When converting θ = π/3 to a Cartesian equation, let x = ____
1/2 r
√2/2 r
√3/2 r

Answers

Answer 1

The equations

[tex]x = r*\cos(\theta)\\\\y = r*\sin(\theta)[/tex]

are useful to convert from polar to Cartesian

So,

[tex]x = r*\cos(\theta)\\\\x = r*\cos\left(\frac{\pi}{3}\right)\\\\x = r*\frac{1}{2} \ \text{ use unit circle} \\\\x = \frac{1}{2}r[/tex]

Answer: Choice A


Related Questions

Han wants to convert his Canadian dollars to euros for his trip to France. He has 427 Canadian dollars. the current exchange rate is 1.28 Canadian dollars per euro. how many euros will he have.

Answers

Answer:

333.59375 Euro

Step-by-step explanation:

427 Canadian dollars converted to Euro

rate of exchange: for every 1.28 Canadian dollars=1 Euro

                                              427                              = ?? Euro

427/1.28=333.59375 Euro

Figure out the pattern, fill in
the blank

Answers

Answer:

384

Step-by-step explanation:

The pattern is: the sum of the multiplication of the 2 numbers underneath the blank.

48 * 8 = 384

Hope this helps! Please tell me if I did something wrong, thanks!

Input: 15 , Output: 5, Input: 9, Output: -1. What would be the rule now ?

Answers

Answer:

Subtract 10

Step-by-step explanation:

The first option, "take the ones digit", is obviously incorrect because the ones digit of 9 is not -1. The second one is incorrect because you are dividing by 2 and then adding 5. Dividing odd numbers by 2 will give you a decimal and a decimal plus an integer (the integer is 5 in this case) will still be a decimal (provided that the decimal is not an integer as well). However, both of the outputs are integers, so we know that the second one is wrong. The third one is wrong as well because 9 / 3 = 3, not -1. The last one is correct because 15 - 10 = 5 and 9 - 10 = -1.

Which of these below correctly solves for y of the equation 3x - 2 = 4y + 5?

Answers

Answer:

I think the answer is

y= 3/4x - 7/4

(Not sure though)

Find the missing number to make these fractions equal.

Answers

Answer:

66/8 = 3/4

Step-by-step explanation:

Let the unknown number be x

[tex]\frac{3}{4} = \frac{x}{8} \\\\Cross \: Multiply\\4\times x = 3 \: \times 8\\\\4x =24\\\\Divide \:both\:sides \:of\:the\:equation\: by\: 4\\\frac{4x}{4} = \frac{24}{4} \\\\x = 6[/tex]

Answer:

6

Step-by-step explanation:

Given

[tex]\frac{3}{4}[/tex] = [tex]\frac{?}{8}[/tex]

The 4 on the denominator is multiplied by 2 to obtain 8

The same operation must be applied to the numerator to make them equal.

Thus

3 × 2 = 6

[tex]\frac{3}{4}[/tex] = [tex]\frac{6}{8}[/tex] ← are equal fractions

a mouse runs across a 5.56 m kitchen floor in 3.42 seconds.What is the velocity of the mouse?

Answers

Answer:

v = 1.62 m/s

Step-by-step explanation:

Given that,

Distance covered by the mouse is 5.56 m is in 3.42 seconds.

We need to find the velocity of the mouse. It is equal to the total distance covered divided by time taken. So,

[tex]v=\dfrac{d}{t}\\\\v=\dfrac{5.56\ m}{3.42\ s}\\\\v=1.62\ m/s[/tex]

So, the velocity is 1.62 m/s.

Move the center of rotation back to the origin (0, 0) of the coordinate plane. Now alter pentagon ABCDE by moving one or more line segments on the pentagon to a different location. Rotate the pentagon using the slider. How many times does the pentagon map back onto itself in this situation? What can you conclude about the kinds of polygons that can map back onto themselves? Describe them.

Answers

The changed pentagon maps back onto itself only one time, when the value of α is 360°. A polygon must be regular to map back onto itself more than once. In a regular polygon, all of the sides are equal and all of the angles are equal.

Step-by-step explanation:

Answer:

The changed pentagon maps back onto itself only one time, when the value of α is 360°. A polygon must be regular to map back onto itself more than once. In a regular polygon, all of the sides are equal and all of the angles are equal.

Step-by-step explanation:

Sample Answer

Given f(x)=2x+1 evaluate f(4) Please help with this question.

Answers

Answer:

9

Step-by-step explanation:

f(x)=2x+1

f(4)=2 x 4+1

   = 8+1

  = 9

Answer:

Wherever we see an  x , we just input  4  to find  f ( 4 ) :  f ( 4 ) = 2 ( 4 ) − 1 = 8 − 1 = 7  

Hope this helps

Graph the interval represented in interval notation on the number line.
(-Infinite, -4] U [6, infinite)

Answers

Answer:

The upper reason is your answer.....

The product of six and a number increased by six?​

Answers

Answer: 6•(n+6)

Step-by-step explanation:

n is number

can be any letter

Answer:

6(n+6)

Step-by-step explanation:

the product means multiplication so you're going to need to multiply 6 by the number increased by 6. n represents the number, so n increased by 6 would be n+6. the parentheses represent the multiplication. put it together and you get the answer  6(n+6)

Round 96.1825899389 to 4 decimal places.

Answers

Answer:

96.1826

Step-by-step explanation:

to make that decimal numbers in 4 decimal places, then you count the number at the right hand side after the point, when u get to the 4th digit, you stop, then if the 5th digit is more than 4, they you add 1 to the 4th digit and there u have 96.1826

The Round 96.1825899389 to 4 decimal places will be 96.1826

What is rounding a number to some specific place?

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to Round 96.1825899389 to 4 decimal places.

To make that decimal numbers in 4 decimal places, then we count the number at the right hand side after the point, when u get to the 4th digit.

Therefore, the Round 96.1825899389 to 4 decimal places will be 96.1826

Learn more about rounding numbers  here:

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True or False
15. (True or False) Any 3 distinct points are always coplanar.
16. (True or False) Any 2 distinct circles are always coplanar.
17. (True or False) If 2 lines intersect once then the lines are coplanar.

18. (True or False) Two lines that are skew can sometimes intersect.

19. (True or False) An angle and a circle can have more than 3 intersections

20. (True or False) Two distinct circles can have more than 2 intersections.

21. (True or False) Any given line and point are always coplanar.

Answers

Answer:

15. True

16. False

17. True

18. False

19. True

20. False

21. True

Step-by-step explanation:

15. The three points can be taken as being two points on a line adjacent to a point which always forms a plain when the ends of the line are connected to the point

16. The two circles can be on different planes

17. With one line fixed, the other line can be rotated until both lines are in the flat plane

18. The definition of skew lines are lines in different planes that are not parallel and that do not intersect

19. Whereby the angle crosses the circumference of the circle twice, the number of intersections = 4

20. Two distinct circles can only intersect twice

21.  A plane can always be drawn with any three points

a circle has a radius of 7ft. Find the radian measure of the central angle 0 that intyercepts an arc of length 16ft

Answers

Answer:

2.29 rads

Step-by-step explanation:

The  length of the arc of a circle of radius r is given by;

l = rθ            ---------------------------(i)

Where;

l = length of the arc

θ = central angle o that intercepts that arc and measured in radians.

From the question:

l = 16ft

r = 7ft

Substitute these values into equation (i) as follows;

16 = 7θ

Make θ subject of the formula

θ = [tex]\frac{16}{7}[/tex]

θ = 2.29    

Therefore, the radian measure of the central angle is 2.29 rads

A square has a side length 15.8cm.If 3 such squares are linked side to side in a straight line, what is the perimeter of the whole shape?

