Work done on cart
:
W
=
6000
J
Kinetic energy of cart
:
E
K
=
6000
J
Explanation:
Work done
W
is defined as the product of force
F
and distance
s
:
⇒
W
=
F
⋅
s
Let's substitute the values of
F
and
s
into the equation:
⇒
W
=
300
N
⋅
20
m
⇒
W
=
300
kg
⋅
m s
−
2
⋅
20
m
⇒
W
=
300
⋅
20
kg
⋅
m
2
s
−
2
⇒
W
=
6000
kg
⋅
m
2
s
−
2
∴
W
=
6000
J
The gain in kinetic energy
E
K
is the same amount as the work done moving the cart:
∴
E
K
=
6000
(a) Using the table, give the values fo rthe inverse
1) original table of values:
x 1 2 3 4 5
f(x) 0 1 1 5 3
2) The inverse of the function is obtained by exchanging x and f(x), this is:
( x, f(x) ) → ( f(x), x)
3) So, the table of values of the inverse of the given function is:
x 0 1 1 5 3
f⁻¹ (x) 0 1 2 3 4
(b) Is the inverse a function?
No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.
This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.
Answer:
2,025
Step-by-step explanation:
Given:
Third term ar² = 45
Seventh term ar⁶ = 3,645
Find:
ar x ar³
Computation:
From 7th term / 3rd term
ar⁶ / ar² = 3,645 / 45
r⁴ = 81
r = 3
So,
ar² = 45
a(3)² = 45
a = 5
So,
ar x ar³
(5)(3) x (5)(3)³
2,025
1/2x-7=1/3x-4,
1/2x-3=1/3x,
1/2x-1/3x=3
1/6x=3/1/6
Final answer x=18
I hope you understand and best wishes!!
We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
<h3>
How to get the sum of the first 8 terms?</h3>
In an arithmetic sequence, the difference between any two consecutive terms is a constant.
Here we know that:
There are 7 times the common difference between these two values, so if d is the common difference:
Then the sum of the first 8 terms is given by:
So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
If you want to learn more about arithmetic sequences:
brainly.com/question/6561461
#SPJ1
