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
Need help not sure if my question is true or false
Alika [10]
The answer is false. The radius is half the diameter, not 2 times it.
7 0
3 years ago
Henrietta interviewed her classmates on their favorite subjects. She recorded their gender and favorite subject. She concluded t
Tamiku [17]
<span>no, the relative frequency of males who like math is different from the relative frequency of females who like science.</span>
4 0
3 years ago
Read 2 more answers
1. What is the domain of the function graphed below?
Nimfa-mama [501]

Answer:

D. 0<x<5

Step-by-step explanation:

3 0
3 years ago
Which doubles fact helps you solve 8+7=15? Write the number sentence.
12345 [234]
8 + 8 = 16
16 - 1 = 15

or

7 + 7 = 14
14+1 = 15
7 0
3 years ago
Read 2 more answers
It says factor each expression 49x-28?
NARA [144]

Answer:

7(7x -4)

Step-by-step explanation:

49x-28

We can factor a 7 from each term

49x = 7*7x

28 = 7*4

7(7x -4)

3 0
3 years ago
Other questions:
  • At what altitude did the balloon remain the longest? how long was that ?
    15·1 answer
  • In the morning, the temperature was -8°F. By noon, the temperature had risen 15°F. What was the temperature at noon?
    10·2 answers
  • What is the solution to the system of equations?
    7·1 answer
  • The water level of a lake fell by 1 1/4 in. during a 1 1/2 week long drought what is the average rate at which the water level c
    13·1 answer
  • caroline and sarah win some money and share it in the ratio of 6:1 caroline gets £70 more than her how much did they get altoget
    10·1 answer
  • What is the measure of each exterior angle of a pentagon
    10·1 answer
  • A flare was launched straight up from the ground with an initial velocity of 176 ft/s and returned to the ground after 11 s. The
    8·2 answers
  • Write the equation of a line in slope-intercept form with a slope of 2 and
    7·1 answer
  • What is 30 inch 30 inch 15 inch 30 60 inch for me this is hard..
    9·1 answer
  • Least common factor 12, 11​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!