What are the values of r and a1
2 answers:
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Answer:
(3 square root of 2 , 135°), (-3 square root of 2 , 315°)
Step-by-step explanation:
Hello!
We need to determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.
We know that the polar coordinate system is a two-dimensional coordinate. The two dimensions are:
- The radial coordinate which is often denoted by r.
- The angular coordinate by θ.
So we need to find r and θ. So we know that:
(1)
x = rcos(θ) (2)
x = rsin(θ) (3)
From the statement we know that (x, y) = (3, -3).
Using the equation (1) we find that:
Using the equations (2) and (3) we find that:
3 = rcos(θ)
-3 = rsin(θ)
Solving the system of equations:
θ= -45
Then:
r = 3\sqrt{2}[/tex]
θ= -45 or 315
Notice that there are two feasible angles, they both have a tangent of -1. The X will take the positive value, and Y the negative one.
So, the solution is:
(3 square root of 2 , 135°), (-3 square root of 2 , 315°)
Answer:
The cup can hold 235.5 cubic cm of popcorn.
Step-by-step explanation:
A cone shaped popcorn cup has a radius of 5 cm and a height of 9 cm.
Use 3.14 as an approximation for pi.
Now, to find cubic cm of popcorn the cup can hold.
Radius (r)= 5 cm
Height (h)= 9 cm
= 3.14 (as per question).
So, to get the cubic cm of popcorn the cup can hold we put formula of volume:
Volume= r
h
3
Volume= 3.14 x 5 × 9
3
Volume= 3x14 x 25 x 3
Volume= 235.5 cubic cm.