An explosion is recorded by two forest rangers, one at a primary station and the other atan outpost 6 kilometers away. The ranger at the primary station hears the explosion 6 seconds before the ranger at the outpost. a. Assuming sound travels at 0.35 kilometer per second, write an equation in standard form that gives all the possible locations of the explosion. Use a coordinate system with the two ranger stations on the x-axis and the midpoint between the stations at the origin. b. Graph the equation that gives the possible locations of the explosion. Show the locations of the ranger stations in your drawing.
An explosion is recorded by two forest rangers, one at a primary station and the other atan outpost 6 kilometers away. The ranger at the primary station hears the explosion 6 seconds before the ranger at the outpost. a. Assuming sound travels at 0.35 kilometer per second, write an equation in standard form that gives all the possible locations of the explosion. Use a coordinate system with the two ranger stations on the x-axis and the midpoint between the stations at the origin. b. Graph the equation that gives the possible locations of the explosion. Show the locations of the ranger stations in your drawing.
Solution Summary: The author explains the equation in the standard form that describes the possible points of explosion when the distance between the two rangers is 6km.
An explosion is recorded by two forest rangers, one at a primary station and the other atan outpost 6 kilometers away. The ranger at the primary station hears the explosion 6 seconds before the ranger at the outpost. a. Assuming sound travels at 0.35 kilometer per second, write an equation in standard form that gives all the possible locations of the explosion. Use a coordinate system with the two ranger stations on the x-axis and the midpoint between the stations at the origin. b. Graph the equation that gives the possible locations of the explosion. Show the locations of the ranger stations in your drawing.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Directions: Use the equation A = Pet to answer each question and be sure to show all your work.
1. If $5,000 is deposited in an account that receives 6.1% interest compounded continuously, how much money is in the
account after 6 years?
2. After how many years will an account have $12,000 if $6,000 is deposited, and the account receives 3.8% interest
compounded continuously?
3. Abigail wants to save $15,000 to buy a car in 7 years. If she deposits $10,000 into an account that receives 5.7% interest
compounded continuously, will she have enough money in 7 years?
4. Daniel deposits $8,000 into a continuously compounding interest account. After 18 years, there is $13,006.40 in the account.
What was the interest rate?
5. An account has $26,000 after 15 years. The account received 2.3% interest compounded continuously. How much was
deposited initially?
TRIANGLES
INDEPENDENT PRACTICE
ription Criangle write and cow
Using each picture or description of triangle write and solve an equation in ordering the
number of degrees in each angle
TRIANGLE
EQUATION & WORK
ANGLE MEASURES
A
B
-(7x-2)°
(4x)
(3x)°
(5x − 10)
C
(5x – 2)
(18x)
E
3.
G
4.
H
(16x)°
LL
2A=
2B=
ZE=
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