Given:
Rectangular coordinate = (8, 6)
To convert:
Rectangular coordinate to polar coordinate with r > 0 and 0 ≤ θ < 2π.
Solution:
Let us find r:
r = 10
Now, find θ:
Cancel the common factor 2.
θ = 36.87°
The polar coordinates are (r, θ) = (10, 36.87°).
Answer:
<u>The radius of the cylinder and sphere is 2.48 cm and the volume of the sphere is 64 cm³</u>
Step-by-step explanation:
Let's review the information given to us to answer the question correctly:
Volume of a cylinder = π * r² * h
π * r² * h = 48
r² * h = 48/3.1416
r² * h = 15.28
r = 2.48 cm, h = 2.48 cm
Now, we can calculate the volume of the sphere this way:
Volume of the sphere = 4/3 * π * r³
Volume of the sphere = 4/3 * π * 2.48³
Volume of the sphere = 4/3 * π * 15.28
Volume of the sphere = 1.33 * 3.1416 * 15.28
<u>Volume of the sphere = 64 cm³</u>
Answer: D) right 9 units
<u>Step-by-step explanation:</u>
The Vertex form of a quadratic equation is: y = a(x - h)² + k where
- a is the vertical stretch <em>or shrink</em>
- (x, h) is the vertex
→ h is the horizontal shift (+ is right, - is left)
→ k is the vertical shift (+ is up, - is down)
y = f(x - 9)
↓
h=9
Since h is positive, the graph moves 9 units to the RIGHT
Answer:
x = 2
Step-by-step explanation:
See the given figure attached.
Given that RQ and ST are parallel and angle PRQ is equal to 120°.
Now. ∠ PRQ and ∠ QRS are supplementary.
Hence, ∠ QRS = 180° - 120° = 60°
Again, as RQ ║ ST so, ∠ QRS = ∠ UST {Corresponding angles}
So, ∠ UST = 60°.
Now, given that 15(x + 2) = ∠ UST = 60°
⇒ x + 2 = 4
⇒ x = 2 (Answer)