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A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 38 miles north of the t
1 answer:
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Answer:
63.7% or 33.35 miles
Step-by-step explanation:
The hint suggests that we find the points where the drive begins and ends picking up the transmitter. We suspect both of those points will have irrational coordinates, so finding the distance between them will involve dealing with squares and roots of irrational numbers. We want to see if there's an easier way.
The distance from the transmitter to the path being driven can be found using the "distance to a line" formula. First, we need the equation of the line in general form. In intercept form, it is ...
y/38 +x/36 = 1
19x +18y -684 = 0 . . . . . . multiply by LCM(36, 38) and subtract that amount
Then the distance from the origin to the line is ...
d = |19·0 +18·0 -684|/√(19² +18²) = 685/√685 ≈ 26.1243
The distance (x) along the line from the point where the transmitter is first picked up until the point of closest approach can be found from the Pythagorean theorem:
x² + (26.1243)² = 31²
x² = 31² -(684/√685)² = 190429/685
x ≈ 16.6733
The driving distance for which the transmitter is picked up is twice this, so is ...
2x = 2(16.6733) ≈ 33.3466 . . . miles
The total drive length is also given by the Pythagorean theorem:
drive length = √(36² +38²) = √2740 ≈ 52.3450 . . . miles
Then the fraction of the drive during which the signal is picked up is ...
fraction = (33.3466 mi)/(52.3450 mi) ≈ 0.6371 ≈ 63.7%
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The signal is picked up for 33.35 miles, about 63.7% of the drive.
______
The intercept-form equation for a line is ...
x/(x-intercept) +y/(y-intercept) = 1
The distance from (x, y) to line ax+by+c=0 is given by ...
d = |ax+by+c|/√(a²+b²)
The Pythagorean theorem relates legs a, b and hypotenuse c of a right triangle this way:
c² = a² +b²
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Answer:
because they are opposite sides of a parallelogram.
Step-by-step explanation:
First of all, let us have a look at the definition of a parallelogram.
<em>A parallelogram is a closed 4 sided figure (i.e. a quadrilateral) made up with two pairs of straight lines such that the two pairs are parallel and equal to each other.</em>
<em></em>
For example, let us consider a quadrilateral ABCD as attached in the diagram in answer area.
The two pair of lines are:
AB, DC and BC, AD
For ABCD to be a parallelogram, the lines
AB and DC must be parallel to each other and AB = DC
AND
BC and AD must be parallel to each other and BC = DA
------------------------------
In the given question, we are given that the quadrilateral MNOP is a parallelogram.
The two pairs opposite lines are OP, NM and PM, ON.
As per the definition of a parallelogram,
OP and NM must be <em>parallel and equal </em>to each other.
AND
PM and ON must be <em>parallel and equal </em>to each other.
.
Hence proved.
Answer:
8038.65
Step-by-step explanation: