Does anyone know how to solve this question? i have been stuck on it for a while and i can't figure it out. could someone explain,

The general formula for sine wave is given as:

y = A sin (w x) + B

where,

y = height of the ladybug

A = is the amplitude of the wave or the highest peak

w = the angular frequency = 2 π f

x = seconds after landing

B = y intercept of the function

A. The A in the function refers to how high and how low the wheels turn. So it has a maximum value of 7 in the top and also 7 in the bottom. The negative sign simply means that the wheel starts going down first rather than going up (classic sine is the reverse). Therefore the diameter of the wheel is:

diameter = maximum top + maximum bottom

diameter = 7 + 7 = 14 cm

B. From the equation,

w = 2 π f = 0.4 π

Calculating for frequency f,

f = 0.2 rev / s

The period p it takes to make one revolution is the reciprocal of f:

p = 1 / 0.2

p = 5 seconds

C. From B, it takes 5 seconds to complete 1 revolution and in 1 revolution there is 360°. Therefore:

degrees in 1 seconds = 360° / 5 seconds = 72° / 1 second

Hence, the ladybug turns 72° in 1 second.

D. The value of B gives the initial height of the ladybug. Therefore the minimum and maximum heights is:

h = B ± diameter

h = 11 ± 7

h = 4, 18

Hence the min height is 4 cm and max height is 18 cm above the ground.

E. Simply plug in x = 3

y = -7 sin(0.4π*3) + 11

y = -0.46 + 11

y = 10.54 cm above the ground

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

i hope this is what you were looking for.

see attached graph