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
IrinaVladis [17]
3 years ago
13

Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the inter

val 0<_t<_0.5. Solve algebraically, and show your work and final answer in the response box. Hint: Use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. Graph the equation and explain how it confirms your solution(s).

Mathematics
1 answer:
hoa [83]3 years ago
5 0

Answer:

0.20 and 0.36

Step-by-step explanation:

y(t) = 2 sin (4π t) + 5 cos (4π t)

We wish to convert this to:

y = A sin(ωt + φ)

We know that ω = 4π.  We also know the following:

5 = A sin φ

2 = A cos φ

Divide the first equation by the second equation:

5/2 = tan φ

φ = tan⁻¹(5/2)

Now, square the two equations and add them together.

5² + 2² = (A sin φ)² + (A cos φ)²

29 = A²

A = √29

The equation of the wave is therefore:

y = √29 sin(4π t + tan⁻¹(5/2))

The maximum negative position is -√29.  And half of that is -½√29.

-½√29 = √29 sin(4π t + tan⁻¹(5/2))

-½ = sin(4π t + tan⁻¹(5/2))

7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)

7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π

t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24

Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.

t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24

t ≈ 0.20 or 0.36

You might be interested in
Help plzzzzzzzzzzzzzzzz
agasfer [191]

Answer:

One pound of raw chicken will serve approximately four people. or 12 ounces

so A

Step-by-step explanation:

5 0
2 years ago
Thomas paid $50 for a box of multicolor file folder for his office there were 100 folders in the box what was the cost of each f
Yuliya22 [10]
For the answer to the question above asking what was the cost of each file folder if Thomas paid $50 for a box of the multicolor file folder for his office, there were 100 folders in the box?
this is a grade 2 problem. If you know how to divide you will get the answer.
Just d<span>ivide $50 by 100. Then you'll get the answer. </span>

4 0
3 years ago
A box turtle hibernates in a sand at -1 5/8 feet. A spotted turtle hibernates at -1 16/25 feet. Which turtle is deeper?
g100num [7]
The turtle that hibernates deeper is the box turtle.
4 0
3 years ago
Read 2 more answers
Please HELP!!!!
dedylja [7]
Absolute value equations have more than one solution because when the answer is in abs. value, it is positive, so there could be a negative answer and it would still be positive. For example |-5|=5 and |5|=5 as well. 
4+|2x|=-1 would have no solution because you cannot have the equation equal a negative since the 2x is in absolute value. 
8 0
3 years ago
Why is the number 6 scared of the number 7?
Lady_Fox [76]
This is a well known joke:

Why six afraid of seven? Because seven ate nine!

It is supposed to be a "word game" where instead of writing eight, the authour wrote ate, which sound the same but means something different.


Hope it helped,

Happy homework/ study/ exam!
8 0
3 years ago
Read 2 more answers
Other questions:
  • Find two numbers, if their sum is 97 and their difference is 7.
    12·1 answer
  • Find the lowest common denominator of 3/x^3y and 7/xy^4
    14·2 answers
  • 3. A recipe calls for 1 1/2 cups of flour, 3/4 a cup of white sugar, and 1/8 a cup of brown sugar. (a) How many total cups of in
    15·1 answer
  • Which fraction us equal to 2/3 : 4/7 8/12 6/9
    7·1 answer
  • Which development would most likely cause the supply of a product to decrease?
    6·2 answers
  • I'm working with varibles on both sides. This is math, also algebra 1. The expression is... 8-4a=16-8a I'm so confused on which
    11·2 answers
  • 0.88 the value of 0.8 is
    5·1 answer
  • Write an equivalent fraction for 2/8. (Remember to find an equivalent fraction you need to either multiply or divide you numerat
    6·1 answer
  • Help please for 40 points!! This is due tonight and i don’t know how to do it
    13·1 answer
  • (16) In 2008, the number tourists visiting France was 7.94 x 1017. The
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!