3(6 - 4) + 7² = what’s is it help me pls
2 answers:
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Answer:
The volume of the sphere is 2048 in³.
Step-by-step explanation:
The volume of a sphere is given by:
Where:
r: is the radius = 8 in
Having the radius and by using 3 for π, the volume is:
Therefore, the volume of the sphere is 2048 in³.
I hope it helps you!
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
Mug 2 can hold the most as its volume is greater than that of mug 1
Step-by-step explanation:
To find out which mug holds more let us find the volume of each mug
As we know
Height of first mug =H1= 3 in
Diameter of first mug= D1= 5.5 in
Radius of first mug = R1=
= 2.75 in
The volume of first mug M1 is V1
The formula used will be
V=πr2h
V1 will be equal to
V1 = 51.81
Similarly
As we know
Height of second mug = H2= 4 in
Diameter of second mug = D2 = 4.5 in
Radius of second mug = R2=
= 2.25 in
The volume of second mug M2 is V2
the formula used will be
V=πr2h
V2 will be equal to
V2 = 56.52
So as V2(56.52) is greater than V1(51.81) so mug 2 can hold the most
Keywords: volume of cylinder
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