(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where

then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,

(b) The velocity after 3 seconds is

(c) The particle is at rest when its velocity is zero:

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.
(e) The total distance traveled is given by the definite integral,

By definition of absolute value, we have

In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as

and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to

Answer:
6π cm³
Step-by-step explanation:
V = Ah ( A is the base area and h the height ), then
3πh = 18π ( divide both sides by 3π )
h = = 6
Then the height of the smaller cylinder = 6 - 3 = 3 cm
V = 3π × 3 = 9π cm³ ← volume of smaller can
Step-by-step explanation:
Answer:
$280
Step-by-step explanation:
According to the problem, calculation of the given data are as follows:
Principal amount (P) = $1,000
Rate of interest (r) = 7%
Time period (t) = 4 years
Here we use simple interest formula to calculate interest after 4 years.
I = P × r × t
By putting the value, we get
I = $1,000 × 7% × 4
= $70 × 4
= $280
Answer:
27.74cm^2
Step-by-step explanation:
area of circle: 3 times 3 times pi = 28.26cm^2
area of square: 8 times 7 = 56cm^2
subtract area of circle from square
56-28.26=27.74cm^2
Answer:
The first shape
Step-by-step explanation:
as you can tell the side numbers are increasing for example...
triangle=3 sides
square=4 sides
pentagon=5 sides
so on and so forth
have a wonderful day!