An architect maps two buildings, which are located on a piece of land, onto a coordinate plane. He wants to build a wall at the diagonal AC to divide the piece of land into two parts. What will be the length of the wall? A. 65–√ units B. 6 units C. 237−−√ units D. 2 units

An Architect Maps Two Buildings, Which Are Located On A Piece Of Land, Onto A Coordinate Plane. He Wants

Answers

Answer 1

Answer:

[tex] 6\sqrt{5} units [/tex]

Step-by-step Explanation:

The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).

Distance formula between two points on a graph (d) = [tex] \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] A(-6, -2) = (x_1, y_1) [/tex]

[tex] C(6, 4) = (x_2, y_2) [/tex]

[tex] d = \sqrt{(6 - (-6))^2 + (4 -(-2))^2} [/tex]

[tex] d = \sqrt{(6 + 6)^2 + (4 + 2)^2} [/tex]

[tex] d = \sqrt{(12)^2 + (6)^2} [/tex]

[tex] d = \sqrt{144 + 36} [/tex]

[tex] d = \sqrt{180} [/tex]

[tex] d = \sqrt{36*5} [/tex]

[tex] d = 6\sqrt{5} [/tex]

The length of the wall = [tex] 6\sqrt{5} units [/tex]


Related Questions

Find the measure of c.

Answers

Answer:

140°

Step-by-step explanation:

The circle has a central angle of 80. This means that the arc it intercepts is also 80°. Therefore, the rest of the circle not intercepted by the arc is 360-80=280°

Remember that inscribed angles have one-half of the arc-length it intercepts. We can see that Angle C intercepts the entire circle except for the arc intercepted by Angle O. Therefore, the arc intercepted by Angle C is 280°. This means that Angle C is the half of 280, or 140°.

The answer is C is equal to 140

Sue's ice cream has 6 more scoopsthan Tessa's ice cream cone.

Sue's ice cream cone has 9 scoops.

How many scoops are on Tessa's ice cream cone?​

Answers

Answer:

Tessa has 3 ice-cream scoops

Step-by-step explanation:

URGENT!!!! PLEASE HELP NOW!!! WHO EVER GIVES THE CORRRECT ANSWER WILL GET BRAINLIEST!!!

Items Sold at a Clothing Store
The bar graph shows the number of each item sold at a clothing store. Which
statement about the graph is true?​

Answers

Answer:

The correct ans is..... ( which i believe )

3rd option

Hope this helps...

Pls mark my ans as brainliest

If u mark my ans as brainliest u will get 3 extra points

Answer:

3rd option

Step-by-step explanation:

because 2/5 of 40 is equal to 16, and thats the equivelent of the pants sold.


Find the sine and cosine of each angle as a fraction and as a decimal. Round to the nearest hundredth.

Answers

Answer:

1st triangle:

sin(C): 0.64, [tex]\frac{16}{25}[/tex]

cos(C): 0.8, [tex]\frac{4}{5}[/tex]

Second triangle:

sin(C): 0.75, [tex]\frac{\sqrt{5} }{3}[/tex]

cos(C): 0.67, [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Using SOH CAH TOA, we know that to find the sin of an angle, it's Opposite/Hypotenuse.

To find the cos of an angle, it's adjacent/hypotenuse.

In the 1st triangle:

The adjacent to C is 16, the hypotenuse is 25.

[tex]\frac{16}{25} = 0.64[/tex] is the sin of C.

The adjacent to C is 20, and the hypotenuse is 25.

[tex]\frac{20}{25} = 0.8[/tex] is the cos of C.

In the second triangle:

The opposite to C is [tex]\sqrt{5}[/tex] and the hypotenuse is 2.

[tex]\frac{\sqrt{5} }{2} \approx0.75[/tex] is the sin of C.

The adjacent to C is 2 and the hypotenuse is 3.

[tex]\frac{2}{3} \approx 0.67[/tex] is the cos of C.

Hope this helped!

0.64 because it makes the most sense to me well because I looked it up too

Jill paid $36 for calendars marked down $5 apiece from the original price, she could have gotten 5 fewer calendars. How many cards did she buy

Answers

Answer:

she bought 7 cards

Step-by-step explanation

7x5=35 and im sure there is tax

She bought 7 cards .. I say that bc if you divide 36 and 5 you’d get 7 and 5x7 is 35

Help and show work plz

Answers

Answer:

RK: 4 and BC: 6

Step-by-step explanation:

SImilar triangles

find unknown / know sides

Which means (2x+2)/6 = (4x+2)/9

  (X+1)/3 = (4x+2)/9

Multiply 9 to both sides

9/3 (x+1) = (4x+2)

3x+3 = 4x+2

1 = x

Answer: RK = 4, BC = 6

Step-by-step explanation:

In a similar triangle, the ratios of corresponding sides are the same.  Thus, because of sides MK and AC, the triangles have a ratio of 6/9, or 2/3.  Thus, you can determine that 2/3(4x+2)=2x+2.

