Answer:
Step-by-step explanation:
LHS = 1/1-secA + 1/1+secA
![= \frac{1*(1+Sec A)}{(1-Sec A)(1+Sec A)}+\frac{1*(1-Sec A)}{(1+Sec A)*(1-Sec A)}\\\\=\frac{(1+Sec A)}{1-Sec^{2} A}+\frac{(1-Sec A)}{1-Sec^{2} A}\\\\=\frac{1+Sec A+1-Sec A}{(1-Sec^{2} A)}\\\\= \frac{2}{(1-Sec^{2} A)}\\\\=\frac{2}{-(Sec^{2} A - 1)}\\\\= \frac{-2}{Tan^{2} A}\\\\= -2Cot^{2} A](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%2A%281%2BSec%20A%29%7D%7B%281-Sec%20A%29%281%2BSec%20A%29%7D%2B%5Cfrac%7B1%2A%281-Sec%20A%29%7D%7B%281%2BSec%20A%29%2A%281-Sec%20A%29%7D%5C%5C%5C%5C%3D%5Cfrac%7B%281%2BSec%20A%29%7D%7B1-Sec%5E%7B2%7D%20A%7D%2B%5Cfrac%7B%281-Sec%20A%29%7D%7B1-Sec%5E%7B2%7D%20A%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%2BSec%20A%2B1-Sec%20A%7D%7B%281-Sec%5E%7B2%7D%20A%29%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B2%7D%7B%281-Sec%5E%7B2%7D%20A%29%7D%5C%5C%5C%5C%3D%5Cfrac%7B2%7D%7B-%28Sec%5E%7B2%7D%20A%20-%201%29%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B-2%7D%7BTan%5E%7B2%7D%20A%7D%5C%5C%5C%5C%3D%20-2Cot%5E%7B2%7D%20A)
<span>V(o) = 1/3 πr²h - old volume
</span>V(n) = 1/3 π(2r)²(h/2)=1/3 π(2r)²(h/2)=1/3*4/2* πr²h=1/3*2* πr²h
V(n)/V(o)=1/3*2* πr²h/1/3 πr²h=2/1
V(n)/V(o)=2/1 - ratio
the volume will be doubled
10 students averaged 80, so the sum of their scores was (10 x 80) = 800
20 students averaged 89, so the sum of their scores was (20 x 89) = 1,780
All together, the sum of all 30 scores was (800 + 1,780) = 2,580
30 students totaled 2,580, so their average was (2,580 / 30) = <em> 86</em> .
Answer:
%82.5
Step-by-step explanation:
- The final exam of a particular class makes up 40% of the final grade
- Moe is failing the class with an average (arithmetic mean) of 45% just before taking the final exam.
From point 1 we know that Moe´s grade just before taking the final exam represents 60% of the final grade. Then, using the information in the point 2 we can compute Moe´s final grade as follows:
,
where FG is Moe´s Final Grade and FE is Moe´s final exam grade. Then,
.
So, in order to receive the passing grade average of 60% for the class Moe needs to obtain in his exam:
![FE=\frac{ 0.60-0.60*0.45}{0.40}=0.825](https://tex.z-dn.net/?f=FE%3D%5Cfrac%7B%200.60-0.60%2A0.45%7D%7B0.40%7D%3D0.825)
That is, he need al least %82.5 to obtain a passing grade.
Answer:
D
Step-by-step explanation: