A curve in the xy-plane is defined by (x(t),y(t)), where x(t)=sin(2t) and y(t)=cos(3t). Which of the following is equivalent to d/dt (x(t),y(t)) ? A=(cos(2t), sin(3t))
B=(2cos(2t), -3sin(3t))
C=(2cos(2t), 3sin(2t))
D= (-2cos(2t), -3sin(3t))

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

the circumference of a circle is, 10.676 cm.

step-by-step explanation:

the formula for circumference of a circle is given by:

where

c is the circumference of a circle and

d is the diameter of a circle.

given: diameter(d) = 3.4 cm and use

substitute these values in [1] we get;

cm

therefore, the circumference of a circle is, 10.676 cm