Answer: 2 1/4
Step-by-step explanation:
Answer:
Y= 2e^(5t)
Step-by-step explanation:
Taking Laplace of the given differential equation:
s^2+3s-10=0
s^2+5s-2s-10=0
s(s+5)-2(s+5) =0
(s-2) (s+5) =0
s=2, s=-5
Hence, the general solution will be:
Y=Ae^(-2t)+ Be^(5t)………………………………(D)
Put t = 0 in equation (D)
Y (0) =A+B
2 =A+B……………………………………… (i)
Now take derivative of (D) with respect to "t", we get:
Y=-2Ae^(-2t)+5Be^(5t) ....................... (E)
Put t = 0 in equation (E) we get:
Y’ (0) = -2A+5B
10 = -2A+5B ……………………………………(ii)
2(i) + (ii) =>
2A+2B=4 .....................(iii)
-2A+5B=10 .................(iv)
Solving (iii) and (iv)
7B=14
B=2
Now put B=2 in (i)
A=2-2
A=0
By putting the values of A and B in equation (D)
Y= 2e^(5t)
The average of a set of data is equal to the sum of the values divided by the number of data present. So, if we have three numbers, the average would be:
let x, y and z represent the three numbers
average = x + y + z / 3 = 45
Two number are equal in value, so let x = y. Substituting the value to the expression of average,
45 = x + x + z / 3
45 = 2x + z / 3
It said that the last number is 89 so z is equal to 89.
45 = 2x + 89 / 3
135 = 2x + 89
46 = 2x
x = 23
Therefore, the two numbers are both 23.
Answer:
3a^2+12a-7
Step-by-step explanation:
Angle BDC is given as 38° but not drawn in the figure. Amateurs.
We calculate angle DBC
DBC = 180° - 96° - 38° = 180° - 134°
We won't bother subtracting because we're really after
angle ABD = 180° - DBC = 134°
Now we have a Law of Cosines situation,
AD² = AB² + BD² - 2(AB)(BD) cos ABD
AD = √( 5.8² + 27.3² - 2(5.8)(27.3) cos 134°)
AD ≈ 31.61 m
Answer: 31.6 m
