Answer:
y=x+2
Step-by-step explanation:
In this picture ( step by step )
The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
Answer:
225 frogs
Step-by-step explanation:
Total population of frogs = 300 frogs.
Observed population of frogs = 24
6 of the 24 observed frogs had spots
Which means , the number of frogs that did not have spots = 24 - 6 = 18 frogs.
We were told to find how many of the total population can be predicted to NOT have spots. We would form a proportion.
If 24 frogs = 18 frogs with no spots
300 frogs = Y
Cross multiply
24Y = 300 × 18
Y = (300 × 18) ÷ 24
Y = 5400 ÷ 24
Y = 225 frogs.
This means out of 300 frogs, 225 frogs do not have spots.
Therefore, the total population that can be predicted to NOT have spots is 225 frogs.
the total population can be predicted to NOT have spots
A =
5 and -5
-1 and 3
¹/₃B =
-6 and 12
-7 and 7
¹/₃B + A =
-1 and 7
-8 and 10
