The table shows an indifference schedule for several combinations of X and Y.

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. At time = 1.25 seconds, the gum is at a maximum height above the ground and 1 second later the gum is on the ground again.

a. If the diameter of the wheel is 68 cm, write an equation that models the height of the gum in centimeters above the ground at any time, t, in seconds.

b. What is the height of the gum when Lamaj gets to the end of the block at t = 15.6 seconds?

c. When are the first and second times the gum reaches a height of 12 cm?

Answer:

Step-by-step explanation:

a)

We are being told that:

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. This keeps the wheel of his bike in Simple Harmonic Motion and the Trigonometric equation that models the height of the gum in centimeters above the ground at any time, t, in seconds. can be written as:

$\mathbf {y = 34cos (\pi (t-1.25))+34}$

where;

y = is the height of the gum at a given time (t) seconds

34 = amplitude of the motion

the amplitude of the motion was obtained by finding the middle between the highest and lowest point on the cosine graph.

$\mathbf{ \pi}$ = the period of the graph

1.25 = maximum vertical height stretched by 1.25 m to the horizontal

b) From the equation derived above;

if we replace t with 1.56 seconds ; we can determine the height of the gum when Lamaj gets to the end of the block .

So;

$\mathbf {y = 34cos (\pi (15.6-1.25))+34}$

$\mathbf {y = 34cos (\pi (14.35))+34}$

$\mathbf {y = 34cos (45.08)+34}$

$\mathbf{y = 58.01}$

Thus, the gum is at 58.01 cm from the ground at t = 15.6 seconds.

c)

When are the first and second times the gum reaches a height of 12 cm

This indicates the position of y; so y = 12 cm

From the same equation from (a); we have :

$\mathbf {y = 34 cos(\pi (t-1.25))+34}$

$\mathbf{12 = 34 cos ( \pi(t-1.25))+34}$

$\dfrac {12-34}{34} = cos (\pi(t-1.25))$

$\dfrac {-22}{34} = cos(\pi(t-1.25))$

$2.27 = (\pi (t-1.25)$

t = 2.72 seconds

Similarly, replacing cosine in the above equation with sine; we have:

$\mathbf {y = 34 sin (\pi (t-1.25))+34}$

$\mathbf{12 = 34 sin ( \pi(t-1.25))+34}$

$\dfrac {12-34}{34} = sin (\pi(t-1.25))$

$\dfrac {-22}{34} = sin (\pi(t-1.25))$

$-0.703 = (\pi(t-1.25))$

t = 2.527 seconds

Hence, the gum will reach 12 cm first at 2.527 sec and second time at 2.72 sec.

7 0

3 years ago

You are choosing between two health clubs. Club A offers membership for a fee of $28 plus a monthly fee of $24. Club B offers me

Schach [20]

Answer:

The cost will be the same after 1 month

Step-by-step explanation:

Step 1: set up the equation

club A= 28x+24 club B= 35x+17

club A=club B: 28x+24=35x+17

Step 2: Get rid of the smallest X

28x+24=35x+17

-28 -28

24=7x+17

Step 3: Get rid of the constant next to the variable to isolate the variable

24=7x+17

-17 -17

7=7x

Step 4: Inverse operation to remove variable

7÷7x=7x÷7x

1=1

I hope this helped, im not too good at explaining but im positive the solution is correct.

3 0

3 years ago

I will love you forever if someone can help me with this

g100num [7]

It should be B. right angle and C. complementary angles

8 0

3 years ago