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
jenyasd209 [6]
3 years ago
10

A small radio transmitter broadcasts in a 48 mile radius. if you drive along a straight line from a city 61 miles north of the t

ransmitter to a second city 62 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Physics
1 answer:
schepotkina [342]3 years ago
3 0
<span>40.7 miles.
   For this problem, we want to know the length of the chord created by the line and the circle. So let's first create the equations needed.

   The slope intercept equation for a line is:
 y = ax + b
 the value for a will be the the difference in y divided by the difference in x. We're going from y=61 to y=0 for a chance of -61 and from x=0 to x=62 for a change of 62. So the value of a is
-61/62, giving us the formula
 y = -(61/62)x + b
 Substituting x = 0, we can calculate b
 61 = -(61/62)0 + b
 61 = b
   So the equation for the line is: y = -(61/62)x + 61

   Now for the equation for the circle. Since the circle is centered at the origin, the equation is:
 x^2 + y^2 = 48^2

   Now we to calculate the intersections.
 y = -(61/62)x + 61
 x^2 + y^2 = 48^2
 x^2 + (-(61/62)x + 61)^2 = 48^2
 x^2 + (3721/3844)x^2 - (3721/31)x + 3721 = 2304
 (7565/3844)x^2 - (3721/31)x + 3721 = 2304
 (7565/3844)x^2 - (3721/31)x + 1417 = 0
 1.968002081x^2 - 120.0322581x + 1417 = 0

   And we have a rather ugly quadratic equation which we can solve using the quadratic formula, giving the solutions x = 16.00512574 and x = 44.98681081

   Now we need to calculate the y values for those 2 x values.
 y = -(61/62)x + 61
 y = -(61/62)16.00512574 + 61 y = 45.25302145
   y = -(61/62)x + 61
 y = -(61/62)44.98681081 + 61
 y = 16.73878292

   So the 2 endpoints are (16.00512574, 45.25302145) and (44.98681081, 16.73878292)
   The distance between those points can be calculated using the Pythagorean theorem.
 sqrt((16.00512574 - 44.98681081)^2 + (45.25302145 - 16.73878292)^2) = sqrt(-28.98168506^2 + 28.51423853^2) =
sqrt(839.938069 + 813.0617988) =
sqrt(1652.999868) = 40.65710107

   And finally, we have the solution of 40.7 miles.</span>
You might be interested in
How to solve for time given distance and velocity
Virty [35]

Answer:

Well, I think you're talking about kinematics, especially uniform rectilinear motion. We know that there is a specific equation for that:

S = Vt + S0

With S being the distance, V the velocity, t the time and S0 the initial distance (initial displacement).

From this you can calculate t, if that's what you want.

8 0
2 years ago
A convex mirror has a focal length of -10.8 cm. An object is placed 32.7 cm from the mirror's surface. Determine the image dista
KonstantinChe [14]

Answer:

-353.16

Explanation:

4 0
2 years ago
A merry-go-round of radius 2 m is rotating at one revolution every 5 s. A
galben [10]

Answer:

a) The angular speed of the child is approximately 1.257 rad/s

b) The angular speed of the teenager is approximately 1.257 rad/s

c) The tangential speed of the child is approximately 1.257 m/s

d) For the child, r = 2 m

The tangential speed of the teenager is approximately 2.513 m/s

Explanation:

The revolutions per minute, r.p.m. of the merry-go-round = 1 revolution/(5 s)

The radius of the merry-go-round = 2 m

The location of the child = 1 m from the axis

The location of the teenager = 2 m from the axis

1 revolution = 2·π radians

Therefore, we have;

The angular speed, ω = (Angle turned)/(Time elapsed) = (2·π radians)/(5 s)

∴ The angular speed of the merry-go-round, ω = 2·π/5 radians/second

a) The angular speed of the child = The angular speed of the merry-go-round = 2·π/5 radians/second ≈ 1.257 rad/s

b) The angular speed of the teenager = The angular speed of the merry-go-round = 2·π/5 radians/second ≈ 1.257 rad/s

c) The tangential speed, v = r × The angular speed, ω

Where;

r = The radius of rotation of the object

For the child, r = 1 m

The tangential speed of the child = 1 m × 2·π/5 radians/second = 2·π/5 m/s ≈ 1.257 m/s

d) For the child, r = 2 m

The tangential speed of the teenager = 2 m × 2·π/5 radians/second = 4·π/5 m/s ≈ 2.513 m/s

8 0
2 years ago
What happens to the coefficient of friction when the weight is increased? Why is this?
Crazy boy [7]

Answer:

Usually the coefficient of friction remains unchanged

Explanation:

The coefficient of friction should in the majority of cases, remain constant no matter what your normal force is. When you apply a greater normal force, the frictional force increases, and your coefficient of friction stays the same. Here's another way to think about it: because the force of friction is equal to the normal force times the coefficient of friction, friction is increased when normal force is increased.

Plus, the coefficient of friction is a property of the materials being "rubbed", and this property usually does not depend on the normal force.

6 0
3 years ago
Read 2 more answers
Consider the numbers 23.68 and 4.12. The sum of these numbers has ____ significant figures, and the product of these numbers has
damaskus [11]

Answer:multiplying will give us 7 significant figures and addition will give us 3 significant figures

Explanation:

After multiplying the two numbers they resulting value will give a value in its 4 decimal places because both given values are in 2 decimal places. The 4 dp is gotten by the addition of the decimal places of both given numbers (2+2) and

The result of its addition will give us a value in its 1dp and 3 significant figures since the addition of 23.68 and 4.12 will give us 27.8

7 0
3 years ago
Other questions:
  • Can u answer 4 and 5 for me
    11·1 answer
  • A crate is given a push across a horizontal surface. The crate has a mass m, the push gives it an initial speed of 1.90 m/s, and
    5·1 answer
  • What is the difference between a permanent magnet and a temporary magnet
    10·2 answers
  • Which of the following values has the greatest number of significant figures? Justify your answer?
    8·1 answer
  • The energy of a photon is 9.7eV what is the wavelength
    14·1 answer
  • 20 A measure of the speed and direction of an object's motion
    7·1 answer
  • An airplane propeller is 2.16 m in length (from tip to tip) with mass 100 kg and is rotating at 2900 rpm (rev/min) about an axis
    14·1 answer
  • A
    8·1 answer
  • The graph indicates Linda’s walk.
    5·2 answers
  • How do light travels
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!