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
Hatshy [7]
3 years ago
14

A particle moves along a straight line. The distance of the particle from the origin at time t is modeled by the equation below.

​s(t)equals2 sine t plus 3 cosine t Find a value of t between 0 and StartFraction pi Over 2 EndFraction that satisfies the equation ​s(t)equalsStartFraction 2 plus 3 StartRoot 3 EndRoot Over 2 EndFraction .
Mathematics
1 answer:
laiz [17]3 years ago
4 0

Answer:

The value of t that will satisfy the equation is π/6 (which is 30 degrees)

Step-by-step explanation:

The function that models the movement of the particle is given as;

S(t) = 2 sin(t) + 3 cos (t)

Now we want to the value of t between 0 and pi/2 that satisfies the equation;

s(t) = (2+ 3√3)/2 = 1 + 3√3/2

What we do here is simply find that value of t that would ensure that;

2sin(t) + 3cos(t) = 1 + 3√3/2

Without any need for rigorous calculations, this value of t can be gotten by inspection.

From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2

We can make a substitution for it in this equation.

We obtain the following;

2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2

Do not forget however that we have a range. And the range in question is between 0 and π/2

Kindly that π/2 in degrees is 90 degrees

So our range of values here is between 0 and 90 degrees.

So to follow the notation in the question, the value within the range that will satisfy the equation is π/6

You might be interested in
The price of a technology stock has dropped to $9.71 today. Yesterday's price was $9.80. Find the percentage decrease.
Vadim26 [7]

Answer:

The percentage decrease = 0.9%

Step-by-step explanation:

  • Initial value = $9.80
  • Final value = $9.71

Using the formula

Percentage Decrease = [ (Initial Value - Final Value) / |Initial Value| ] × 100

                                    = [(9.80 - 9.71 ) / (9.80)] × 100

                                    = [0.09 / 9.80] × 100

                                    = 0.009 × 100  

                                    = 0.9%

Therefore, the percentage decrease = 0.9%

4 0
3 years ago
Bishwant and sunayana cimplete a oiece of a work in 6 days working together.if bishwant alime can complete it n 10 days.in how m
alina1380 [7]

Step-by-step explanation:

sunaina's alona work=

1/6-1/10

10-6/60

4/60

1/15

therefore sunaina can alone do the work in 15 days

4 0
3 years ago
A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possib
Semenov [28]
1000/7 = <span>142.857142857

Because this is not an even number we take "142", then times it by 7 teachers.

142*7= 994

1000 - 994 = 6 Pencils left</span>
3 0
3 years ago
Multiplying Binomials<br> pls help
allsm [11]

Answer:

Answer C

Step-by-step explanation:

3 0
3 years ago
please answer the question in the photo below ,will mark brainleat when gives me option to do it! Thanks :)
Juliette [100K]

Answer:

um yes it can  it can if you look at a ruler in try it it would be the same

Step-by-step explanation:

please just say thank you in please rate this

6 0
3 years ago
Read 2 more answers
Other questions:
  • Luke and Leia are selling hot dogs and hamburgers at a minor league baseball game. At the end of the day they determine they hav
    9·1 answer
  • Apply the square root principle to solve (x-5)^2-40=0
    6·1 answer
  • Select the ordered pair that is a solution
    15·1 answer
  • What set of numbers are shaded on the hundred chart.
    13·2 answers
  • Find the sum for these angles
    13·1 answer
  • A tree measured 40 1/2 feet tall. Over the next 7 1/2 years, it grew to a height of 57 feet. During the 7 1/2 years, what was th
    12·1 answer
  • 39. The ratio of new houses to antique houses in a village is 4:5. If there are
    12·1 answer
  • Ethan rolls the number cube and then spins the arrow on the
    11·1 answer
  • I need help on this question and answering it
    6·2 answers
  • What is the answer please<br><br><img src="https://tex.z-dn.net/?f=%5Csqrt%7B4%7D%5Cdiv%202%5Csqrt%7B3%7D" id="TexFormula1" titl
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!