Distribute

8/3x + 4/3 = 2x + 2

Subtract 2x

2/3x + 4/3 = 2

Subtract 4/3

2/3x=2/3

Divide by 2/3

x = 1

Then, simply plug-in 1 for x to get that RK is 4 and BC is 6

Hope it helps <3

If we transform the parabola y=(x+1)^2+2 by shifting 7 units to the right and 5 units down, what is the vertex of the resulting parabola? Vertex of resulting parabola: (__ a0,__ a1)

Answers

Hey there! I'm happy to help!

The vertex form of a parabola is y=a(x-h)²+k. The h represents the horizontal transformation, while the k represents the vertical. The vertex of a parabola in this form is (h,k). The a represents a vertical stretch or shrink.

Our parabola is y=(x+1)²+2. This is already in vertex form, so we do not need to change the equation. There is no a (basically a=1), which means that the parabola has not been stretched or shrunk from its parent form.

We see that the h is -1. This is because in the original equation it is (x-h)², so it has to be -1 because the two negatives make a positive which is the +1. (x--1)=(x+1).

We see that the k value is 2.

Since the vertex is (h,k), this vertex is (-1,2).

However, we have to shift the parabola 7 units to the right and 5 units down. So, we add 7 to the x-value and subtract 5 from the y-value of the vertex.

(x,y)⇒(x+7,y-5)

(-1,2)⇒(6,-3)

Therefore, the vertex of the resulting parabola is (6,-3).

Have a wonderful day! :D

I did the math and the other comment is correct

help me plz can i have help

Answers

Answer:

[tex]10^{-4}[/tex]

Step-by-step explanation:

6x10^-4 because the decimal is in the thousands place

The coefficient of 6x is
1
6
Х

Answers

Answer:

6

Step-by-step explanation:

If a number and a variable were together in a term, the number would the the coefficient. The coefficient would multiply the variable.

In '6x', the number '6' is the coefficient. '6' would be multiplying 'x'.

The correct answer should be 6.  

The coefficient of 6x is 6. This is because the coefficient is before the variable and 6 is before x.

What’s x ?? Help plzzz

Answers

Answer:

x = 69°

Step-by-step explanation:

1). JFGHI is a pentagon, every angle in a Pentagon is equal to 108°.

2). angle JIH + angle HIE = 180°; angle JIH = 108, so angle HIE = 72°.

3).  angle JDI is equal to 39° and angle IEH; so angle IEH = 39°

4). Now we know 2 out of the three angles in the triangle IHE, so we can find x!

5). x + angle HIE + angle IEH = 180°

    x + 72° + 39° = 180°

    x = 69°

Simplify (−3c3w5)3. −9c6w8 −9c9w15 −27c6w8 −27c9w15

Answers

Answer:

-6723cw

Step by Step:

(-3c * 3w * 5) * 3 - 9c * 6w* 8 - 9c * 9w * 15 - 27c * 6w * 8 - 27c * 9w * 15

The answer to you question is -6723cw

What is h decreased by 20

Answers

Answer:

h minus 20

Step-by-step explanation:

H - 20




This is because decreased means or signifies “-“

If 120 is divided into 3 parts which are proportional to 1, [tex]\frac{1}{2} [/tex], and [tex]\frac{1}{6}[/tex], what is the middle part?

Answers

[tex]k+\frac{k}{2}+\frac{k}{6}=120\\\\6k+3k+k=720\\10k=720\\k=72[/tex]

72,36,12

answer: 36

So if we put 120 Into 3 parts 72,36,12 then the answer would be 36

Solve for x show work plz

Answers

Answer:

20

Step-by-step explanation:

We know that ΔBAC and ΔBED are similar becuase of the AA Postulate (they both have a right angle and they both share ∠B). Since AC is 15/3 = 5 times longer than ED, the scale factor is 5 which means AB is 5 times longer than EB. This makes EB = 25 / 5 = 5. Since AB = AE + EB and we know that AB = 25, AE = x and EB = 5, 25 = x + 5 which means x = 20.

Did u figure it out?

Find the equation of the parabola with focus (2, 3) and directrix y = -1.
es

Answers

Answer:

Below in bold.

