Answer: the speed of the plane in still air is 135 km/h
the speed of the wind is 23 km/h
Step-by-step explanation:
Let x represent the speed of the plane in still air.
Let y represent the speed of the wind.
Flying to England with a tailwind a plane averaged 158km/h. This means that the total speed of the plane is (x + y) km/h. Therefore,
x + y = 158 - - - - - - - - - - - - - -1
On the return trip, the plane only averaged 112 km/h while flying back in the same wind. This means that the total speed of the plane is (x - y) km/h. Therefore,
x - y = 112 - - - - - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
2x = 270
x = 270/2 = 135 km/h
Substituting x = 135 into equation 2, it becomes
135 - y = 112
y = 135 - 112
y = 23 km/h
Answer:
The statements are incorrect as: The sum of even numbers from 1 to 100(i.e. 2550) is not double\twice of the sum of odd numbers from 1 to 100(i.e. 2500).
Step-by-step explanation:
We know that sum of an Arithmetic Progression(A.P.) is given by:
where 'n' denotes the "number" of digits whose sum is to be determined, 'a' denotes the first digit of the series and '' denote last digit of the series.
Now the sum of even numbers i.e. 2+4+6+8+....+100 is given by the use of sum of the arithmetic progression since the series is an A.P. with a common difference of 2.
image with explanation
Hence, sum of even numbers from 1 to 100 is 2550.
Also the series of odd numbers is an A.P. with a common difference of 2.
sum of odd numbers from 1 to 100 is given by: 1+3+5+....+99
.
Hence, the sum of all the odd numbers from 1 to 100 is 2500.
Clearly the sum of even numbers from 1 to 100(i.e. 2550) is not double of the sum of odd numbers from 1 to 100(i.e. 2500).
Hence the statement is incorrect.
Step-by-step explanation:
Answer:
$25 I believe
Step-by-step explanation:
You would take $37.50 divided by 3 and get $12.50 which is the price of 1 ticket
Then you would multiply $12.50 x 2 to get $25
First we need to define our conditions. Since the angles are complimentary, the sum of the angles must be equal to 90 degrees.
let x = first angle
y = second angle
x + y = 90
from the second condition in the problem
x + y =72 + x -y
solving for x
x= 54
therefore the shorter side is 90 - 54 = y
y = 36 degree, the shorter side
Answer:
0.50 kg of the material would be left after 10 days.
0.25 kg of the material would be left after 20 days.
Step-by-step explanation:
We have been given that the half-life of a material is 10 days. You have one 1 kg of the material today. We are asked to find the amount of material left after 10 days and 20 days, respectively.
We will use half life formula.
, where,
A = Amount left after t units of time,
a = Initial amount,
t = Time,
h = Half-life.
Therefore, amount of the material left after 10 days would be 0.5 kg.
Therefore, amount of the material left after 20 days would be 0.25 kg.