Linear Functions, Determining Slope

Eva8 [605]

tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)

• rewrite tan = sin/cos

… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))

• expand the functions of 2A using the double angle identities

… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))

• factor out sin(A) cos(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))

• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))

• rearrange terms in the product

… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)

… = 4 sin(A) cos(A) / (2 - 1/cos²(A))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(A) cos(A) / (2 - sec²(A))

• divide through again by cos²(A)

… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(A) / (2 sec²(A) - sec⁴(A))

• factor out sec²(A) in the denominator

… = 4 tan(A) / (sec²(A) (2 - sec²(A)))

• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)

… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))

• simplify

… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))

• condense the denominator as the difference of squares

… = 4 tan(A) / (1 - tan⁴(A))

(Note that some of these steps are optional or can be done simultaneously)

7 0

3 years ago

Suppose (1,19) is on the graph of y = f (x). Which of the following points lies on the graph of the transformed function y = f(1

o-na [289]

Answer:

(5,19) lies on the graph of the transformed function y = f(1/5x)

Step-by-step explanation:

Suppose (1,19) is on the graph of y = f (x)

the graph of the transformed function y = f(1/5x)

$y=f(\frac{1}{5}x)$

1/5 is multiplied with x in f(x)

1/5 is less than 1 so there will be a horizontal stretch in the graph by the factor of 1/5

To make horizontal stretch we change the point

f(x)=f(bx) then (x,y) --->( x/b,y)

We divide the x coordinate by the fraction 1/5

(1,19) ----> $(\frac{1}{\frac{1}{5}} , 19)= (5,19)$

So (5,19) lies on the graph of the transformed function y = f(1/5x)

8 0

3 years ago

Lisa wrote the following statement: "You can only draw one unique isosceles triangle that contains an angle of 65°." Which state

JulijaS [17]

Triangles always equal 180 degrees

4 0

3 years ago

In Ellen's math class, there were 2 boys to every 3 girls. Which of the following could be the ratio of girls to boys in the cla

FinnZ [79.3K]

Answer:

A . 17/21

B . 14/21

C . 7/14

D. 11/17

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The punch bowl at felicia's party is getting low so she adds 12 cups of punch to the bowl two guests serve themselves 1.25 cups

Eduardwww [97]

2.75 cups were in the punch bowl before felicia refilled it .

Step-by-step explanation:

Here we have , the punch bowl at felicia's party is getting low so she adds 12 cups of punch to the bowl two guests serve themselves 1.25 cups and 2 cups and 2 cups of punch the punch bowl now contains 11.5 cups of punch . We need to find how many cups were in the punch bowl before felicia refilled it let n=number of cups bowl before felicia refilled it. Let's find out:

Initially we have , n number of cups of punch ! Than 12 additional cups were added , given below is the equation framed for the number of cups present:

⇒ $n+12$