What is the best estimate of 289 and 7
1 answer:
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Answer:
D=
Step-by-step explanation:
Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance
The distance formula is given as
Here we are given two coordinates as
Substituting these values in the Distance formula given above we get
Hence this is our answer
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
