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 transmitter to a second city 36 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter? Hint: assume that the transmitter is at the origin. Write the equations of the line and circle.

Answers

Answer 1

9514 1404 393

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%

__

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

A Small Radio Transmitter Broadcasts In A 31 Mile Radius. If You Drive Along A Straight Line From A City

Related Questions

Please Help! 100 Points to whoever does!

Answers

Answer:

cross multiply

(3+2) 10^3==

5*10^3

What is 12n+36m+60= pls answer

Answers

Answer:

you can't do that because they are different variables, so there are no like terms

Step-by-step explanation:

there is no answer for this equation

Answer:

Step-by-step explanation:

12n+36m+60=0

12n+36m=-69

12(n+3m)=-69

n+3m=-69/12

Find the quotient of z1 by z2. .Express your answer in trigonometric form.

Answers

Answer:

[tex]\frac{z_1}{z_2} = 3(cos(240^o) + isin(240^o))[/tex]

Step-by-step explanation:

Given

[tex]z1 = 12(cos(320^o) + isin(320^o))[/tex]

[tex]z2 = 4(cos(80^o) + isin(80^o))[/tex]

Required

[tex]Quotient = \frac{z_1}{z_2}[/tex]

We have:

[tex]Quotient = \frac{12(cos(320^o) + isin(320^o))}{4(cos(80^o) + isin(80^o))}[/tex]

Divide 12 by 4

[tex]Quotient = \frac{3(cos(320^o) + isin(320^o))}{(cos(80^o) + isin(80^o))}[/tex]

Solve using the following rule:

[tex]\frac{(cos(a) + isin(a))}{(cos(b) + isin(b))} = \cos(a - b) + isin(a - b)[/tex]

So, we have:

[tex]Quotient = \frac{3(cos(320^o) + isin(320^o))}{(cos(80^o) + isin(80^o))}[/tex]

[tex]Quotient = 3(cos(320^o-80^o) + isin(320^o-80^o))[/tex]

[tex]Quotient = 3(cos(240^o) + isin(240^o))[/tex]

Hence:

[tex]\frac{z_1}{z_2} = 3(cos(240^o) + isin(240^o))[/tex]

PLS HELP
a) What is the equation of line A

b) What is the equation of line B

Answers

The equation of line A : y = 4
The equation of line B : x = 8

Answer:

The equation of a line A:x=4The equation of a line B:y=8

Step-by-step explanation:

i hope this helps u have a nice day .

What is the equation of the graph
-2
y = 1x + 1
O y = 1x-2
y = 2x - 2
O y = 2x + 1

Answers

9514 1404 393

Answer:

  the correct choice is marked

Step-by-step explanation:

The line has a rise of 2 for a run of 1, so a slope of 2. The line crosses the y-axis at y=-2, so the y-intercept is -2. The slope-intercept equation for the line is ...

  y = mx + b . . . . . . for slope m and y-intercept b

  y = 2x -2

Answer:

the answer is c y=2x-2

Step-by-step explanation:

:)

30
7
0.7
dbksb
FS MATHS L2
Practise the Skill
1)
There are 14 women and 7 men in a café.
What is the probability that a person picked at random will be a woman?
Give your answer as a fraction in its lowest terms.
2)
Sally has a pack of playing cards and she chooses a card at random.
a) What is the probability that she picks an ace?
Give your answer as a fraction in its lowest terms.​

Answers

Answer:

1) 2/1

2) 13/1

Step-by-step explanation:

Given f(x) = 3x2 + x and g(x) = 2x. What is Limit of g (f (x)) as x approaches negative 4?

44
88
104
188

Answers

Answer: 88

Step-by-step explanation:

got it right 2022 edge

14. Which makes the number sentence true?
12 - 3= 7+_

Answers

The answer is 2 in order to make the sentence true

SOMEONE HELPPP PLEASE!! Complete the table to represent the number of seashells in the collection after the first four summers

Answers

Answer:

6 number of seashells for 1 Summer. 21 number of seashells for two summers. 36 number of seashells for three summers. 51 number of seashells for 4 summers.

Step-by-step explanation:

15 substituted in for f and x is the the number of summers.

Answer:

6

21

36

51

Illuminate test.

Si se tira un dado, ¿cuál es la probabilidad de que se obtenga un divisor de 6?

Answers

Answer:

si se tirs undado you need to

A parking lot charges $2 per hour for the first 4 hours, then $3 per hour after that. Which equation(s) describes the total cost as a function of the hours x?
A. Y=3x+8
B. Y=2x+12
C. Y=2x for x of 4 or less / y=2x+3x for x of 5 or more
D. Y=2x for x of 4 or less / y=8x+3(x-4) for x of 5 or more

Answers

Answer:

A.

Step-by-step explanation:

2/hour

2×4 hours =8 dollars ;

Then 3x(because we dk the time taken, so replaced by x and then times 3)

Equation =8+3x

Does anyone understand this?

