The radius of the sphere decreases at the rate of 6 m/ sec
That is,
Surface Area of the sphere of radius r is given by
Differentiating with respect to t,
Answer:
r = 144 units
Step-by-step explanation:
The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;
In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.
Substituting the terms of the equation and the derivative of r´, as follows,
Doing the operations inside of the brackets the derivatives are:
1 )
2)
Entering these values of the integral is
It is possible to factorize the quadratic function and the integral can reduced as,
Thus, evaluate from 0 to 16
The value is
Answer:
Variable represents the slope of the equation.
Step-by-step explanation:
Given that the administrative fees that company charge is $3.50.
Also, the Zhao has a bill of $63.25.
The equation used by Zhao is
We can compare the equation of a line in the slope-intercept form.
We can see the y-intercept is $3.50 that is a fixed cost. And the company charged $63.25 that is the dependent variable.
Also, variable that is the rate per kilowatt-hour (kWh) represents the slope of the equation.
-2Step-by-step explanation:
Write the set of points from -6 to 0 but excluding -4 and 0 as a union of intervals
First we take the interval -6 to 0. In that -4 and 0 are excluded.
So we split the interval -6 to 0.
Start with -6 and go up to -4. -4 is excluded so we break at -4. Also we use parenthesis for -4.
Interval becomes [-6,-4) . It says -6 included but -4 excluded.
Next interval starts at -4 and ends at 0. -4 and 0 are excluded so we use parenthesis not square brackets
(-4,0)
Now we take union of both intervals
[-6,-4) U (-4,0) --- Interval from -6 to 0 but excluding -4 and 0