If you sketch the triangle, you need to understand that 12 is the length of opposite side (opposite to theta). Then the longest side is 13 is the hypotenuse. The other side with length 5 is the adjacent side. Thus from the definition of sin(theta)=opposite side/hypotenuse=12/13. A question for you, what is cos(theta)? cos(theta)=5/15 and tan(theta)=12/5
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)
Answer:
D, E
Step-by-step explanation:
All sides are not the same length so not A
Two sides are not the same length so not B
Not all angles are less than 90 so not C
All sides are different length so D
There is a right angle so E
Not all sides are greater than 90 so not F
You know how there are 4 different areas in the graph, rotating it 180 degrees from that position will make it be in quadrant 2 (top left). in order to graph the ponts, since it is right across, then you just have to flip the shape around. like how you take a selfe, it flips the capture image around
Answer:
0.0158 = 1.58% probability that all of them are under 18.
Step-by-step explanation:
Probability of independent events:
If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:
The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.
This means that 
If one person is selected from each city, what is the probability that all of them are under 18?
Since the three people are independent:
0.0158 = 1.58% probability that all of them are under 18.
