Answer:
Step-by-step explanation:
Let y be the amount of water in the bottle x seconds after the faucet was turned on.
We have been given that the gauge on the bottle indicates that it contains 19 ounces of water after it has been filling for 5 seconds. After it has been filling for 11 seconds, the gauge indicates the bottle contains 37 ounces of water.
We have two points on the line 
and 
.
Let us find slope of the line passing through these points.
We will write our required equation in slope-intercept form 
, where, m represents slope and b represents the y-intercept.
Let us find y-intercept by substituting and coordinates of point in slope intercept form.
Therefore, our required equation would be .
Answer:42
Step-by-step explanation:
7 multiplied by 6= 42
(Divide then multiply by 100 and you get your answer)
- - Answer: 70%
Answer:
I'm not sure how to answer is but i think its called < CDE or < EDC or it is an acute angle.
Step-by-step explanation:
Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
