We use the binomial theorem to answer this question. Suppose we have a trinomial (a + b)ⁿ, we can determine any term to be:
[n!/(n-r)!r!] a^(r) b^(n-r)
a.) For x⁵y³, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.
r = 5
n - r = 3
Solving for n,
n = 3 + 5 = 8
Therefore, the coefficient is equal to:
Coefficient = n!/(n-r)!r! = 8!/(8-5)!8! = 56
b.) For x³y⁵, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.
r = 3
n - r = 5
Solving for n,
n = 5 + 3 = 8
Therefore, the coefficient is equal to:
Coefficient = n!/(n-r)!r! = 8!/(8-3)!8! = 56
Answer:
ΔF=125.22 %
Explanation:
We know that drag force on the car given as

=Drag coefficient
A=Projected area
v=Velocity
ρ=Density
All other quantity are constant so we can say that drag force and velocity can be given as

Now by putting the values



Percentage Change in the drag force



ΔF=125.22 %
Therefore force will increase by 125.22 %.
Answer:
a)α= 53.13°
b)The velocity at the highest point = 15 m/s
The acceleration at the highest point = 9.8
c)h=15 m
V=18.02 m/s
Explanation:
Speed of water ,u= 25 m/s
So the horizontal component of speed u = u cos α
Given that horizontal distance cover by water in 3 s is 45 m.
So We know that in projectile motion horizontal acceleration is zero.
In horizontal direction
Distance = Velocity x time
45 = u cos α x 3
u cos α = 45
45 = 25 cos α x 3
cos α = 45/75
α= 53.13°
So the velocity at the highest point = u cos α
The velocity at the highest point = 15 m/s
The acceleration at the highest point = 9.8
Now the velocity along vertical direction(Vo) = u sin α
Vo= 25 sin 53.13°
Vo =20 m/s


h=15 m
So at 15 m above the ground water will strike .
The y-component of velocity after 3 sec
Vy= Vo - g t
Vy = 20 - 10 x 3
Vy= -10 m/s
The horizontal component of velocity will remain 15 m/s.
The resultant velocity

V=18.02 m/s
Answer: B) 30 km/h
Explanation:
The speed of Ben and Jerry on their way to the store is given by

where
d is the distance they covered
t is the time they took
From the graph, we see that Ben and Jerry travelled for a distance of d=60 km in a time of t=2 h, so their speed is