Step-by-step explanation:

Let (x, y) be a point on the parabola. As the graph is a parabola, the distance of this point to the focus is equal to the distance of  this point from the directrix. So:

√(( x - 2)^2 + (y - 3)^2) = y - (-1)

Squaring both sides:

(x - 2)^2 + (y - 3)^2 = (y + 1)^2

x^2 - 4x + 4 + y^2 - 6y + 9  = y^2 + 2y + 1

x^2 - 4x  + 4 + 9 - 1 = 2y + 6y

8y = x^2 - 4x + 12

y = 1/8(x^2 - 4x + 12)

or we can write it as

y = 1/8x^2 - 1/2 x + 3/2.

Y=1/8^2-1/2x + 3/2 would be the answer

The following dot plot shows the number of books each student checked out from the library last month. Each dot represents a different student. Which of the following is a typical number of books one student checked out?

Answers

Answer:

The answer isn't 1 because most of the students checked out more than 1 bookThe answer isn't 4 because most of the students checked out more than 4 booksThe answer isn't 12 because most of the students checked out fewer than 12 booksThe answer is 7 because most of the students checked out more books than 1, 4, and 12

In 7, seven kids checked out 7. [tex]7*7=49[/tex] (Correct answer because 49 is the biggest number here)

In 1, only two kids checked out 1. [tex]1 *2=2[/tex] (Wrong answer because 2 is lower than 49)

In 4, only eight kids checked out 4. [tex]4*8=32[/tex] (Wrong answer because 32 is lower than 49)

In 12, only two kids checked out 12. [tex]12*2=24[/tex] (Wrong answer because 24 is lower than 49)

So 7 is the correct answer because [tex]7*7=49[/tex] is the greatest equation here.

The 0 and 11 number book is the typical book one student checked out.

Given, the dot plot shows the no. of book  each student checked out from the library last month.

Since each dot represent a different student, so clearly from the dot plot the 8 number book is checked out by the most of the students because it has most of the dots.

Since the number 0 and 11 has only one dot it represent that only 1 student checked out these books last month.

Hence the 0 and 11 number book is the typical book one student checked out.

For more details on dot plot follow the link:

https://brainly.com/question/4398979

The net of a right rectangular prism is shown below: Find the volume of the prism with the given net (in cubic inches).

Answers

Answer:

240 inches cubed

Step-by-step explanation:

Volume equals length times width times height. Imagine the net is folded into its shape. The product of the base, 6 x 10 = 60, and the height, 4, equals 240. Remember that each square accounts for two inches. Hope this helps.

It is two hundred and forty inches cubed.

solve for m. √m-7 = n+3 It is worth like 40 points

Answers

Answer:

sqrt of (m-7) = n+3

m = (n+3)^2 + 7 or m= n^2 + 6n + 16

sqrt of (m)-7 = n+3

m = (n+10)^2 or m =n^2 + 20n + 100

Step-by-step explanation:

(2) move the constants to the other side, and square

or  (1) square and move constants

then you can solve for m

Answer:

[tex]n^2+6n+16[/tex]

Step-by-step explanation:

I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not  [tex]\sqrt{m} - 7 = n+3[/tex].

[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]

Hope this helped!

Tamara walked 3/4 mile in 1/2 hour. Which of the following represents the unit rate that Tamara walked? A. 1/2 mi/h B. 2/3 mi/h C. 3/4 mi/h D. 1 1/2 mi/h Include ALL work please!

Answers

Answer:

1 1/2 miles / hour

Step-by-step explanation:

We want distance / time

3/4 miles

---------------

1/2 hour

3/4 ÷ 1/2

Copy dot flip

3/4 * 2/1

3/2

1 1/2 miles / hour

Answer:

D

Step-by-step explanation:

Multiple (3/4)  by 2 to find the information for one hour)

6/4 in one hour

3/2 or 1 + 1/2 mi/h

D is the answer

Name five fractions whose values are between 3/8 and 7/12

Answers

Answer:

convert them to decimasls

Step-by-step explanation:

convert thhem to decimals to make it easier

Answer:

1/2 2/4 4/8 6/12 9/18

Step-by-step explanation:

i’ll mark you brainliest, please show work!! i’ll also give more points

Answers

Answer:

414

Step-by-step explanation

80+10hrs=230

23bacteria:1hr

414bacteria:18hrs

The answer is 414 I’m pretty sure

Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4 How much more is the rate of change of function A than the slope of function B? 3 6 2 9

Answers

Answer:

6

Step-by-step explanation:

Function A

y = 9x + 4

Function B

y = max+b

m = 3 and b = 4

y = 3x+4

The difference in the slopes is 9-3 = 6

Answer:

6

Step-by-step explanation:

The two functions are A and B.

