Answer:
Step-by-step explanation:
The position of an object moving horizontally after t seconds is given by the function
s = 3t - t³
a) The object is stationary when there is no external force acting on the body. When the body is at rest, the body remains in a position and here is no distance covered by the object i.e s = 0
b) velocity is the change in displacement of a body with respect to time.
v = ds/dt
S = 3t - t³
V = ds/dt = 3-3t²
at t = 2
Velocity = 3-3(2)²
Velocity = 3-12
Velocity = -9m/s
c) acceleration is the change in velocity of a body with respect to time.
acceleration = dv/dt
If v = 3-3t²
a = dv/dt = -6t
When v = 0
0 = 3-3t²
-3 = -3t²
t² = 1
t = ±√1
t = 1sec
The acceleration of the object at v = 0 occurs at t = 1sec and -1sec
a = -6(1)
a = -6m/s²
d) Given the speed of the body v modelled by the function
v = 3-3t²
The speed is decreasing when it is less than zero as shown:
3-3t²< 0
3<3t²
1<t²
±1<t
1<t and -1<t
t>±1
t >1 and t>-1
The speed is decreasing when
3-3t²<0 and t>1 or t>-1
The equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8
<h3>Equation of a line</h3>
The equation of a line in point slope form is expressed as:
y - y1 = m(x-x1)
Given the equation y = -x + 2, the slope of the line parallel to the line is -1
Substitute the slope and point (-3, -5)
y -(-5) = -1(x - (-3))
y+5 = -(x + 3)
y+5 =-x - 3
y = -x - 3 - 5
y = -x - 8
Hence the equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8
Learn more on equation of a line here: brainly.com/question/18831322
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Answer:
Annuity C: Deposit $72,000 one lump sum
Step-by-step explanation:
The yield is improved when the money is on deposit for a longer period.
If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.
If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.
Annuity C will provide the largest yield.
Hi , Karyn proofreads 5 pages per hour , basically two half hours are equal to 10 pages , then 1 hour equals 5 pages . She will receive 16 dollars for one page , because she receives 20 dollars for 5 pages . The unit rate is 5 pages per hour.
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