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RideAnS [48]
3 years ago
12

A small radio transmitter broadcasts in a 69 mile radius. If you drive along a straight line from a city 93 miles north of the t

ransmitter to a second city 78 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Mathematics
1 answer:
larisa86 [58]3 years ago
3 0

Answer:

See Explanation

Step-by-step explanation:

According to the Question,

  • We have A small radio transmitter that broadcasts in a 69-mile radius. If you drive along a straight line from a city 93 miles north of the transmitter to a second city 78 miles east of the transmitter.

Thus,

The distance that you get reception is the length of the chord created by the intersection of the circle defining the edge of transmission and the line defining the car trip.

  •  x2 + y2 = 69²               this is the circle

And,

The Transmitter at the origin

City to the north at (0,93)  & City to the east at (78,0)  

the Slope is M=(-93/78)

Intercept is B= y - mx ⇒  93 - (-93/78)(0) = 93

The equation of the line between the cities is y = (-93/78)x + 93

  • y = -93x/78 + 93           this is the line

Now, Solve the above two Equations

The intersection is gotten from the picture or solving:

x^2 + [(-93/78)*x + 93]^2 = 69^2

  • on solving we get, the points approximately are: (67.952,11.98 ) and (23.6277, 64.82)

Now,

From the Pythagorean theorem the total distance of the trip is:  

d1 = √(93^2 + 78^2) ≈ 121.37miles  

And the distance when the signal is picked up is:

d2 =√ [(67.952-23.627)^2 + (64.82 - 11.98)^2] ≈ 68.96 miles

You will pick up a signal from the transmitter in (d2/d1)*100 = 56% of the drive.

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Step-by-step explanation:

1) 3 gallons=36 miles

16 gallons=?

so it will be

36 \times 16 = 576

576 \div 3 =  192

or you can do like this

1 gallons=12 miles so if 16 gallons multiply with 12 it will be 192

2)2 hours=$28.50

? =$99.75

so it will be

99.75 \times 2 = 199.5

199.50 \div 28.50 = 7

so it will be 7 hours

3) 4.5 km= 5 hours

? =60 hours

60 \times 4.5 = 270

270 \div 5 = 54

the answer will be 54 kilometer

4) $9.60=3cm

$22.40=?

22.40 \times 3 = 67.20

67.20 \div 9.60 = 7

7 cm

5) $145.50=50 miles

$552.90=?

552.90 \times 50 =27645

27645 \div 145.50 = 190

190 miles

6)$239.85=359

$1.95=?

359 \times 1.95 = 700.05

700.05 \div 239.85 = 2.92

2.92 liter

7)

220=60 hours

?=3 hours

220 \times 3 = 660

660 \div 60 = 11

11 miles

8)1 gallon= $17.50

8.2 gallon=?

17.50 \times 8.2 = 143.50

$143.50

9)7cm=2 minute

? =13 minute

13 \times 7 = 91

91 \div 2 = 45.5

45.5 cm

10)17=4 acres

? =244 acre

244 \times 17 = 4148

4148  \div 4 = 1037

1037 kg

11) 1= $2.85

4.4=?

2.85 \times 4.4 = 12.54

$12.54

12)

$2.50=5 oz

$32.50=?

32.50 \times 5 = 162.50

162.50  \div 2.50 = 65

65 oz

5 0
3 years ago
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