Answer:
sin θ = 15/17
Step-by-step explanation:
First we have to know how much the hypotenuse measures.
to take out the hypotenuse we will use pitagoras, with the following formula.
h^2 = c1^2 + c2^2
c1 = 8
c2 = 15
h^2 = 8^2 + 15^2
h^2 = 64 + 225
h = √ 289
h = 17
well to start we have to know the relationships between angles, legs and the hypotenuse.
a: adjacent
o: opposite
h: hypotenuse
sin θ = o/h
cos θ= a/h
tan θ = o/a
we want to know the sin of θ
sin θ = o/h
sin θ = 15/17
Answer:
A, B and C
Step-by-step explanation:
A. Adding another researcher to provide ratings will make the study less biased.
B. A quiz or exam will show which students have a better understanding of the math material. Better quiz or exam results show that the site is more effective for a student with or without the supplemental instruction.
C. Having a greater sample size is better because a greater scope of students is covered. Different students have different abilities and learning preferences.
Answer:
i think its rational.
Step-by-step explanation:
(a) Take the Laplace transform of both sides:
where the transform of 
comes from
![L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)](https://tex.z-dn.net/?f=L%5Bty%27%28t%29%5D%3D-%28L%5By%27%28t%29%5D%29%27%3D-%28sY%28s%29-y%280%29%29%27%3D-Y%28s%29-sY%27%28s%29)
This yields the linear ODE,
Divides both sides by 
:
Find the integrating factor:
Multiply both sides of the ODE by 
:
The left side condenses into the derivative of a product:
Integrate both sides and solve for 
:
(b) Taking the inverse transform of both sides gives
![y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B7t%5E2%7D2%2BC%5C%2CL%5E%7B-1%7D%5Cleft%5B%5Cdfrac%7Be%5E%7Bs%5E2%7D%7D%7Bs%5E3%7D%5Cright%5D)
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that 
is one solution to the original ODE.
Substitute these into the ODE to see everything checks out:
