Simplify the expression by using a double-angle formula or a half-angle formula. 7cos^2(theta/9)-7sin^2(theta/9)
sin(theta/6)cos(theta/6)

Answers

Answer 1

Answer: Double-angle formulas:
2sinФcosФ=sin(2Ф) /:2
sinФcosФ=1/2*sin(2Ф)

sin(Ф/6)cos(Ф/6)=1/2*sin(2*Ф/6)=1/2*sin(Ф/3)

cos²Ф-sin²Ф=cos(2Ф)/*7
7cos²Ф-7sin²Ф=7cos(2Ф)

7cos²(Ф/9)-7sin²(Ф/9)=7cos(2*Ф/9)=7cos(2Ф/9)

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Prove the identity
cos(A+B+C)=cosAcosBcosC-cosAsinBsinC-sinAcosBcosC-sinAsinBcosC

Answers

Hello !

cos (a+b) = cos a cos b - sin a sin b
sin (a+b) = sin a cos b + sin b cos a

cos (a+b+c) = cos (a+(b+c))
cos (a+b+c) = cos a cos (b+c) - sin a sin (b+c)
cos (a+b+c) = cos a (cos b cos c - sin b sin c) - sin a (sin b cos c + sin c cos b)
cos (a+b+c)=cos a cos b cos c - cos a sin b sin c - sin a sin b cos c - sin a cos b sin c

HELPPP ASAPPP! PLZWhich system has no solution?
A.4y = 2x – 6

B.3x + 5y = 7
4x = 2y – 5

C.2y = 4x + 2

D.2x = 5y + 4
15y = 6x – 12

Answers

Answer : D

2x=5y+4

15y=6x-12

Solve 2x=5y+4 for x

Divide both sides by 2

2x/2=(5y+4)/2

x = 5/2 y +2

Substitute 5/2 y +2 for x in 15y=6x-12

15y= 6x-12

15y= 6(5/2 y +2 ) -12

Simplify both sides of the equation

15y=15y

Add -15y to both sides

15y-15y= 15y-15y

0=0

Hey Lily , I hope this help and if you have question(s) please let me know . Thanks

Ink rode his bike at a steady rate of 15 miles per hour for 2 1/2 hours. what distance did he travel?

Answers

Answer:

37.5 miles

Step-by-step explanation:

At a skills competition, a target is being lifted into the air by a cable at a constant speed. An archer standing on the ground launches an arrow toward the target. The system of equations below models the height, in feet, of the target and the arrow t seconds after it was fired. Which statement most likely describes the situation modeled by this system?h=8+2t
h=4+32t-16t^2

1The arrow is fired with an initial upward velocity of 2 ft/s.
2The arrow is fired with an initial upward velocity of 4 ft/s.
3The arrow is fired with an initial upward velocity of 8 ft/s.
4 The arrow is fired with an initial upward velocity of 32 ft/s.

Answers

By definition, the equation of movement in its generic form is given by:

$h(t) = -(1)/(2)gt^2 + v0t + h0$

Where,

g: acceleration due to gravity

v0: initial speed

h0: initial height

The equation for the arrow is given by:

$h = 4 + 32t-16t ^ 2$

Then, according to the definition, the initial velocity of the arrow is:

$v0 = 32$

Answer:

4 The arrow is fired with an initial upward velocity of 32 ft / s.

From the kinematic equations, s(t) = s_in + (v_in)(t) – (1/2)(g)(t^2). This means that there is an initial distance of 4, initial velocity of 32 and acceleration (in opposite direction of the motion) of 32. Option 4 shows the correct answer.

An inlet pipe on a swimming pool can be used to fill the pool in 40 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 14 filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool? Round your answer to two decimal places, if needed.

Answers

Answer:

It would take 90 hours to fill the pool.

Step-by-step explanation:

There is a mistake in the question so it is corrected below:

An inlet pipe on a swimming pool can be used to fill the pool in 40 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 1/4 filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool?

Now, to find the hours would it take to fill the 1/4 pool.

Let the hours it take to fill the $(1)/(4)$ pool be $h.$