(a)
We can see that
this is a straight line
and this is the graph of velocity
we know that
acceleration is the derivative of velocity
so, slope of curve of velocity is acceleration
so, we will find slope of this line
We can select any two points
(0,4) and (5,7)
we can use slope formula
now, we can plug points
we know that slope of line is always constant irrespective of any value of t
so, acceleration will always be same irrespective of any value of t
so, we will get acceleration
............Answer
(b)
we can see that acceleration is constant
and we know that
derivative of constant is always 0
so, instantaneous rate of acceleration at t=10s is 0........Answer
Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
Answer:
T-shirt costs £10
Hat costs £3
Step-by-step explanation:
£93-£43=£50
9-4=5
£50/5=10
1 t-shirt=£10
£10x9=£90
£93-£90=£3
T-shirt = £10
Hat= £3
Answer:
d= 17.03
Step-by-step explanation:
Answer:
12 pints
Step-by-step explanation:
There are 24 students & each one gets 1 cup, so you will need 24 cups total. There are 2 cups in a pint. You divided the 24 cups you need by 2 cups in a pint to get the answer of 12 pints.
You can double check: 12 pints converted to cups (2 cups in a pint) is 12 x2 = 24 cups
