, first of all we have a straight line and the second equation is a circle with ratio equal to 1. Therefore, in a mathematical language this is established as follows:

(1)[tex]y = \frac{-7x}{4}[/tex]
(2)[tex]x^{2}+y^{2}=1[/tex]

We introduce (1) into (2):

[tex]x^{2}+(\frac{-7x}{4})^{2}=1[/tex]
[tex]x^{2}+\frac{49x}{16}^{2}=1[/tex]
[tex]65x^{2}=16[/tex]

There are two values, namely:

[tex]\left \{ {{x_{1} = +0.4961 } \atop {x_{2} = -0.4961 }} \right.[/tex]

Then, substituing these values in the first (1) equation, we find:

[tex]\left \{ {{y_{1} = -0.8681 } \atop {y_{2} = +0.8681 }} \right.[/tex]

Finally, the points are two:

[tex]P_{1}=(0.4961,-0.8681)[/tex]
[tex]P_{2}=(-0.4961,0.8681)[/tex]

Related Questions

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

let Vc : cone's volume, Vp : pyramid's Volume, r radius, h height. w width and l length.

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.

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

In an isosceles triangle, the angles opposite to the two equal sides are also congruent.
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!

Final answer:

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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TIMED, need the answer ASAP, will give brainiest

Answers

I think it's four?...

Solve the system of equations using the substitution method.

{2x+8y=4 x=−3y+5

Enter your answers in the boxes.

Answers

Hi!
I believe the answer is (14,-3)
have a great day & good luck!

Need this geometry answer quick!

(I think its answer c but not sure)

Answers

180 is the answer....

angle B =50
angle C = 130

When the polynomial is written in standard form, what are the values of the leading coefficient and the constant? 5x + 2 - 3x^2

Answers

Leading coefficient = -3
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.

Four girls and eight boys are running for president or vice president of the student council. find each probability: find the prbability that two girls are elected

Answers

The probability is 1/11.

The probability that a girl is elected for one office is 4/12, since there are 4 girls out of 12 students.

The probability that a girl is elected for the second office is 3/11. This is because after one girl is elected, there are 3 girls left out of 11 students left.

Together, this gives us
4/12(3/11) = 12/132 = 1/11

The probability that two girls are elected president and vice president from a group of 4 girls and 8 boys is calculated using a hypergeometric distribution, resulting in a probability of 1/11.

The question is asking for the probability that two girls are elected president and vice president of the student council when there are four girls and eight boys running for these positions. This is an example of a hypergeometric distribution problem, as we are selecting without replacement from a finite population divided into two groups.

To find the probability, we need to determine the number of successful outcomes divided by the total number of possible outcomes. The successful outcome is that the two elected individuals are both girls. Since there are 4 girls, there are 4 choose 2 ways to select 2 girls, which equates to 6 possible successful outcomes. The total number of ways to choose 2 individuals from 12 candidates (4 girls + 8 boys) is 12 choose 2, resulting in 66 possible outcomes.

The probability can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.

Probability = Successful outcomes / Total outcomes = 6 / 66 = 1 / 11

Given the system of inequalities below: -3x - y < 12 and 2x + 3y ≥ 9

Answers

y>3x+12
y(less than or equal to)-2/3x+9

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

Final answer:

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 feet

To 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.

Help! Thanks in advance!
Screenshotted question!

Answers

The answer is (2g)-3

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 answers are follow

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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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

Hey there! :D

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

Muffins: 28
Donuts: 49

Muffins to donuts: 28/49

Answer = 28/49 = 4/8 = 1/2

~Hope this helped~

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

the correct answer is B

Simplify: 8x - 4(2x - 5) - 2

Answers

Hey there!

[tex]8x - 8x + 20 - 2 \\ = 18[/tex]

Hope this helps. - M

Consider this system of linear equations:

22x − y = -23 (equation 1)

11x + 12y = 1 (equation 2)

Answers

To solve this problem you must apply the proccedure shown below:

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

Using subtraction method or elimination method

22x − y = -23
-
(11x + 12y = 1) *2

22x − y = -23
-
22x + 24y = 2
0 -25y = -25
y = 1

22x - 1 = -23
x = 1

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)

Answers

The answer is 3,726 m2

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

Answers

it will probably be A Hopes This Helps.

If it costs $7.50 to park, how much will the stadium make from parking 10,600 vehicles?

Answers

the answer would be 79,500 because you would multiply 10,600 x 7.50 = 79,500..

For this problem, you must multiply 7.50 by 10,600, which equals $79,500 It would cost $79,500 to park all those cars! Hope this helps!

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

Hello,
Please, see the attached file.
Thanks.

Answer:

Step-by-step explanation:

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?

Answers

To solve this problem you must apply the proccedure shown below:

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.

The Freshman class has 27 more boys than girls. If there are 283 freshman, how many are girls?

Answers

You can write an equation to represent this situation. Let x represent the number of girls.

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! :)

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

For this case we first define variables:
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

x2+y2-4+2y-11=0 what are the center and radius of the circle?

Answers

[tex] x^2 + y^2 - 4x + 2y - 11 = 0 [/tex]

You need to complete the square for both x and y.

[tex] x^2 - 4x + y^2 + 2y = 11 [/tex]

[tex] x^2 - 4x + 4 + y^2 + 2y + 1 = 11 + 4 + 1 [/tex]

[tex] (x - 2)^2 + (y + 1)^2 = 16 [/tex]

[tex] (x - 2)^2 + (y + 1)^2 = 4^2 [/tex]

The center is (2, -1).
The radius is 4.

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%?

Answers

Here, i = $3500*0.025*(1/2) = $43.75 in simple interest.

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

D = 1.5n + 12
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.

it would be in between 9 to 10 weeks because the answer is 9.333 repeating

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

no. it is not a fair game because each roll is worth $15 and no matter what u roll, you won't get $15 or more so you'll just be losing money every time u roll

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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simplify. x-2/(x^2+4x-12)

Answers

Simplifying the above expression we shall proceed as follows:
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)

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.

HELP ASAP WILL GIVE BRAINLIEST

Answers

It should be zero solutions since the lines never intersect.

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

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

It's the first and third one... I just took the practice test.

Answer:a&c

Step-by-step explanation:

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