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KIM [24]
3 years ago
11

Describe in words the region of R3 reperesented by the equations or inequalities x2+y2+z2≤3

Mathematics
1 answer:
Vaselesa [24]3 years ago
8 0

Answer:

The region represented by the equation is a full sphere of radius √3 centered in the origin of coordinates.

Step-by-step explanation:

<em>In a plane xy, the equation that represents a circle with center in the origin, of radius r is</em>

x^2+y^2=r^2

<em>in R³, or a space xyz, we can represent a sphere with its center in the origin, and of radius r, with the equation</em>

x^2+y^2+z^2=r^2

So, in this problem we have that

3=r^2

which means that the sphere has a radius of √3.

<u>Finally, our equation is an inequality</u>, and the sphere is equal to, and less than, the calculated radius.

Therefore, the sphere is "full" from the surface to its center.

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3. Find the volume for the rectangular prism.<br> 7.5 ft<br> 9.25 ft<br> 4 ft
Sunny_sXe [5.5K]

Answer:

277.5 square units

Step-by-step explanation:

To find the volume of a rectangular prism you must multiply length times width times height. When you multiply 7.5 x 9.25 x 4 you get the answer 277.5. Hope this helps:))

6 0
3 years ago
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation ℎ(
maw [93]
  1. The irrigation system is positioned 9.5 feet above the ground to start.
  2. The spray reaches a maximum height of <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> away from the sprinkler head.
  3. The spray reaches all the way to the ground at about 10.87 feet away​

<h3>How to determine the position?</h3>

Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

<h3>How to determine the maximum height?</h3>

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -10/2(-1)

Xmax = 5.

Thus, the maximum height on the vertical axis is given by:

h(x) = -x² + 10x + 9.5

h(5) = -(5)² + 10(5) + 9.5

h(5) = -25 + 50 + 9.5

h(5) = 34.5 feet.

Therefore, the spray reaches a maximum height of <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> away from the sprinkler head.

Also, the spray reaches all the way to the ground at about:

Maximum distance = √34.5 + 5

Maximum distance = 10.87 feet.

Read more on maximum height here: brainly.com/question/24288300

#SPJ1

<u>Complete Question:</u>

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away​

8 0
2 years ago
Lacey picks blueberries and raspberries from her garden. She has 1/5 as many pounds of blueberries as raspberries. If she picks
murzikaleks [220]

Answer:

1/5 + 1 4/5 = x.

Step-by-step explanation:

3 0
2 years ago
7) Explain how to divide $53.56 by 10 WITHOUT USING A CALCULATOR
Sophie [7]

Answer: Okay first think back you surely have divided whole numbers by 10 it is the same with decimals for each 0 in the thing you are dividing it by you move the dot one to the left. So if you divide it by 10 it is 5.356 by 100 it would be 0.5356.

Hence the answer is 5.356.

Step-by-step explanation:

Hope it helps

4 0
2 years ago
The largest number that rounds to 2,500 when rounded to the nearest ten?
Savatey [412]
2504, as 2499 is 5 less, yet rounds to 2.5K. It is the highest possible for rounding to the tens, as 2505 rounds to 2510.
5 0
3 years ago
Read 2 more answers
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