![skyemichellec](/avatars/3321.jpg)
skyemichellec
05.08.2019 •
Physics
Asmall radio transmitter broadcasts in a 48 mile radius. if you drive along a straight line from a city 61 miles north of the transmitter 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?
Solved
Show answers
More tips
- L Leisure and Entertainment How to Choose the Perfect Gift for Men on February 23rd?...
- H Health and Medicine How to Treat Whooping Cough in Children?...
- H Health and Medicine Simple Ways to Lower Cholesterol in the Blood: Tips and Tricks...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
- S Style and Beauty Intimate Haircut: The Reasons, Popularity, and Risks...
- A Art and Culture When Will Eurovision 2011 Take Place?...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
Answers on questions: Physics
- P Physics What is the gravitational potential energy of a 1.3 kg book that is 473 meters above the ground? (Take in account for gravity, g = 9.8 m/s2) 2 points...
- P Physics What is the mass, in kg, of a 136 pound gymnast on Earth?...
- P Physics Which chemical equation is unbalanced? A ) K + H2O -- K2O + H2 B) MgO + 2HCI -- MgCI2 + H2O C) CaO2 + HCI -- CaCI2 + H2O D) CO2 + H2O -- H2CO2 (B Is the correct answer)...
- P Physics A DNA molecule is made up of a sugar backbone and four flavors of a molecule called al These nucleotides are arranged along the backbone in a unique order. Moving up a level of organization,...
- B Biology Choose all the answers that apply. Our bodies exhale carbon dioxide (CO2). Carbon dioxide is a compound has two atoms of oxygen is made of oxygen and carbon s an element has two molecules...
- M Mathematics A square has a perimeter represented by the expression -8.8 s - 20. Write an expression to represent the length of one of one side of the square....
- M Mathematics Which is a valid prediction about the continuous function f(x)? х -5 -3 -1 1 3 5 7 f(x) 8 4 0 -2 -2 O f(x) 0 over the interval [5, 00). O f(x) 0 over the interval (-1, 09). O f(x)...
- M Mathematics 12 15 9 . Forms a right triangle?...
- P Physics What power output is required of a motor that needs to lift a 450 kg elevator car 12 meters in 8.0 seconds? If mechanical energy is conserved, the kinetic energy you end up with always...
- A Arts What happened during Family Feud on November 9, 2017?...
Ответ:
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.
Ответ: