All categories

3 years ago

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:

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

$x^2+y^2=r^2$

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

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

So, in this problem we have that

$3=r^2$

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

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

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

You might be interested in

A suitcase measures 24 inches long and the dialogue is 30 inches long. How much material is needed to cover one side of the suit

borishaifa [10]

Answer:

432 in.^2

Step-by-step explanation:

The side of the suitcase is a rectangle. One length is 24 inches. The diagonal of the rectangle is 30 inches long. The diagonal is a hypotenuse of a right triangle. The length is a leg. We need to find the other leg.

We use the Pythagorean theorem,

a^2 + b^2 = c^2

(24 in.)^2 + b^2 = (30 in.)^2

576 in.^2 + b^2 = 900 in.^2

b^2 = 324 in.^2

b = sqrt(324 in^2)

b = 18 in

area of rectangle = length * width

A = 24 in. * 18 in.

A = 432 in.^2

6 0

3 years ago

Hector is dividing students into groups for an HR wants to divide the boys and girls so that each group has the same number of t

Roman55 [17]

Answer:

7 groups, 3 boys and 8 girls

Step-by-step explanation:

Let total number of groups be $x$

and total hikers in one group be $y$

if number of girls and boys in every group is same, then

$\frac{21}{x} + \frac{56}{x} = y$

$\frac{21 + 56}{x} = y\\x*y = 77$ ....(1)

from (1) $x$ will either be 11 or 7

for $x = 11$ the values won't be real.

For $x = 7\\y = \frac{77}{7} \\y = 11$

so there will be 7 groups with 11 hikers in each groups and every group will have $\frac{21}{7} = 3$ boys and $\frac{56}{7} = 8$ girls

6 0

3 years ago

Solve 3x^2 + 6x+15=0

Elden [556K]

Answer:

The solution of given equation is ( - 1 + 2 i ) , ( - 1 - 2 i )

Step-by-step explanation:

Given equation as :

3 x² + 6 x +15 = 0

The value of x fro the quadratic equation a x² + b x + c = 0 is obtained as

x = $\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

So , from given eq , the value of x is now obtain as

x = $\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Or, x = $\frac{-6\pm \sqrt{6^{2}-4\times 3\times 15}}{2\times 3}$

Or, x = $\frac{\sqrt{-144} }{6}$

∴ x = ( - 1 + 2 i ) , ( - 1 - 2 i )

Hence The solution of given equation is ( - 1 + 2 i ) , ( - 1 - 2 i ) Answer

6 0

3 years ago

Determine A:B:C, if A:B= 2:3 and B:C =4: 5

cestrela7 [59]

I’m confused what we are suppose to do

6 0

3 years ago

Create an expression, to equal 13, using any grouping of addition, subtraction, multiplication, and division. You must use all t

aleksandrvk [35]

(29 - 2 + (6 * 2)) / 3 = 13

4 0

3 years ago

Read 2 more answers