ANSWER:
Let t = logtan[x/2]
⇒dt = 1/ tan[x/2] * sec² x/2 × ½ dx
⇒dt = 1/2 cos² x/2 × cot x/2dx
⇒dt = 1/2 * 1/ cos² x/2 × cosx/2 / sin x/2 dx
⇒dt = 1/2 cosx/2 / sin x/2 dx
⇒dt = 1/sinxdx
⇒dt = cosecxdx
Putting it in the integration we get,
∫cosecx / log tan(x/2)dx
= ∫dt/t
= log∣t∣+c
= log∣logtan x/2∣+c where t = logtan x/2
There are 60 players on football team that are not seniors.
Step-by-step explanation:
<u>Method 1:</u>
Given
Total students = 84
Also given that
2 out of 7 are seniors
Which is 2/7
So in order to find the total number of seniors we will multiply the whole number of students to 2/7
So there are 24 seniors on the football team.
Players that are not seniors = 84 - 24 = 60
There are 60 players who are not seniors.
<u>Method 2:</u>
We can divide the total number by 7, to get how many sets of 7 players will be there
= 84/7 = 12
Now,
Multiplying 12 with 2 will give us the number of seniors in football team.
12*2 = 24 seniors
So,
Not seniors =84-24 = 60
Keywords: Percentage, Units
Learn more about percentage at:
#LearnwithBrainly
Answer: Lesser = 19, Greater = 21
See picture reply.
Answers:
- <u>24000 dollars</u> invested at 4%
- <u>18000 dollars</u> was invested at 7%
======================================================
Work Shown:
x = amount invested at 4%
If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%
She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account
This means we have
0.04x+0.07(42000-x)
0.04x+0.07*42000-0.07x
0.04x+2940-0.07x
-0.03x+2940
This represents the total amount of money earned after 1 year.
We're told the amount earned in interest is $2220, so we can say,
-0.03x+2940 = 2220
-0.03x = 2220-2940
-0.03x = -720
x = -720/(-0.03)
x = 24000 dollars is the amount invested at 4%
42000-x = 42000-24000 = 18000 dollars was invested at 7%
----------------------
As a check, we can see that
18000+24000 = 42000
and also
0.04x = 0.04*24000 = 960 earned from the first account
0.07*18000 = 1260 earned from the second account
1260+960 = 2220 is the total interest earned from both accounts combined
This confirms our answers.
Answer:
$855,000
Step-by-step explanation:
$855,000 it's alot of money.
I helped you a lot... I'm sure you will pass
