1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mila [183]
4 years ago
5

Convert the cartesian equation x2 +y2=16 to a polar equation

Mathematics
1 answer:
VARVARA [1.3K]4 years ago
3 0
X^2+y^2 = 16
can be written as
(x-0)^2+(y-0)^2 = 4^2

We see that the second equation is in the form
(x-h)^2 + (y-k)^2 = r^2

where
(h,k) = (0,0) is the center
r = 4 is the radius

The polar form of the equation is simply r = 4. Why is this? Because the radius is fixed to be 4 no matter what happens with theta. As theta goes from 0 to 360, the points generated all form a circle centered at (0,0) with radius 4. 

Answer: r = 4
You might be interested in
Daria makes and sells stuffed toys. She uses special fabric to cover a foam cube to make a number cube. How much fabric did Dari
denis-greek [22]

Answer:294

Step-by-step explanation: you’re trying to find the surface area of the cube to find out how much material Daria needs. To do so find the area of 1 face of the cube (which is a square). The problem gives us 1 side of the square as 7cm. A square has the same length for its 4 sides, so to find the area of that 1 face do 7 x 7=49. The question also gives the hint that a cube has 6 faces so you would multiply the 49 by 6 to get the total surface area of the cube. 49 x 6=294.

Not sure if this is right but hope it helps.

8 0
3 years ago
Read 2 more answers
What is the equation of the directrix of a parabola defined by the equation y = x2 − 2x − 3?
meriva
<span><span>Graph <span>x2<span> = 4</span>y</span><span> and state the vertex, focus, axis of symmetry, and directrix.</span></span><span>This is the same graphing that I've done in the past: </span><span>y = (1/4)x2</span><span>. So I'll do the graph as usual:</span></span><span> </span><span>The vertex is obviously at the origin, but I need to "show" this "algebraically" by rearranging the given equation into the conics form:<span>x2 = 4y</span> Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved<span>
(x – 0)2 = 4(y – 0)</span><span>This rearrangement "shows" that the vertex is at </span><span>(h, k) = (0, 0)</span><span>. The axis of symmetry is the vertical line right through the vertex: </span><span>x = 0</span>. (I can always check my graph, if I'm not sure about this.) The focus is "p" units from the vertex. Since the focus is "inside" the parabola and since this is a "right side up" graph, the focus has to be above the vertex.<span>From the conics form of the equation, shown above, I look at what's multiplied on the unsquaredpart and see that </span><span>4p = 4</span><span>, so </span><span>p = 1</span><span>. Then the focus is one unit above the vertex, at </span>(0, 1)<span>, and the directrix is the horizontal line </span><span>y = –1</span>, one unit below the vertex.<span>vertex: </span>(0, 0)<span>; focus: </span>(0, 1)<span>; axis of symmetry: </span><span>x<span> = 0</span></span><span>; directrix: </span><span>y<span> = –1</span></span></span><span><span><span>Graph </span><span>y2<span> + 10</span>y<span> + </span>x<span> + 25 = 0</span></span>, and state the vertex, focus, axis of symmetry, and directrix.</span><span>Since the </span>y<span> is squared in this equation, rather than the </span>x<span>, then this is a "sideways" parabola. To graph, I'll do my T-chart backwards, picking </span>y<span>-values first and then finding the corresponding </span>x<span>-values for </span><span>x = –y2 – 10y – 25</span>:<span>To convert the equation into conics form and find the exact vertex, etc, I'll need to convert the equation to perfect-square form. In this case, the squared side is already a perfect square, so:</span><span>y2 + 10y + 25 = –x</span> <span>
(y + 5)2 = –1(x – 0)</span><span>This tells me that </span><span>4p = –1</span><span>, so </span><span>p = –1/4</span><span>. Since the parabola opens to the left, then the focus is </span>1/4<span> units to the left of the vertex. I can see from the equation above that the vertex is at </span><span>(h, k) = (0, –5)</span><span>, so then the focus must be at </span>(–1/4, –5)<span>. The parabola is sideways, so the axis of symmetry is, too. The directrix, being perpendicular to the axis of symmetry, is then vertical, and is </span>1/4<span> units to the right of the vertex. Putting this all together, I get:</span><span>vertex: </span>(0, –5)<span>; focus: </span>(–1/4, –5)<span>; axis of symmetry: </span><span>y<span> = –5</span></span><span>; directrix: </span><span>x<span> = 1/4</span></span></span><span><span>Find the vertex and focus of </span><span>y2<span> + 6</span>y<span> + 12</span>x<span> – 15 = 0</span></span></span><span><span>The </span>y<span> part is squared, so this is a sideways parabola. I'll get the </span>y stuff by itself on one side of the equation, and then complete the square to convert this to conics form.<span>y2 + 6y – 15 = –12x</span> <span><span>
y</span>2 + 6y + 9 – 15 = –12x + 9</span> <span>
(y + 3)2 – 15 = –12x + 9</span> <span>
(y + 3)2 = –12x + 9 + 15 = –12x + 24</span> <span>
(y + 3)2 = –12(x – 2)</span> <span>
(y – (–3))2 = 4(–3)(x – 2)</span></span><span><span>Then the vertex is at </span><span>(h, k) = (2, –3)</span><span> and the value of </span>p<span> is </span>–3<span>. Since </span>y<span> is squared and </span>p<span> is negative, then this is a sideways parabola that opens to the left. This puts the focus </span>3 units to the left of the vertex.<span>vertex: </span>(2, –3)<span>; focus: </span><span>(–1, –3)</span></span>
4 0
4 years ago
Read 2 more answers
Durante la settimana visiteranno il parco 72 bambini.per ogni bambino viene preparata una scatola rettangolare,in cui sistemare
Mnenie [13.5K]

Answer:

4,320\ cm  or  43.2\ m

Step-by-step explanation:

The question in English is

During the week 72 children will visit the park. For each child is prepared a rectangular box, in which to arrange what will be collected during the visit. Each box is 18 cm long and 12 cm wide. How long is the strip of cardboard that is used to make the edge of all boxes.

Let

x ----> the length of the box

y -----> the width of the box

we know that

The perimeter of the box is equal to

P=2(x+y)

we have

x=18\ cm

y=12\ cm

step 1

Find the perimeter of one box

P=2(18+12)

P=60\ cm

step 2

Find the perimeter of 72 box

Multiply the perimeter of one box by 72

P=(72)60=4,320\ cm

Convert to meters

Divide by 100

4,320/100=43.2\ m

5 0
3 years ago
Help please i’ll give extra points
Studentka2010 [4]
One output for each imput
5 0
3 years ago
Solve for me please 4x^2+6x=12
Anit [1.1K]
4x^2+6x=12
16x+6x=12
22x=12
x=12/22 or 0.55

The decimal is rounded to the nearest hundreth
4 0
4 years ago
Other questions:
  • What is the solution to this equation? 4x+10+3x=40-3x
    7·1 answer
  • A red string of holiday lights blinks once every 3 seconds, while a string of blue lights blinks once ever 4 seconds. How many t
    9·2 answers
  • Draw a quick picture to find the sum or difference . 2.46+0.78=
    7·1 answer
  • I need help with number 3 and 4
    10·2 answers
  • A gumball machine contains gumballs in several different colors.
    7·1 answer
  • A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?​
    12·1 answer
  • What is the equation of the graph?
    8·2 answers
  • One bag contains a mixture of 30% black sand and 70% red sand. A second bag
    15·1 answer
  • Solve each equation by factoring.<br> x^2 + 3x + 2 = 0
    6·1 answer
  • Which property justifies the statement below
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!