1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AlladinOne [14]
3 years ago
9

Kaliska is jumping rope. The vertical height of the center of her rope off the ground R(t) (in cm) as a function of time t (in s

econds) can be modeled by a sinusoidal expression of the form a cos(b. t) + d. , At t = 0, when she starts jumping, her rope is 0 cm off the ground, which is the minimum. After \frac{\pi }{12} seconds it reaches a height of 60 cm from the ground, which is half of its maximum height. Find R(t). t should be in radians.
Mathematics
1 answer:
xz_007 [3.2K]3 years ago
7 0

Answer:

R (t) = 60 - 60 cos (6t)

Step-by-step explanation:

Given that:

R(t) = acos (bt) + d

at t= 0

R(0) = 0

0 = acos (0) + d

a + d = 0 ----- (1)

After \dfrac{\pi}{12} seconds it reaches a height of 60 cm from the ground.

i.e

R ( \dfrac{\pi}{12}) = 60

60 = acos (\dfrac{b \pi}{12}) +d --- (2)

Recall from the question that:

At t = 0, R(0) = 0 which is the minimum

as such it is only  when a is  negative can acos (bt ) + d can get to minimum at t= 0

Similarly; 60 × 2 = maximum

R'(t) = -ab sin (bt) =0

bt = k π

here;

k  is the integer

making t the subject of the formula, we have:

t = \dfrac{k \pi}{b}

replacing the derived equation of k into R(t) = acos (bt) + d

R (\dfrac{k \pi}{b}) = d+a cos (k \pi) = \left \{ {{a+d  \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.

Since we known a < 0 (negative)

then d-a will be maximum

d-a = 60  × 2

d-a = 120 ----- (3)

Relating to equation (1) and (3)

a = -60 and d = 60

∴ R(t) = 60 - 60 cos (bt)

Similarly;

For R ( \dfrac{\pi}{12})

R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60

where ;

cos (\dfrac{\pi b}{12}) =0

Then b = 6

∴

R (t) = 60 - 60 cos (6t)

You might be interested in
Rays QR and QS are tangents to circle P at R and S. If Q measures to 54°, find RS
Ainat [17]

Answer: 126^{\circ}

Step-by-step explanation:

If we draw RP and PS, then in the quadrilateral formed, we know that \angle PRQ=\angle PSQ=90^{\circ}, and since angles in a quadrilateral add to 360 degrees, this means \angle SPR=126^{\circ}.

Thus, arc RS also measures 126 degrees

8 0
2 years ago
1.When two variables are proportional which of the following is constant?
grin007 [14]

Answer:

Their Ratio

Step-by-step explanation:

You switched the numbers 2 and 3 btw

5 0
3 years ago
Helen used 1/4 of her savings for her first year of college. 3/8 of that money was spent on her housing and meals. Which equatio
iren [92.7K]
3/32
just multiply the fractions
8 0
3 years ago
Read 2 more answers
What is 20% of 120 ??? HELP ME
maksim [4K]

Answer:

24

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Happy book lovers day
Temka [501]

Answer:

thank you

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • PLEASE I NEED HELP FAST!!!!
    12·2 answers
  • Partial products 42x5
    9·2 answers
  • What is the Prime factorization of 104? Explain.
    11·2 answers
  • Please answer this IS MY TEST PLEASE ANSWER PLEASE dont give UP-_-
    7·1 answer
  • im not really smart i need help bad, i will give you all of my points and brainliest. it would mean alot if you help
    9·1 answer
  • Mariah purchases three hair barrettes by using a gift card, which starts with a balance of $35.79. Which expression models her p
    8·2 answers
  • What’s the slope of these two lines if right u hey brainlist
    12·1 answer
  • If I'm putting £100 a month into a fund that has 13.03% annual interest annually for 48 years, what's the the total?
    13·1 answer
  • Number of spots
    5·1 answer
  • The cargo of the truck weighs at most 2,900 pounds. Use w to represent the weight (in pounds) of the cargo.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!