A's equation is khown

● y =9x + 4

B is also khown. We should only gather tge information.

● the rate of change is 3

●the y-intercept is 4

So B's equation is:

● y = 3x + 4

3 is the rate of change wich is khown as the slope.

Divide A's slope by B's slope to khow how much A's slope is bigger than B's.

● 9/3 = 3

Substract 3 from 9 and you get the difference 9-3= 6

-5+2(10b-2)=31 need help thanks!

Answers

Answer:

[tex]\Large \boxed{b=2}[/tex]

Step-by-step explanation:

-5+2(10b-2)=31

Expand brackets.

-5+20b-4=31

-9+20b=31

Add 9 on both sides.

20b=40

Divide both sides by 20

b=2

Answer:

b = 2

Step-by-step explanation:

-5+2(10b-2)=31

Multiply the terms in the bracket

That's

- 5 + 20b - 4 = 31

Group like terms

Send the constants to the right side of the equation

That's

20b = 31 + 4 + 5

Simplify

20b = 40

Divide both sides by 20

We have the final answer as

b = 2

Hope this helps you

What is the total surface area of the square pyramid below? A square pyramid. The square base has side lengths of 10 centimeters. The triangular sides have a height of 14 centimeters. 100 cm2 200 cm2 280 cm2 380 cm2

Answers

Answer:

380 cm^2

Step-by-step explanation:

10*10=100(base square)

Each triangle= (14*10) /2=70

4 sides, so therefore: 70*4=280

280+100=380

Since the square base has side 10 cm and triangular side has height 14 cm, the total surface area of square pyramid is 380 cm²

To answer the question, we need to find the total surface area of the square pyramid

Total surface area of a square pyramid.

Since a square pyramid has a square base and four triangular sides, its surface area, A = area of square base + 4 × Area of triangular side.

Area of square base

Area of square with side, L is A = L²

Area of triangular base

Area of triangle with height, h and base, L which is the length of the square base is A' = 1/2Lh

So, total surface area of square pyramid is A" = L² + 4 × 1/2Lh

= L² + 2Lh

Given that the length of the square base is 10 cm and the height of the triangular side is 14 cm.

We have that

L = 10 cm and h = 14 cm

So, substituting the values of the variables intot he equation, we have

A" = L² + 2Lh

A" = (10 cm)² + 2 × 10 cm × 14 cm

A" = 100 cm² + 280 cm²

A" = 380 cm²

So, the total surface area of square pyramid is 380 cm²

Learn more about total surface area of square pyramid here:

https://brainly.com/question/22744289

#SPJ2

5. Find the measures of the following. Round to the nearest whole number

Answers

Answer:

a - HT = 17

b - ∠T = 62

c - ∠H = 28

answer is:

a-17


b-62


c-28

What is 5 divided by 3,678

Answers

Answer:

Simple division..

divide 5 by 3,678

you'll get answer

0.00135943447

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

      Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]5\ \div \ 3678[/tex]

[tex]= \frac{5}{3678}[/tex] (Decimal: 0.001359)

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

If this helped you, could you maybe give brainliest..?

❀*May*❀

Given f(x) = -4(x-3)^2-2
a) Determine the inverse of f(x)
b) List the domain and range of inverse.

Answers

Answer:

[tex]\sqrt{\frac{x+2}{-4} }+3=y[/tex] d=(-infinity,-2) r=(3,+infinity)

Step-by-step explanation:

i did the math

It’s d=(-infinity,-2) and r=(3, plus infinity) :) hope this helped

PLEASE HELP! 10 POINTS Which line would be the line of best fit for the scatter plot?

Answers

Answer:

The first one

Step-by-step explanation:

This line is the best fit for the scatter plot because it touches a lot more points than the second

Answer:

The first line

Step-by-step explanation:

Hey there!

Well the first lie is a positive slope just like the dots whereas,

the second line is a negative slope.

Therefore, the first line is the line of best fit.

