Answer:
The independent quantity in the situation is the length of the diameter.
Step-by-step explanation:
Consider a relationship between two variables.
Of the two variables one variable is dependent upon the other.
Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variable values are changed.
Independent variables are the variables that are being altered to see a proportionate change in the dependent variable.
In this case, it is provided that Grissom knows there is a relationship between the volume of the sphere and the length of its diameter.
With every sphere that Grissom draws, the volume of the sphere changes according to its diameter length.
That is the volume of the sphere depends upon the length of its diameter.
Thus, the independent quantity in the situation is the length of the diameter.
Answer:
Step-by-step explanation:
Note that the expression is the difference of squares.
36 - 9m² = 6² - (3m)²
6² - (3m)² = (6 + 3m) (6 - 3m)
Answer:
(-3, 3)
Step-by-step explanation:
Substitute for y:
x+6 = -2x -3
3x = -9 . . . . . . . add 2x -6 to both sides
x = -3 . . . . . . . . divide by 3
y = (-3) +6 = 3 . . substitute for x in the first equation
The solution is ...
(x, y) = (-3, 3)
Given:
The x and y axis are tangent to a circle with radius 3 units.
To find:
The standard form of the circle.
Solution:
It is given that the radius of the circle is 3 units and x and y axis are tangent to the circle.
We know that the radius of the circle are perpendicular to the tangent at the point of tangency.
It means center of the circle is 3 units from the y-axis and 3 units from the x-axis. So, the center of the circle is (3,3).
The standard form of a circle is:
Where, (h,k) is the center of the circle and r is the radius of the circle.
Putting 
, we get
Therefore, the standard form of the given circle is .
Answer:
4
Step-by-step explanation:
slope, m = (y₂ - y₁)/(x₂ - x₁)
plug in the values, and we get m = (3 - (-1))/((3 - 2) = 4
As x increases by 1, y increases by 4.
