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I have solved some examples. it's in the picture.
Answer:
Rate of plane 735 km/hr
Rate of wind 65 km/hr
Step-by-step explanation:
Calculation to determine the rate of the plane in still air
Let Va represent the velocity of the airplane
Let Vw represent the velocity of the wind
When flying with the wind:
(Va+Vw)*(6 hours) = 4800
6Va + 6Vw = 4800
6Vw = 4800 - 6Va
Vw=4800/6-Va
Vw = 800 - Va
When flying against the wind:
(Va-Vw)*(6 hours) = 4020 km
6Va - 6Vw = 4020
Substitute 800-Va for Vw and solve for Va:
6Va - 6(800-Va) = 4020
6Va -4800 + 6Va = 4020
12Va = 8820
Va=8820/12
Va = 735 km/hr
Therefore the rate of the plane in still air is 735 km/hr
Calculation to determine the rate of the wind
Rate of wind:
Vw = 800 - Va
Vw= 800 -735
Vw= 65 km/hr
Therefore the rate of the wind is 65 km/hr
Answer:
Yes
Step-by-step explanation:
Given that a relation R is defined on the set Z by "a R b if a - b is divisible by 5
for a, b in the set of integers.
Reflexive:
We have
for any a, 
i.e. (a,a) is related. Hence reflexive
ii) Symmetric:
If a-b is divisible by 5, then b-a is also divisible by 5. Hence symmetric
iii) Transitive
If 
adding we get
Hence R is transitive
It follows that R is an equivalence relation on Z
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Answer:
- shortest: 13 in
- middle: 17 in
- longest: 23 in
Step-by-step explanation:
Let s represent the shortest side. Then the longest side is (s+10) and the middle side is (s+(s+10)-19). The perimeter is the sum of the sides.
s + (2s-9) +(s+10) = 53
4s +1 = 53
s = (53 -1)/4 = 13
The side lengths are ...
- shortest: 13 in
- middle: 17 in
- longest: 23 in
The answer is 10. Well assuming when they buy 45 bottles those are 5 gift packs worth of bottles. First you make the ratio 7:2 ( 7 is the not-spicy and 2 is the spicy in each pack) and if someone bought 5 gift packs (45 bottles) then you would multiply 7 and 2 by 5 and you would have the new ratio of 35:10. Your last step is simple, since we are trying to find out the amount of spicy salsa bottles their are, we take the 10 out of the ratio and make it our answer.
