This question has two parts, First, answer Part A Then, answer Part B
1 answer:
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Answer:
Part a)
Part b) The total cost is
Part c) see the explanation
Step-by-step explanation:
Part a) Write a linear equation to represent this situation
Define the variables
Let
x ----> the number of hours
y ----> the total cost in dollars
we know that
The linear equation in slope intercept form is equal to
where
m is the slope or the unit rate
b is the y-intercept or initial value (value of y when the value of x is equal to zero)
In this problem we have that
The unit rate or slope is equal to
The y-intercept or initial value is equal to
substitute
Part b) Use the equation to find the total cost to rent skis from 8:30 am to 3:00 pm
Remember that
3:00 pm=15:00
so
from 8:30 am to 3:00 pm, the total hours is equal to
15:00 -8:30=6:30=6.5 h
For x=6.5 h
substitute in the linear equation and solve for y
Part c) What does your answer mean in context of the problem?
we have that
y=220.25
That means -----> The total cost to rent skis for 6.5 hours is equal to $220.25
Answer: The fire is 3.5 miles from tower B
Step-by-step explanation: Please refer to the attached diagram. The triangle in the attached diagram illustrates the clues given in the question. Both rangers are standing at points A and B respectively with a distance of 5 miles between them, which is line AB. Also, one ranger spots a fire from a tower at an angle of 42 degrees, which is point A. Another ranger spots the same fire from another tower, but from an angle of 64 degrees, which is point B. The fire is at point C on the triangle. Now we have a triangle with only one side known (5 miles) and three angles known (the third angle is computed as 180 - {64+42} which equals 74) which are 64 degrees, 42 degrees and 74 degrees.
The distance from the fire to tower B is calculated using the law of sines. (Note that this is not a right angled triangle, hence we cannot use trigonometric ratios). The law of sines is expressed as follows;
a/SinA = b/SinB or
a/SinA = c/SinC
Depending on the sides and angles we are given and the ones we are to calculate.
The distance from the fire to tower B is line BC, labeled as a in our diagram. Using the law of sines
a/SinA = c/SinC
(Note also that a is directly facing angle A, c is directly facing angle C, and so on)
a/SinA = c/SinC
a/Sin 42 = 5/Sin 74
By cross multiplication we now have
a (Sin 74) = 5 (Sin 42)
Divide both sides of the equation by Sin 74 and we now arrive at
a = 5 (Sin 42)/Sin 74
a = 5 (0.6691)/0.9613
a = 3.3455/0.9613
a = 3.4802
{rounded to the nearest tenth of a mile, a equals 3.5}
Therefore the distance from tower B to the fire is approximately 3.5 miles