Answers

Answer:

126.4 cm

Step-by-step explanation:

1. 15.8 * 3 = 47.4 (This is the length)

2. Find half of the rectangle

47.4 + 15.8 (width) = 63.2

3. Find the whole perimeter

63.2 * 2 = 126.4

Answer:

126.4

Step-by-step explanation:

If you put three squares that are all 15.8cm together, you get a rectangle that is 47.4cm by 15.8cm. To get 47.4, you multiply 15.8 x 3 because it's three 15.8 squares together. Then to find the perimeter of the rectangle, you add all the sides together to get the answer 126.4.

What is this decimal expressed as a percent?

Answers

Answer:

13%

Step-by-step explanation:

To fraction ;

[tex]0.13=\frac{0.13\times \:100}{100}\\\\=\frac{13}{100}[/tex]

To percentage

[tex]\frac{0.13}{1}\times \frac{100}{100}\\ \\= 13/100\\\\= 13\%[/tex]

please help! really needing help solve the problem

Answers

Answer:

7

Step-by-step explanation:

By Basic proportionality theorem:

[tex] \frac{10}{8} = \frac{3x - 6}{12} \\ \\ \frac{10 \times 12}{8} = 3x - 6 \\ \\ \frac{120}{8} = 3x - 6 \\ \\ 15 = 3x - 6 \\ 15 + 6 = 3x \\ 21 = 3x \\ \frac{21}{3} = x \\ 7 = x \\ \\ \huge \red { \boxed{x = 7}}[/tex]

What is 2x 2 + 2x - 12 = ?

Answers

Answer:

(x-6)(2x+2)

Step-by-step explanation:

2x^2 + 2x - 12

by using splitting method

2x^2 - 12x + 2x -12

taking separate common from both pairs

2x(x - 6) + 2(x - 6)

(x - 6)(2x + 2)

What is 3/15 in simplest form

Answers

Answer:

3/15 in the simplest form is 1/5....

when you divide by 3 it gives 1/5.

The fraction 3/15 in simplest form is 1/5.

What is 3/15 in simplest form?

A fraction is in its simplest form if the numerator and denominator have no common factors other than 1.

In other words, you cannot divide the top and bottom any further and have them still be whole numbers. The simplest form is also called lowest terms.

In this case, 3 and 15 have a common factor, which is 3. Thus, 3/15 in simplest form will be:

3/15 = 1/5  (divide both numerator and denominator by 3)

Learn more about fraction on:

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What is the solution to the equation 6 m = 60?

Answers

Answer:

m = 10

Step-by-step explanation:

Divide both sides of this equation by 6.  We get:

m = 60/6 = 10.

Solution:  m = 10

Answer:

m =10

Step-by-step explanation:

Which of the following expressions cannot be simplified?
A) 8x-5x
B) 8x-1
C -(8x+3)
D 8(x-2)

Answers

Answer:

B) 8x-1

Step-by-step explanation:

A) 8x-5x  Like terms  = 3x

B) 8x-1   Not like terms  8x-1

C -(8x+3)  Distribute the minus sign  -8x -3

D 8(x-2) Distribute the 8   8x - 16

Answer:

B. 8x - 1

Step-by-step explanation:

Notice that all of these expressions can be simplified except for option B. 8x-1.

Option A has two like terms, 8x and -5x which could be reduced to 3x

Option B has two distinct terms, 8x and -1 which can only be combined into 8x-1

Option C has a leading negative, and can be simplified with the distributive property to be -8x + -3

Option D has a leading 8 that can be distributed to the term (x-2) to form 8x - 16.

Thus, choose option B.

Cheers.

What is Equivalent to the square root of 16

Answers

Answer:

4

Step-by-step explanation: 4*4 is 16. 4^2 is 16. So the square root of 16 is 4.

