Answer:
x = 20
Step-by-step explanation:
The sum of the three angles in the diagram is 180 degrees since they form a straight line
x + 100 + 3x = 180
Combine like terms
100 +4x = 180
Subtract 100 from each side
100+4x-100 =180-100
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
Answer:
"35.84 years" is the appropriate solution.
Step-by-step explanation:
The given values are:
Rate of savings generation,
![s'(t)=300e^{\frac{t}{20} }](https://tex.z-dn.net/?f=s%27%28t%29%3D300e%5E%7B%5Cfrac%7Bt%7D%7B20%7D%20%7D)
System cost to install,
= $30000
Now,
The total savings will be:
⇒ ![s(t)=\int\limits s'(t) \ dt](https://tex.z-dn.net/?f=s%28t%29%3D%5Cint%5Climits%20s%27%28t%29%20%5C%20dt)
On substituting the values, we get
⇒ ![= \int\limits 300e^{\frac{t}{20} } \ dt](https://tex.z-dn.net/?f=%3D%20%5Cint%5Climits%20300e%5E%7B%5Cfrac%7Bt%7D%7B20%7D%20%7D%20%5C%20dt)
⇒ ![s(t)=\frac{300e^{\frac{t}{20} }}{\frac{1}{20} }+c](https://tex.z-dn.net/?f=s%28t%29%3D%5Cfrac%7B300e%5E%7B%5Cfrac%7Bt%7D%7B20%7D%20%7D%7D%7B%5Cfrac%7B1%7D%7B20%7D%20%7D%2Bc)
When,
Savings = 0
t = 0, then
⇒ ![0=6000e^o+c](https://tex.z-dn.net/?f=0%3D6000e%5Eo%2Bc)
⇒ ![c=-6000](https://tex.z-dn.net/?f=c%3D-6000)
The formula will be:
⇒ ![s(t)=6000[e^{\frac{t}{20} }-1]](https://tex.z-dn.net/?f=s%28t%29%3D6000%5Be%5E%7B%5Cfrac%7Bt%7D%7B20%7D%20%7D-1%5D)
On putting the values in the above formula, we get
⇒ ![30000=6000(e^{\frac{t}{20} }-1)](https://tex.z-dn.net/?f=30000%3D6000%28e%5E%7B%5Cfrac%7Bt%7D%7B20%7D%20%7D-1%29)
![5=e^{\frac{t}{20}}-1](https://tex.z-dn.net/?f=5%3De%5E%7B%5Cfrac%7Bt%7D%7B20%7D%7D-1)
![e^{\frac{t}{20} }=6](https://tex.z-dn.net/?f=e%5E%7B%5Cfrac%7Bt%7D%7B20%7D%20%7D%3D6)
On taking log, we get
⇒ ![\frac{t}{20} =log \ 6](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7B20%7D%20%3Dlog%20%5C%206)
![t=20 log 6](https://tex.z-dn.net/?f=t%3D20%20log%206)
43 is 40+3 and 962 is900+60+2
Answer:
11.1
Step-by-step explanation:
We have the hypotonouse but need the opposite side
We will therefore use SOH
sin(68)=x/12
12sin(68)=x
x=11.1