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scoray [572]
3 years ago
14

Describe in words the region of R3 reperesented by the equations or inequalities y2+z2=16

Mathematics
1 answer:
Anastasy [175]3 years ago
5 0

Answer:

It represents an infinite cylinder of radius 4.

Step-by-step explanation:

The first thing to notice is that

y^2+z^2=4^2

<u>represents a circle of radius 4</u>, with its center in the origin of a plane yz, of cartesians coordinates.

Starting from here, we have to put the coordinate x, for all values of x, to complete the space R³. <em>This will enlarge this circle we had on the plane, to infinity</em> (positive and negative on the x-axis).

Finally, we have that this region is a cylinder of radius 4, with center in y=0 and z=0, and of infinite length in the x coordinates.

You might be interested in
The Han dynasty lasted from 206 B.C. to 9 A.D. How many years did the dynasty last?
cricket20 [7]

Answer:

The Han dynasty last was, 215 years

Step-by-step explanation:

Given statement: The Han dynasty lasted from 206 B.C. to 9 A.D.

To find how many years did the dynasty last.

B.C. represents Before Christ

A.D. represents After Death

To find the difference between two dates,

  • When the endings are the same you subtract
  • When they are different you add

You can see that the endings in the given 206 B.C. and 9 A.D. are B.C. and A.D. are different.

Just add these 206 and 9 we get;

206 + 9 = 215 years

Therefore, 215 years did the Han dynasty last.


4 0
3 years ago
Triangle def has vertices d(2,-5) e(6,-1) and f(5,6) verify that def is isosceles
goldfiish [28.3K]
To prove that the given triangle is an isosceles, two of its sides must have equal lengths.

Between D(2,-5) and E(6,-1):
d = √(6 - 2)² + (-1 - ⁻5)² = 4√2

Between E(6,-1) and F(5,6):
d = √(5 - 6)² + (6 - ⁻1)² = 5√2

Between D(2,-5) and F(5,6)
d = √(5 - 2)² + (6 - ⁻5)² = √130

<em>Since there are no equal lengths, the triangle is NOT an isosceles triangle.</em>

The bisector of angle F is a line segment from vertex F to the midpoint of line DE.

Midpoint: x = (2+6)/2 = 4; y = (-5+-1)/2 = -3
The midpoint is at (4,-3).
The equation of the line follows the point-slope formula:
y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁)
Substituting using points (5,6) and (4,-3)
y - 6 = [(⁻3 - 6)/(4 - 6)](x - 5)
y - 6 = (9/2)(x - 5)
2(y - 6) = 9(x - 5)
2y - 12 = 9x - 45
<em>2y - 9x = -33 </em>

4 0
3 years ago
What is time in the equation
kotegsom [21]
Where is the equation
3 0
3 years ago
Please help me ASP please
mylen [45]

trapezoid area = 1/2(a+b) h

area= 1/2 (120 + 145) 50

area = 25(265)

= 6,625 yards

5 0
3 years ago
Express each rate as a unit rate. 720 miles traveled on 60 gallons of gasoline=
Brut [27]
720 miles traveled on 60 gallons of gasoline.
Express this on its Unit Rate.
To get the answer, we need to divide 720 miles by 60 gallons of gasoline
=> 720 / 60 = 12 miles /gallons
Thus, in every 1 gallon of gasoline, you can travel 12 miles.
So, the expression would be like this:
720 miles / 60 gallons = 12 miles / gallon
Let’s check our answer
=> 12 miles x 60 gallons = 720 miles.
Thus, we got the correct answer.



7 0
3 years ago
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