Answer:
sinΘ = ![\frac{24}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B25%7D)
Step-by-step explanation:
sinΘ = ![\frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
The opposite is 24, but we require the hypotenuse h
Using Pythagoras' identity
h² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )
h =
= 25
Thus
sinΘ = ![\frac{24}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B25%7D)
The domain is -1,0,1,2. The range is 3,5,7,9.
Using the formula A=P(1+i/100)^n
where A is the investment/loan after n years, P is the original investment/loan and i% is the interest per annum.
A=5000(1+0.05)^48
A=52006.35
Answer:convergent
Step-by-step explanation:
Given
Improper Integral I is given as
![I=\int_{-\infty}^{0}1000e^xdx](https://tex.z-dn.net/?f=I%3D%5Cint_%7B-%5Cinfty%7D%5E%7B0%7D1000e%5Exdx)
![I=1000=\int_{-\infty}^{0}e^xdx](https://tex.z-dn.net/?f=I%3D1000%3D%5Cint_%7B-%5Cinfty%7D%5E%7B0%7De%5Exdx)
integration of
is ![e^x](https://tex.z-dn.net/?f=e%5Ex)
![I=1000\times \left [ e^x\right ]^{0}_{-\infty}](https://tex.z-dn.net/?f=I%3D1000%5Ctimes%20%5Cleft%20%5B%20e%5Ex%5Cright%20%5D%5E%7B0%7D_%7B-%5Cinfty%7D)
![I=1000\times I=\left [ e^0-e^{-\infty}\right ]](https://tex.z-dn.net/?f=I%3D1000%5Ctimes%20I%3D%5Cleft%20%5B%20e%5E0-e%5E%7B-%5Cinfty%7D%5Cright%20%5D)
![I=1000\times \left [ e^0-\frac{1}{e^{\infty}}\right ]](https://tex.z-dn.net/?f=I%3D1000%5Ctimes%20%5Cleft%20%5B%20e%5E0-%5Cfrac%7B1%7D%7Be%5E%7B%5Cinfty%7D%7D%5Cright%20%5D)
![I=1000\times 1=1000](https://tex.z-dn.net/?f=I%3D1000%5Ctimes%201%3D1000)
so the integration converges to 1000 units