In solving these problems, you have to work on the complicated side first. But in this case both of them are complicated so we will solve them together.
(Numerator) We can add sinxcosx+cosxsinx since they are same terms..
(Denominator)
cosx · cosx= cos²x
sinx · sinx= sin²x
So it will equal to 1+cos²x-sin²x
We could recognize that
1-sin²x=cos²x
Right side:
We can already change cotx=cosx/sinx
The equation is divided by 1/sin²x, we can take the reciprocal of it and multiply it to the equation.
6.
Left side:
2 is reduced and cos as well. We’ll
get sinx/cosx
Right side:
so the equation is reduced to
sinx/cosx
Eventhough they are already the
same we can still reduce it…
7.
Sinx/cosx = tanx
Thanks for your help..hehe..
8.
Problem no. 2 Permutations
9.
I’m J.r. Manleigh and I am the manager of the new band called “Private”. I have here the list of the possible provinces that we can have the concert. Pangasinan Bataan Bukidnon Leyte Batangas Sulu Romblon La Union Surigao Del Norte Bohol Cavite Surigao Del Sur Cebu Laguna Mindanao(green) Visayas(yellow) Luzon(red)
10.
11.
If the band plays 6 provinces in total, how many different concert schedules can be created if there is no restrictions in which they play?
Order is important thing in a touring schedule, so use permutations.
Out of 12 possible provinces, the band wants to create a schedule with
only 6.
Pick Formula :
n P r = n !
( n - r )!
nPr is read as “n Pick r”
where n is the number of objects to pick from
r is the no. of objects to be arranged
12.
n P r = n !
( n - r )!
14 P 6 = 14 !
( 14 - 6 )!
14 !
8!
= 2,162,160
or using your calculator…
14 P 6 = 2,162,160 different concert schedules
13.
If the band the band must play all provinces in Luzon, 3 in Visayas and 2 in Mindanao how many different schedules can be created?
The 6 provinces in Luzon can be ordered in 6 P 6 ways.
The 3 provinces in Visayas can be ordered in 3 P 4 ways.
The 2 provinces in Mindanao can be ordered in 2 P 4 ways.
6P 6 · 4P 3 · 4P 2 = 207,360 different schedules
14.
If the band decides not to go to Bataan and Sulu (because many rumors about those provinces that they are anti-Private people). How many different schedules can be created if the band plays all provinces in Luzon and Mindanao , and only 3 for Visayas ?
We can already ignore Bataan and Sulu from the selection pool.
The first 5 cities in Luzon can now be ordered in 5P5 ways.
The 3 cities in Visayas can be ordered in 4P3 ways.
The 3 cities in Mindanao can be ordered in 3P3 ways.
So…
5P5 · 4P3 · 3P3 = 17280 ways that the concert schedule can be created
15.
Problem no. 3
Logarithms
16.
Rio really likes the model of Honda Civic 2007 which will cost you a brand new one $24, 950 but cannot afford to buy it now. She’s planning to save up some money first then buy it. After 3 years, she will have enough money to buy a used car Honda Civic 2007. But she has 3 dealers to choose from if she wants to get a low priced car.
Andrei who offers a Civic that depreciates 0.02% daily for 3 years.
Danny who offers a Civic that depreciates 0.5% monthly for 3 years.
Ronnie who offers a Civic that depreciates for 0.15% weekly for 3 years.
Who will be the best to go to if she wants the cheapest one?
17.
Andrei who offers a Civic that depreciates 0.02% daily for 3 years.
A o = 24, 950
model = 0.02% -> 0.0002 (percent to decimal)
t = 365 x 3(because 365 days in a year and it is for 3 years)
A = ?
p = 1
A = 20, 042.4379
or
$20, 042.44
18.
Danny who offers a Civic that depreciates 0.5% monthly for 3 years.
A o = 24, 950
model = 0.5% -> 0.005 (percent to decimal)
t = 12 x 3 (because 12 months in one year and it is for 3 years)
A = ?
p = 1
A = 20, 830.5845
or
$20, 830.58
19.
Ronnie who offers a Civic that depreciates for 0.15% weekly for 3
years.
A o = 24, 950
model = 0.15% -> 0.0015 (percent to decimal)
t = 52 x 3 (because 52 weeks in one year and it is for 3 years)
A = ?
p = 1
A = 19, 741.0090
or
$19, 741.01
20.
We all know that Ronnie is the cheapest one
So Riolyn will choose him.
21.
Problem no. 4 Conics
22.
What you see above is a tunnel in Winnipeg that has a length of 162 m and a height of 56 m.
23.
If the arch is modeled as an ellipse with the standard form:
(x - h)² + (y - k)² = 1
a² b²
Determine the equation:
First, is to use the measures that was given to you.