Answer: 52.94
Step-by-step explanation:
Length of train A = 480m
Tunnel length = 1320m
Time taken to cross tunnel = 2 mins = 120sec
Length of train B = 420m
Train B is slower than train A
Difference between their speed = 18km/hr
18km/hr = (18×1000)/3600 = 5m/s
Speed of train A :
Speed = distance / time
Speed = 1320 / 120 = 11m/s
Therefore, speed of train B :
(11 - 5)m/s = 6m/s
Relative speed of the two trains is therefore;
(Speed of A + speed of B)
Note : they are moving in opposite direction
( 11 + 6)m/s = 17m/s
Therefore time taken to cross each other :
(Sum of the length of both trains / relative speed of the trains)
Time taken = (480m + 420m) / (17m/s)
Time taken = 900m / 17m/s
Time taken = 52.94s
If one number is the multiple of another number, then the L.C.M. will be the smaller number (the number whose multiple the other number is).
Answer:
- 3.75 bags of ChowChow
- 0.75 bags of Kibble
Step-by-step explanation:
The constraints on protein, minerals, and vitamins give rise to the inequalities ...
40c +30k ≥ 150 . . . . . . required protein
20c +20k ≥ 90 . . . . . . required minerals
10c +30k ≥ 60 . . . . . . . required vitamins
And we want to minimize 10c +12k.
The graph shows the vertices of the feasible region in (c, k) coordinates. The one that minimizes cost is (c, k) = (3.75, 0.75).
To minimize cost, the daily feed should be ...
- 3.75 bags of ChowChow
- 0.75 bags of Kibble
Daily cost will be $46.50.
<h3>
Answer: Choice A</h3>
![x^2\left(\sqrt[4]{x^2}\right)](https://tex.z-dn.net/?f=x%5E2%5Cleft%28%5Csqrt%5B4%5D%7Bx%5E2%7D%5Cright%29)
=====================================================
Explanation:
The fourth root of x is the same as x^(1/4)
I.e,
![\sqrt[4]{x} = x^{1/4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%7D%20%3D%20x%5E%7B1%2F4%7D)
The same applies to x^10 as well
![\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E%7B10%7D%7D%20%3D%20%5Cleft%28x%5E%7B10%7D%5Cright%29%5E%7B1%2F4%7D)
Multiply the exponents 10 and 1/4 to get 10/4
![\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4} = x^{10*1/4} = x^{10/4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E%7B10%7D%7D%20%3D%20%5Cleft%28x%5E%7B10%7D%5Cright%29%5E%7B1%2F4%7D%20%3D%20x%5E%7B10%2A1%2F4%7D%20%3D%20x%5E%7B10%2F4%7D)
![\sqrt[4]{x^{10}} = x^{10/4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E%7B10%7D%7D%20%3D%20x%5E%7B10%2F4%7D)
-----------------------
If we have an expression in the form x^(m/n), with m > n, then we can simplify it into an equivalent form as shown below
![x^{m/n} = x^a\sqrt[n]{x^b}](https://tex.z-dn.net/?f=x%5E%7Bm%2Fn%7D%20%3D%20x%5Ea%5Csqrt%5Bn%5D%7Bx%5Eb%7D)
The 'a' and 'b' are found through dividing m/n
m/n = a remainder b
'a' is the quotient, b is the remainder
-----------------------
The general formula can easily be confusing, so let's replace m and n with the proper numbers. In this case, m = 10 and n = 4
m/n = 10/4 = 2 remainder 2
We have a = 2 and b = 2
So
![x^{m/n} = x^a\sqrt[n]{x^b}](https://tex.z-dn.net/?f=x%5E%7Bm%2Fn%7D%20%3D%20x%5Ea%5Csqrt%5Bn%5D%7Bx%5Eb%7D)
turns into
![x^{10/4} = x^2\sqrt[4]{x^2}](https://tex.z-dn.net/?f=x%5E%7B10%2F4%7D%20%3D%20x%5E2%5Csqrt%5B4%5D%7Bx%5E2%7D)
which means
![\sqrt[4]{x^{10}} = {x^2} \sqrt[4]{x^2}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E%7B10%7D%7D%20%3D%20%7Bx%5E2%7D%20%5Csqrt%5B4%5D%7Bx%5E2%7D)
Step-by-step explanation:
A. a numerical expression I am pretty sure