K is 23.
As for the equation, it is
29=k+6
To solve, subtract 6 from both sides.
Answer:
yes they do
Step-by-step explanation:
both equal 1/3
8/24 = 1/3
5/15 = 1/3
1/3 = 1/3
Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.
Step-by-step explanation:
The equation of a circle in the center-radius form is:
(1)
Where are the coordinates of the center and is the radius.
Now, we are given the equation of this circle as follows:
(2)
And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:
(3)
Rearranging the equation:
(4)
(5)
Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of :
<u>For the first parenthesis:</u>
We can rewrite this as:
Hence in this case and :
<u>For the second parenthesis:</u>
We can rewrite this as:
Hence in this case and :
Then, equation (5) is rewritten as follows:
(6)
<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>
Rearranging:
(7)
At this point we have the circle equation in the center radius form
Hence:
The biggest possible volume of the cylinder will be .
<h3>What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?</h3>
- If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.
- For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is , the diameter and the height of the cylinder are also
- If the side length of a cube is unit, then its diagonal will be unit.
- The formula for the volume of a cylinder is , where is the radius and is the height of the cylinder. If is the diameter, then .
Now, given that the diagonal of the cube is cm. So, if the side length of the cube is cm, then we must have
Thus, the side length of the cube is cm.
So, the height of the cylinder with maximum volume will be cm and the diameter will be cm i.e. the radius will be cm.
So, using the above formula for the volume of a cylinder, we get
.
Therefore, the biggest possible volume of the cylinder will be .
To know more about volume, refer: brainly.com/question/1972490
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