A hexagonal aquarium needs to hold 10 gallons of water and be 24 inches tall. What should be the area of the hexagon?

Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x − 4y − 6z = 22

madam [21]

The equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

Given equation of sphere be $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We are required to express the given equation in the standard form of the equation of sphere.

Equation is basically relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation,quadratic equation, cubic equation or many more depending on the powers of variables. The standard form of the equation of sphere looks like $x^{2} +y^{2} +z^{2} =r^{2}$ .

The given equation is $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We have to break 22 which is in right side into various parts according to the left side of the equation.

$x^{2} +y^{2} +z^{2} +2x-4y-6z=-1-4-9+36$

$x^{2} +y^{2} +z^{2} +2x-4y-6z+1+4+9=36$

$x^{2} +1+2x+y^{2}+4-4y+z^{2} +9-6z=36$

$x^{2} +(1)^{2} +2*1*x+y^{2} +(2)^{2} -2*2y+z^{2} +(3)^{2} -2*3z=36$

$(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$

Hence the equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

Learn more about equations at brainly.com/question/2972832

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7 0

1 year ago

Please help ASAP! It’s due tmr

DIA [1.3K]

Answer:

I will tell you.

Step-by-step explanation:

a.-13

b.13

c.-25

d.25

e.20

f.-6

g.-22

h.-72

6 0

3 years ago

Marcos is mixing a solution in science class. He is mixing 3 ounces of food coloring with every 8 ounces of water. If he wants a

jonny [76]

Answer:

With the 24 ounces of water he would have 9 ounces of food coloring.

Step-by-step explanation:

For ever 8 ounces of water there is 3 ounces of food coloring so if there is 24 ounces of water that mean there is 3 times the original starting amount. So 8x3=24 so there is 24 ounces of the water. Since the8 got multiplied by 3 that means the 3 we haven't used yet will get multiplied by 3 as well so we can find the answer. So 3x3=9. That means we would have 9 ounces of food coloring with the 24 ounces of water.

7 0

3 years ago

I think of a number and add one fourth of it to half of it and the result is twelve. What is the number I thought of?

belka [17]

Suppose that the number u were thinking about is x thus :

$\frac{1}{4} x + \frac{1}{2} x = 12 \\$

Multiply both sides by 4

$4 \times ( \frac{1}{4} x + \frac{1}{2} x) = 4 \times 12 \\$

$x + 2x = 48$

$3x = 48$

Divide both sides by 3

$\frac{3x}{3} = \frac{48}{3 } \\$

$x = 16$

3 0

2 years ago

In 11 years, John's age will be 5 less than 5 times his current age. How old is he? If x represents John's current age, which of

seropon [69]

Answer:

Step-by-step explanation:

Let John's age be x. This gives us that in 11 years, john's age will be 5 less than 5 times his current age. Therefore, we could get: $x+11=5x-5$ . This is your second equation. Solving for x, we get 4x=16 so x=4.

5 0

3 years ago

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