Step-by-step answer:
We are looking at the coefficient of the 22nd term of (x+y)^25.
Following the sequence, first term is x^0y^25, second term is x^1y^24, third term is x^2y^23...and so on, 22nd term is x^21y^4.
The twenty-second term of (x+y)^25 is given by the binomial theorem as
( 25!/(21!4!) ) x^21*y^4
=25*24*23*22/4! x^21y^4
= 12650 x^21 y^4
The coefficient required is therefore 12650, for a binomial with unit valued coefficients.
For other binomials, substitute the values for x and y and expand accordingly.
Question would have been more clearly stated if the actual binomial was given, as commented above.
Answer:
The error is at step (3) .
The correct step (3) will be,
= 
[by using the laws of indices]
All other steps are correct.
Step-by-step explanation:
The error is at the step (3) , because the student has tried to prove the quotient rule of logarithms by using the property i.e., 'The quotient rule of logarithm' itself , i.e. ,by assuming the property does hold before proving it. So, the proof is fallacious.
The correct step (3) will be,
= [by using the laws of indices]
All other steps are correct.
Answer:
If its written as the fourth root of (81^3) the answer is 27.
Answer:
Step-by-step explanation:
The fraction 26/5 can be simplified to 5 and 1/5, which is between the numbers 5 and 6.
Hope it helps :) and let me know if you want me to elaborate.
Answer:
Malcom's maximum speed is 200 km/h
Ravi's maximum speed is 320 km/h
Step-by-step explanation:
First we have to make two equations one that represents the maximum average speed of the 2 together and another that represents the relationship between their maximum speeds
R = Ravi's maximum speed
M = Malcom's maximum speed
(R + M) /2 = 260 km/h
2M = R + 80 km/h
we are going to solve for M in the first equation
(R + M) /2 = 260 km/h
(R + M) = 260 * 2
M = 520 - R
we replace M with (520 - R) in the second equation
2M = R + 80 km/h
2(520 - R) = R + 80
1040 - 2R = R + 80
1040 - 80 = R + 2R
960 = 3R
960/3 = R
320 = R
replace R with its value in the first equation
M = 520 - R
M = 520 - 320
M = 200
Malcom's maximum speed is 200 km/h
Ravi's maximum speed is 320 km/h
