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
One meter is approximately equal to 39.39 inches. About how many inches are in 3 meters
mojhsa [17]
Well if 1 is 39.39 
39.39 times 3 is equal to 118.17 

don't forget to get my answer 5 satrs and thank me- Justin
8 0
3 years ago
Read 2 more answers
What is the median of the data? 68,69,71,71,71,73,74,75,75,78 answers: 71,72,78,72.5
Klio2033 [76]
The answer is 72 because ur supposed to do (71+73)/2
5 0
3 years ago
Read 2 more answers
Can someone please help and explain ​
Nuetrik [128]

Answer:

2

Step-by-step explanation:

that is the least common denominator

3 0
3 years ago
Read 2 more answers
FACTOR !!!<br><br> a) 5x^2+25 <br><br> b) 2x^2-3x-2
Mademuasel [1]

Step-by-step explanation:

(a): 5x^2 + 25 = 5 * x^2 + 5 * 5 = 5(x^2 + 5).

(b): 2x^2 - 3x - 2 = 2x^2 - 4x + x - 2

= 2x(x - 2) + 1(x - 2) = (2x + 1)(x - 2).

3 0
3 years ago
1) After a dilation, (-60, 15) is the image of (-12, 3). What are the coordinates of the image of (-2,-7) after the same dilatio
BARSIC [14]

Answer:

a) k = 5; (-10, -35)

Step-by-step explanation:

Given:

Co-ordinates:

Pre-Image = (-12,3)

After dilation

Image = (-60,15)

The dilation about the origin can be given as :

Pre-Image(x,y)\rightarrow Image(kx,ky)

where k represents the scalar factor.

We can find value of k for the given co-ordinates by finding the ratio of x or y co-ordinates of the image and pre-image.

k=\frac{Image}{Pre-Image}

For the given co-ordinates.

Pre-Image = (-12,3)

Image = (-60,15)

The value of k=\frac{-60}{-12}=5

or k=\frac{15}{3}=5

As we get k=5 for both ratios i.e of x and  y co-ordinates, so we can say the image has been dilated by a factor of 5 about the origin.

To find the image of (-2,-7), after same dilation, we will multiply the co-ordinates with the scalar factor.

Pre-Image(-2,-7)\rightarrow Image((-2\times5),(-7\times 5))

Pre-Image(-2,-7)\rightarrow Image(-10,-35) (Answer)

7 0
3 years ago
Other questions:
  • A handler loads one item every 10 ?minutes, so 48 items are completed in his first day of work. his manager checks his work by r
    5·1 answer
  • Find the length of DE using the distance formula.
    10·2 answers
  • Beakers X and Y contain some water. If 50 ml of water is transferred from Beaker X
    8·1 answer
  • What is the answer now in two minutes
    6·1 answer
  • 1. Suppose you invest $500 at 10% interest, compounded annually. After 5 years, how much money would you have in your account? R
    13·1 answer
  • Triangles A and B are right-angled.
    15·2 answers
  • In the past month, Ann rented 1 video game and 6 DVDs. The rental price for the video game was $2.70 . The rental price for each
    14·1 answer
  • A triangle has a base of 4 units and a height of 3 units. Mark draws the triangle again but
    11·2 answers
  • Compare the two integers: -10 and -3
    14·2 answers
  • Determine the regression equation for the data. Round the final values to three significant digits, if necessary.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!