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2 years ago

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A wildlife researcher is monitoring a black bear that has a radio telemetry collar with a transmitting range of 16 miles. The re

searcher is in a research station with her receiver and tracking the bear's movements. If we put the origin of a coordinate system at the research station, what is the equation of all possible locations of the bear where the transmitter would be at its maximum range?

1 answer:

Aliun [14]2 years ago

7 0

Answer:

The equation of all possible locations of the bear where the transmitter would be at its maximum range is $x^2+y^2=256$ .

Step-by-step explanation:

Consider the provided information.

Let the origin of a coordinate system at the research station, and the range is 16 miles.

That meas the maximum distance bear can cover is 16 miles and bear can move in any direction.

Center (0, 0) = (h, k)

The equation of circle with center at origin is:

$x^2+y^2=r^2$

Where r is the radius.

Substitute r = 16 in above formula.

$x^2+y^2=(16)^2$

$x^2+y^2=256$

Hence, the equation of all possible locations of the bear where the transmitter would be at its maximum range is $x^2+y^2=256$ .

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Troyanec [42]

Answer:

Part A) The length of a straight line between the school and the Fire Station is $4.6\ miles$

Part B) The length of a straight line between the school and the hospital is $2.1\ miles$

Step-by-step explanation:

<u><em>The complete question in the attached figure</em></u>

Let

The positive x-coordinates ----> East

The positive y-coordinates ----> North

The negative x-coordinates ----> West

The negative y-coordinates ----> South

take the point A (0,0) as the Middle School (reference point)

Part A) we have

Town Hall is located 4.3 miles directly east of the Middle School

so

The coordinates of Town Hall are B(4.3,0)

The Fire Station is located 1.7 miles directly North of Town Hall

so

The coordinates of Fire Station are C(4.3,1.7)

What is the length of a straight line between the school and the Fire Station?

Remember that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(0,0) and C(4.3,1.7)

substitute

$d=\sqrt{(1.7-0)^{2}+(4.3-0)^{2}}$

$d=\sqrt{(1.7)^{2}+(4.3)^{2}}$

$d=4.6\ miles$

Part B) we have that

The hospital is 3.1 miles west of the fire station

so

The coordinates of the hospital are D(4.3-3.1,1.7)

D(1.2,1.7)

What is the length of a straight line between the school and the hospital?

Remember that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(0,0) and D(1.2,1.7)

substitute

$d=\sqrt{(1.7-0)^{2}+(1.2-0)^{2}}$

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2 years ago

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mars1129 [50]

<span>(4, 3) Is your answer. </span>

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2 years ago

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Setler [38]

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2 years ago

Suppose that the probability density function for the length x in feet of some type of fish caught by sport fishermen is given b

Firdavs [7]

Answer:

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Step-by-step explanation:

The probability density function or p.d.f. for the length <em>x,</em> in feet, of some type of fish caught by sport fishermen is :

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givi [52]

let's see

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Plug in numbers that you know:

20 + 9 * 8

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