This looks like scalar matrix multiplication. The idea here is to multiply the scalar 3 by each item inside the matrix.
Doing so leads to the answer [3 -12 15 -21]
Side note: I'm assuming the matrix given to you has 1 row and 4 columns.
Answer:
560/800 = 0.7 pounds per dollar
Answer:
<u>416 square centimeters</u>
Step-by-step explanation:
Formula for finding area of a trapezoid :
<u>A = 1/2 x (a + b) x h</u>
- a and b = parallel sides of the trapezoid
- h = height of the trapezoid
Solving :
- A = 1/2 x (38 + 14) x 16
- A = 8 x 52
- A = <u>416 square centimeters</u>
(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:
Answer:
37°
Step-by-step explanation:
∠ECF= ∠ACG
∠ACG= 90° - ∠GAC= 90° - 53°= 37°
