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lys-0071 [83]
3 years ago
8

Katie bought a dozen donuts for $1.99. Write an equation which shows how to find the price (p) of each donut

Mathematics
1 answer:
zimovet [89]3 years ago
3 0
1.99 divided by 12 would give u about 0.66$
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Read the excerpt from “Raymond's Run.” But now, if anybody has anything to say to Raymond, anything to say about his big head, t
dsp73

Answer:

D.  She uses Squeaky’s thoughts and words to tell readers about her character.

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3 years ago
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Three friends go grocery shopping together, and each buys the same kind of
dalvyx [7]

Answer:

C

Step-by-step explanation:

Because if you plug those numbers into the graph, only C and D fit. Now we have to look at the unit price. If LaMar buys 2 lbs and pays 3.00 dollars, we know that the unit price is 3/2=1.5 dollars per pound. You could also check with the other peoples. $7.5/5lbs=1.5 dollars. $4.5/3lbs=$1.5

3 0
3 years ago
Match each of the parametric equations 1-5 with the curve it represents from the list A through E below. 1. r=3 2. r=2sinθ 3. θ=
ira [324]

Answer:

Step-by-step explanation:

1. r=3

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

When r =3,

Then we have

r=3,

x²+y²=3

All points with r = 3 are at

distance 3 from the origin, so r = 3 describes the circle of radius 3, with center at the origin (0,0).

Option C

2. r=2sinθ

When r=2sinθ

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

Now, apply the given information

r=2sinθ

Since Sinθ=y/r

r=2y/r

Cross multiply

r²=2y

x²+y²=2y

x²+y²-2y =0

x²+ (y-1)² -1 =0

x²+(y-1)²=1²

Then,

It is a circle with center (0,1) and radius 1.

Because the sine is periodic, we know that we will get the entire curve for values of θ in [0, 2π). As θ runs from 0 to π/2, r increases

from 0 to 2. Then as θ continues to π, r decreases again to 0. When θ runs from π to

2π, r is negative, and it is not hard to see that the first part of the curve is simply traced

out again, so in fact we get the whole curve for values of θ in [0, π). Thus, check attachment for curve, Now, this suggests that the curve could possibly be a circle,

and if it is, it would have to be the circle x² + (y − 1)² = 1. Having made this guess, we can easily check it. First we substitute for x and y to get (r cos θ)² + (r sin θ − 1)² = 1;

expanding and simplifying does indeed turn this into r = 2 sin θ.

Option E

A circle of radius 1 with center on the x-axis

3. θ=π/4

This is a point on the circle

p=(r, θ)

So, r=0

x = rCosπ/4=rCos45

x=r√2 /2

and

y = rsin(π/4) = rSin45

y=r√2 /2

This makes it very

easy to convert equations from rectangular to polar coordinates.

x²+y²= (r√2/2)²+(r√2/2)²

x²+y²= 2r²/4 + 2r²/4

x²+y²= r²

Since r=0

x²+y²= 0

x²=y²

Therefore, x=y

Option D

The straight line y=x

4. r=4θ

Here the distance from the origin

exactly matches the angle, so a bit of thought makes it clear that when θ ≥ 0 we get the spiral of Archimedes ( check attachment ) When θ < 0, r is also negative, and so the full graph is the right hand picture in the figure. Check attachment

The correct option is B

None of the above

5. r=2Cosθ

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

Now, apply the given information

r=2cosθ

Since cosθ=x/r

r=2x/r

Cross multiply

r²=2x

x²+y²=2x

x²+y²-2x=0

(x-1)² + y² -1 =0

(x-1)² + y² = 1²

Then,

It is a circle with center (1,0) and radius 1.

A circle of radius 1 with center on the y-axis

Option A is correct

7 0
3 years ago
Dylan has a square piece of metal that measures 10 inches on each side. He cuts the metal along the diagonal, forming two right
alexandr402 [8]
Use Pythagoras theorem,
c² =a² +b² 
x² =10² +10<span>² 
</span>x<span>² =100+100
</span>x<span>² =200
</span>x=14.14
x=14.1

3 0
3 years ago
6 goes into 13 how much times
ahrayia [7]

Answer:

2

Step-by-step explanation:

6 can go to 12 but not 13

7 0
3 years ago
Read 2 more answers
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