Hope this helps :)

for n prove by
[tex]3 + 3 {}^{2} + 3 {}^{3} ... + 3 {}^{n} = \frac{3(3 {}^{n} - 1) }{2} [/tex]
thank you​

Answers

Answer:

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

Step-by-step explanation:

Given

[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]

Required

Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]

The above shows the sum of a geometric series and this will be calculated as shown below;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]

Where

a = First term;

[tex]a = 3[/tex]

r = common ratio

[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]

[tex]r = 3[/tex]

Substitute 3 for r and 3 for a in the formula above;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes

[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]

[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]

Hence;

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

12 5 that is the answer for your question

The two points on the coordinate plane represent Jane's house and her friend's house. Find the distance between the houses. Question 3 options: A) units B) units C) units D) units

Answers

Answer:

8.3

Step-by-step explanation:

To do this use the distance formula

[tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

First find the coordinates Jane (-5, -2) Friend (3, -4)

Now solve for d (8.246)

Answer:

10 units or approx. 8.25 units

Step-by-step explanation:

Jane's house is at coordinate (-5,-2) and her friend's house is at coordinate (3,-4).

You can find the answer in 2 ways.

1) Hypotenuse (the diagonal side or side across from the right angle) - approx. 8.25 units

2) Down and Side (go down 2 units and go side 8 units) - 10 units

Hope that helps and maybe earns a brainliest!

Have great day ahead! :)

Other Questions
IIInitial KnowledgeThis morning, Leila's car had 19.79 gallons of fuel. Now, 2.8 gallons are left. How much fuel did Leila use? In an observational study of children in a day care setting, you select one participant at a time for observation. This is an example of using ____. What is the solution to the following system of equations? 3x-2y=12 6x - 4y = 24 Waterway has a standard of 2 hours of labor per unit, at $12 per hour. In producing 3800 units, Waterway used 7350 hours of labor at a total cost of $89670. Waterway's labor quantity variance is a data set includes 110 body temperatures of healthy adult humans having a mean of 98.1F and a standard deviation of 0.64F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans Complete the sequence 8,27,64,125,.........Just next letter A box of chocolates contains five milk chocolates, three dark chocolates, and four white chocolates. You randomly select and eat three chocolates. The first piece is milkchocolate, the second is white chocolate, and the third is milk chocolate. Find the probability of this occuring. In each of the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with appropriate sign (>, 22. f(x) is stretched horizontally by a factor of 2 and reflected across the x-axis. Which choice shows the correct representation of f(x) after these transformations? Options: A. f(1/2x) B. f(2x) C. f(2x) D. f(1/2x) A construction worker uses an electrical device to attract fallen nails and sharp objectsfrom a construction site. What is causing the attraction of the metal objects?O An electrical wave oscillating perpendicular to the electrical device.O An electrical charge radiating perpendicular to the wireO Amagnetic wave radiating perpendicular to an electrical deviceO A magnetic wave and electrical current moving in opposite directions Sara spends $25 for an all-day ticket to an amusement park. After one ride, it begins to rain and she wishes she had never come. Since she has already paid for her ticket, she should stay at the amusement park until it closes or she has wasted her $25.A. TrueB. False Common symptoms of iron-deficiency anemia include muscle weakness, shortness of breath, and lightheartedness. Why does iron deficiency cause these symptoms? what is the solution to this equation -3x=52 In part A, you analyzed genes that contribute to two diseases. (cystic fibrosis and muscular dystrophy) How can scientists use this information to develop new treatments for these diseases? Based on your findings, do you think that scientists will need to develop multiple treatments to control symptoms of these diseases? Explain your reasoning. Which point is located at (5, 2)? 2) A furlong is 1/8 of a mile. What part of a mile is 4 furlongs? Carolyn and Paul are playing a game starting with a list of the integers $1$ to $n.$ The rules of the game are: $\bullet$ Carolyn always has the first turn. $\bullet$ Carolyn and Paul alternate turns. $\bullet$ On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list. $\bullet$ On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed. $\bullet$ If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers. For example, if $n=6,$ a possible sequence of moves is shown in this chart: \begin{tabular}{|c|c|c|} \hline Player & Removed \# & \# remaining \\ \hline Carolyn & 4 & 1, 2, 3, 5, 6 \\ \hline Paul & 1, 2 & 3, 5, 6 \\ \hline Carolyn & 6 & 3, 5 \\ \hline Paul & 3 & 5 \\ \hline Carolyn & None & 5 \\ \hline Paul & 5 & None \\ \hline \end{tabular} Note that Carolyn can't remove $3$ or $5$ on her second turn, and can't remove any number on her third turn. In this example, the sum of the numbers removed by Carolyn is $4+6=10$ and the sum of the numbers removed by Paul is $1+2+3+5=11.$ Suppose that $n=6$ and Carolyn removes the integer $2$ on her first turn. Determine the sum of the numbers that Carolyn removes. How do i do this equation -3(-2y-4)-5y-2= A line of 8cm was measured as 8.04cm what is the percentage error Find the fourth roots of 16(cos 200 + i sin 200).