Question

PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I WILL AWARD MEDAL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

A tower in Maintown sends radio signal a certain distance (in miles) according to the equation:
x^2 + y^2 = 8,100. The Smith family lives 50 miles south and 70 miles east of Maintown.

Part 1: Can the Smith family receive the radio signal from Maintown? (3 points)

Part 2: In complete sentences, explain your reasoning. (3 points)

Answer 1

@tcarroll010

Answer 2

You'll be able to do part a with my hints regarding part b. This original equation is just a circle at the origin with radius of 90. See what the equation would be for the point given with center also at the origin. Big hint: get the radius by the Pythagorean theorem.

Answer 3

Ok lets do it. :)

Answer 4

Good thinking. Here "us" means "you".

Answer 5

The equation `x^2+y^2 = 1800` is a circle. It's center is (0,0) and radius is 90.

The center(0,0) represents the location of the tower. And the radius indicates that all residences or establishments within 90 miles from the tower can receive radio signals.

The location of Smith family is 50 miles south and 70 miles east of the tower in Maintown. This can be express in x and y coordinates which is (70, -50).

The points (0,0) and (70,-50) can be used to determine if the Smith family can receive radio signals from the Maintown. This can be done using the distance formula between two points. If the distance is less than or equal to 90 miles, then the Smith family can receive signals.

`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2) = sqrt[(70-0)^2+(-50-0)^2] = sqrt7400 = 86.02`

So the Smith family is 86.02 miles away from the tower and they are still within the 90 mile radius. Hence, the Smith family can receive signals.

Answer 6

So, all you have to do is see what radius that given point shows:

take the sqrt of 50^2 + 70^2

Answer 7

ANOTHER WAY TO LOOK AT THIS:

The first thing you should do when looking at this problem is identify that the equation given in the problem is the formula for a circle. So, the tower is basically in the center of a circle and emits signal in all directions (360 degrees). Thus, anyone living within (or on) this circle will be able to receive the signal,

The problem does not state whether "x" is the north/south coordinate or the east/west coordinate. Therefore, we can assume that the x coordinate is the east/west coordinate (right/left on a coordinate plane) and the y coordinate is the north/south coordinate (up/down on a coordinate plane). If we substitute the values in for "x" and "y," we get

70^2 + 50^2 = 8100

4900 + 2500 = 8100

7400 = 8100

We can determine from this information that the Smith family does not live on the circle, but lives within the circle. This means that the Smith family will be able to obtain the signal from the tower. Anyone living past...

Answer 8

If you are still confused, here's a diagram:

Answer 9

OK so the answer for part 1 is yes.

Answer 10

Yes. The smaller circle corresponds to the radius for the given point. That is within the radius of the broadcasting which is larger and is 90. The sqrt of 8100.

Answer 11

Ok and part 2. PLease I am just kind of loost

Answer 12

For "b", you can determine the radius of the smaller circle. You don't know it's smaller until you go through the calculations, but you'll see that by using the Pythagorean Theorem, and get the distance of the point from the origin:

d = sqrt( 50^2 + 70^2)

You will see that that radius is smaller than the broadcasting radius, so they can receive the signal since the distance is under 90. In words, you can say that the equation for the circle, centered at the origin, and containing the given point (see my diagram), has a smaller radius that the broadcasting radius.

Answer 13

So the answer for part 2 is
the radius of the circle based on the equation provided for me tells me that it has a smaller radius.

Answer 14

Well, you might want to expand on that. If that's all you write, you won't get full credit. You have to use your own words, but you can include the derivation of the equation of the smaller circle and talk about how that radius is smaller.

Answer 15

Ok so can I say
That the distance of the maintown is shorter than the radius of the radio tower so in this case they will get signal in the maintown.

Answer 16

You would say that the distance from that given location to the transmitting tower is shorter than the broadcasting radius from that transmitting tower, and you have to show that by deriving the equation of the smaller circle. You are working with a circle because that point lies on the circle.

Answer 17

Are you all set now, @magbak ?

Answer 18

Yes thank you very much.@tcarroll010

Answer 19

uw!