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
Svetradugi [14.3K]
3 years ago
15

The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretc

hed and then released.
a. Solve the equation for t.

b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.

c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.
Mathematics
1 answer:
Nady [450]3 years ago
5 0
This is the missing equation that models the hieght and is misssing in the question:

<span>h= 7cos(π/3 t)
</span>

Answers:

<span>a. Solve the equation for t.
</span>

<span>1) Start: h= 7cos(π/3 t)
</span>

2) Divide by 7: (h/7) = <span>cos(π/3 t)
</span>

3) Inverse function: arc cos (h/7) = π/3 t

4) t = 3 arccos(h/7) / π ← answer of part (a)



b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.

<span>1) h = 1 cm ⇒ t = 3 arccos(1/7) / π</span>

t = 1.36 s← answer


2) h = 3 cm ⇒ t = 3arccos (3/7) / π =  1.08s← answer


3) h = 5 cm ⇒ 3arccos (5/7) / π = 0.74 s← answer



c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time.

Use the periodicity property of the function.

The periodicity of <span>cos(π/3 t) is 6.
</span><span>
</span><span>
</span><span>So, the second times are:
</span><span>
</span><span>
</span><span>1) h = 1 cm, t = 6 + 0.45 s = 6.45 s ← answer
</span>

2) h = 3 cm ⇒ 6 + 1.08 s = 7.08 s← answer


3) h = 5 cm ⇒ t = 6 + 0.74 s = 6.74 s ← answer



You might be interested in
Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy
kari74 [83]

Answer:

Notebook is $4

Thumb drive is $23

Step-by-step explanation:

Let notebooks be x and thumb drives be y

6x+7y=$185

14x+12y=$332

These two are simultaneous equation. Multiplying the first equation by 7 and second by 3 we obtain

42x+49y=$1295

42x+36y=$996

Subtracting the third equation from the fourth

996-1295=-$299

(36-49)y=-23y

-23y=-$299

y=$299/13=$23

To get the value of x, we substitute the value of y into the first equation

6x+(7*23)=$185

6x=$185-$161

6x=$24

x=$4

Therefore, price of notebook is $4, price of thumb drive is $23

4 0
3 years ago
You bought a large container of fruit punch. The label on the container says there are
erastovalidia [21]
There are 8 fl ounces in 1 cup.
Divide 128 by 8.
16 cups
6 0
3 years ago
Read 2 more answers
Can someone make sure that I’m right
WARRIOR [948]

Answer:

A

Step-by-step explanation: You are correct!

5 0
3 years ago
Read 2 more answers
What is 6 to the fourth power times 6 to the fourth power
wel

Answer:

6^8

Step-by-step explanation:

6^4 * 6^4

We know that a^b * a^c = a^(b+c)

6^4 * 6^4 = 6^(4+4) = 6^8

7 0
3 years ago
Read 2 more answers
the current temperature in small town - 20 degrees Fahrenheit this is 6 degrees less than twice the temperature that was six hou
Vlad [161]
For problems like this we can use algebra to help us, the farenheight 6 hours ago was:
 (2xt)-6=-20
We have to balance the sides out, first we minus 6
2xt=-26
Now we can divide by 2
t=-13

We now know the temperature 6 hours ago was -13
6 0
3 years ago
Other questions:
  • What is the heroes formula?
    9·1 answer
  • 4x-7&gt;17<br>solve inequality
    5·1 answer
  • Expand the following using either the Binomial Theorem You must show
    9·1 answer
  • Help me out here fast please
    13·2 answers
  • Find the product. y ^4 · y ^3
    10·1 answer
  • In order to answer the following question, please use the following image down below:
    14·1 answer
  • The mass of a tiger at a zoo is 135 kilograms. Randy's cat has a mass of 5,000 grams. How many times greater is the mass of the
    6·2 answers
  • Please someone help it’s for a test that is due sooooonnn
    8·2 answers
  • Find the value of W please help due tomorrow
    14·1 answer
  • [Number Theory, 3 Points]
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!