For a body moving with increasing acceleration, the graph will be in the form of an exponential function. An example of the exponential function is shown in the attached diagram.

Mathematically exponential function can be expressed by the following equation.

<span>F(a) = e^a, where a>0.</span>

8 0

3 years ago

Read 2 more answers

Find the distance traveled by a particle with position (x, y as t varies in the given time interval. x = 3?sin2 t, y = 3?cos2 t,

ANTONII [103]

Assuming the particle's position is given by

$\begin{cases}x(t)=3-\sin2t\\y(t)=3-\cos2t\\0\le t\le4\end{cases}$

then the distance traveled over the interval is

$\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\dfrac{\mathrm dx(t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy(t)}{\mathrm dt}\right)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{(-2\cos2t)^2+(2\sin2t)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{4\cos^22t+4\sin^22t}\,\mathrm dt$
$=\displaystyle2\int_0^4\mathrm dt$
$=2(4-0)=8$

5 0

3 years ago

1 in 3 babies born last year are expected to live to 100years old

kolbaska11 [484]

Divide 720,000 by 3.
Your answer is 240,000.

3 0

3 years ago