Answer:

4

Step-by-step explanation:

4 times 4 = 16, therefore the square root of 16 must be 4

4(-8x+5) - (-33x-26)

Answers

Answer:

Step-by-step explanation:

Use distributive property a(b+c) = a*b +a*c

4(-8x + 5) - (-33x - 26) = 4*-8x + 4 *5 - 33x * (-1) - 26*(-1)

                                    = -32x + 20 + 33x + 26

                                    {add like terms}

                                    = -32x + 33x + 20 +26

                                   = 1x + 46

The product of ten and a number

Answers

Answer:

10n

Step-by-step explanation:

n represents number, its like using X, since we don't have the information on it, we replace it with a letter.

Answer:

Let the number be n.

10× n =10n.

hope you got thè answer.

x-intercept: 3
y-intercept: 2

Answers

Answer:

y = -2/3x + 2

Step-by-step explanation:

Hey there!

Well since we already got the y-intercept to find slope we'll use the points,

(3,0) and (0,2).

Formula: [tex]\frac{y^2 - y^1}{x^2 - x^1}[/tex]

Plug in the given points,

[tex]\frac{2 - 0}{0 - 3}[/tex]

Slope = -2/3

Slope-intercept: y = -2/3x + 2

Hope this helps :)

Answer:

y = -2/3x + 2  or

2x + 3y  = 6   (standard form).

Step-by-step explanation:

I am assuming you want the equation of the straight line that passes through these 2 points.

The 2 points are (3, 0 ) and (0, 2).

The slope of the line =  (2 - 0) / (0 - 3)

= -2/3.

The equation is y = -2/3x + 2  ( as 2 is the y-intercept).

In standard form this is :

3y = -2x + 6

2x + 3y  = 6.

A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?

Answers

Answer:

660.4 millimeters.

Step-by-step explanation:

1 inch = 25.4 millimeters

1 inch = 25.4 millimeters26 inches = ?

26 × 25.4

26 × 25.4= 660.4 millimeters

660.4 millimeters is the answer.

What is the best definition for combining like terms

Answers

Step-by-step explanation:

Combing like terms means that you combine the terms that are alike. So, if you have integers you would combine the integers. If you had a variable like x, you would combine everything with x. For instance, 2x+4+3+7x, to combine like terms add 4+3 and 2x+7x.

Can you guys help me with 15/8m-11=7/4m+1

Answers

Answer:

m=96

Step-by-step explanation:

[tex]\frac{15}{8}m-11=\frac{7}{4}m+1\\\\\frac{15}{8}m -\frac{7*2}{4*2}m=1+11\\\\\frac{15-14}{8}m=12\\\\\frac{1}{8}m=12\\\\m=12*8\\\\m=96[/tex]

A vertical shelving unit consists of five equal-sized square shelves arranged in a column to form a rectangle. The total area of all five shelves is 500 square inches. What is the length, in inches, of the shelving unit?

Answers

Answer:

50 inches

Step-by-step explanation:

Given that

5 equal sized square shelves arranged in a column.

Total area of five shelves = 500 sq inches

To find:

Length of shelving unit = ?

Solution:

First of all, let us find the area of each shelving unit.

Area of each shelving unit = Total area of five shelved divided by 5

Area of each shelving unit = 500 [tex]\div[/tex] 5 = 100 sq units.

Each shelving unit is of square shape and area of a square is given as:

Area = [tex]Side^2[/tex]

100 = [tex]Side^2[/tex]

So, side of shelve = 10 inches

Now, there are 5 squares in the shelving unit.

So, length of shelving unit = [tex]10 \times 5 = \bold{50 \ inches}[/tex]

i need help I legit don't understand please

Answers

Answer:

Its the "range" of x values, so from -2 to 2.

You can write it as [-2, 2]

Make the following conversion. 4mm = _____ cm 0.04 0.4 40 400

Answers

Answer:

0.4 cm

Step-by-step explanation:

10 mm = 1 cm thus 4mm / 10  = 0.4 cm

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