Randall is 15 years younger than Wendy. 8 years ago, Wendy's age was 2 times Randall's age. How old is Randall now?

Prove that sin3a-cos3a/sina+cosa=2sin2a-1

Sloan [31]

Answer:

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

Step-by-step explanation:

we are given

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

we can simplify left side and make it equal to right side

we can use trig identity

$sin(3a)=3sin(a)-4sin^3(a)$

$cos(3a)=4cos^3(a)-3cos(a)$

now, we can plug values

$\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)}$

now, we can simplify

$\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)}$

$\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)}$

$\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}$

now, we can factor it

$\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}$

$\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can use trig identity

$sin^2(a)+cos^2(a)=1$

$\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can cancel terms

$=3-4(1-sin(a)cos(a))$

now, we can simplify it further

$=3-4+4sin(a)cos(a))$

$=-1+4sin(a)cos(a))$

$=4sin(a)cos(a)-1$

$=2\times 2sin(a)cos(a)-1$

now, we can use trig identity

$2sin(a)cos(a)=sin(2a)$

we can replace it

$=2sin(2a)-1$

so,

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

7 0

3 years ago

Read 2 more answers

B) (x + 4) 1999 = 1<br> Find x

gulaghasi [49]

Answer:

Step-by-step explanation:

(X+4)1999=1

Open the bracket by multiplying 1999 by the values in the bracket

1999x + 7996 = 1

Collect like terms

1999x = 1-7996

1999x = -7995

Divide both sides by 1999

X = -3.99

8 0

3 years ago

Itzik 45 seconds to fill an 18 down container how long will it take to fill a 40 gallon container

Akimi4 [234]

When answering this question, I'm assuming "18 down" means 18 gallons
To find the answer, we can divide:
40/18 = 5
( This basically means that there are 5 containers in the 40 gallon container)
knowing this:
45*5 = 225
(Basically solves the time to fill 5 containers)
It will take 225 seconds

4 0

3 years ago

Read 2 more answers

a science quiz has eight multiple choice questions with five choices for each. Find the total number of ways to answer the quest

almond37 [142]

Answer:

390625

Step-by-step explanation:

The questions are all independent -- the answer on one question does not limit the number of possible answers on another question.

The quiz has 5 choices for each question, so there are

$5\times5\times5\times5\times5\times5\times5\times5$ ways to answer the quiz questions.

Notice that this could be written $5^8$ . You could say that the number of ways to answer the questions is

$number \, of \, choices^{number \, of \, questions}$

Use a calculator to find $5^8$

8 0

3 years ago

Question 8 -

FinnZ [79.3K]

Answer:

Her wage on the 8th day is $105 ⇒ answer d

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- The average of set of data = The sum of data/the number of data

- The sum of data = the average of set of data × the number of data

∵ Cindy worked for 15 consecutive days

∵ She is earning an average wage of $91 per day

∴ Her total earning = 91 × 15 = $1365

∵ Her average earning during the first 7 days is $87 per day

∴ Her total earning in the first 7 days = 87 × 7 = $609

∵ Her average earning during the last 7 days is $93 per day

∴ Her total earning in the last 7 days = 93 × 7 = $651

- Her total earning in the 14 days is the sum of the earning in the

first 7 days and the earning during the last 7 days

∵ Her total earning in the 14 days = 609 + 651 = $1260

∵ Her total earning in the 15 days is $1365

- To find her wage on the 8th day subtract her wage of the 14 days

from her wage of the 15 days

∴ Her wage on the 8th day = 1365 - 1260 = $105

* Her wage on the 8th day is $105

7 0

3 years ago