Answers

Answer: understand what

Step-by-step explanation:

Answer:

where qurstion

Step-by-step explanation:

??????????????

What is the product?
2 3 4
5 9 -1 -7
11 5 -3

Answers

Answer:

-1247400

Step-by-step explanation:

See the Image below:) I believe this is what you are looking for.

The transformation of y=f(x) to y=f(2x) is a:

Answers

Answer:

c) vertical stretch by a factor of 2

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

Horizontal stretch by a factor of 1/2.

We can also describe this as a horizontal compression by a factor 2

can someone help 10 points

Answers

Answer:

The volume of this rectangular prism is 72 cubic units. We multiply 6*4*3 to get 72.

(3x2+2−x3)−(−5x3+2x2+1)



Express the answer in standard form.

Enter your answer in the box.

Answers

Answer:

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

ax²+bx+c

Simplify each term.

3x²+2−x³+5x³−2x²−1

Simplify by adding terms.

4x³+x²+1

Step-by-step explanation:

A sample of 1,000 adults showed that 31% of them are
smokers. To estimate the proportion of people in the entire population who smoke, what additional information would you need?

Select one:

A. The size of the population

B. The length of time the people smoked

C. All the information you need is contained in the problem

D. The amount of confidence you desire in your estimate

Answers

Answer:

C. All the information you need is contained in the problem.

310 people of 1000 people smoke.

Step-by-step explanation:

[tex]\frac{y}{1000}: \frac{31}{100}[/tex]

y · 100 = 31 · 1000

100y = 31000

100y ÷ 100 = 31000 ÷ 100

y = 310

which sentence is true iready math

Answers

Could you please use a picture?
I think you forgot to upload a pic?

1 out of 5 pairs of Henry's shoes no longer fit him. what fraction of his shoe collection still fit ?​

Answers

the answer is 4/5.

hope this helps!!

Answer:

4/5

Step-by-step explanation:

here ya are. I hope this helps, it's just 1 pair out of the 5 that don't fit. Meaning the 4 out of 5 fit. therefore 4/5

Round 27346 to 2 significant figures i need a step by step expansion

Answers

Answer:

27000

Step-by-step explanation:

We want to round 27346 to 2 significant figures.

Now, the number already has 5 significant figures, so to reduce it to 2 sig figures, we will have to reduce the 3 digits from the right to zero so that we can have just 2 significant figures by approximating.

Thus, 3 is less than 5 and so 7 cannot increase. Thus, we will have 27000 as the number when reduced to 2 significant figures.

1. Points scored by a basketball player are 12, 15, 8, 12, 15, 10, 3, 14, and 15
Calculate the:
a) mean
b) median
c) mode
d) midrange
e) Use the relative location of the mean, median, and mode calculated describe the sets as
symmetric, skewed left, or skewed right.



Answers

Answer:

mean : add all of them and divide by how much they are

mode: is what repeats it self like 15 is the most repeated.

please help with this question i will mark you brainliest!

Answers

9514 1404 393

Answer:

  equation: y = 4x

  graph is attached

Step-by-step explanation:

Let y represent the cost of the peaches in dollars. Let x represent their weight in pounds. Then the relation between the two variables is ...

  cost = (cost per pound) × (pounds)

  y = 4x

__

This graphs as a line through the origin with a slope of 4. In the attached, the x- and y-axes have different scales so more of the graph can be seen.

Harvey is often late for work. He leaves home late 60% of the time, but then drives very fast. This gives him a 50% chance of getting to work on time. When Harvey leaves home on time, he drives so slowly that he is late 70% of the time. What is the probability that Harvey left home on time if he gets to work on time

Answers

Answer:

40%

Step-by-step explanation:

Find the sum of the series if n = 6, r = 1/4, a = 2.

Answers

Answer:

8.25

[tex]8\frac{1}{4}[/tex]

Step-by-step explanation:

n + r + a

6 + 0.25 + 2

8 + 0.25

8.25

Find the sum of the geometric series if n = 6, r= 1/4, a = 2.

Answers

Sn = a(1-r^n)/(1-r)

Sn= 8(1-1/4096)/3= 2.67

Precision is a measure of how close an answer is to the actual or expected
value.
True or false ?

Answers

i’m pretty sure it’s true

Answer:

False

Step-by-step explanation:

Precision  describes repeatability.  

Accuracy  describes the closeness of a measurement to the actual value.

 So your measurements may be precise but not accurate; for example if you used a faulty measurement system. And of course, you could get accurate results SOME of the time (which describes the exprerience of most researchers).

Errors in precision are usually detected.........eventually, invariably after you have shot your mouth off to your professor.

PLEASE HELPPPP MEEEEE, JUSTFIY PLZZ​

Answers

Answer:

a. Unsure

b. True

c. Unsure

d. True

A - False

B - True

C- False

D- True

A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical store? .78 .50 .28 .22

Answers

Answer:

[tex]p' = 0.22[/tex]

Step-by-step explanation:

Given

[tex]p = \frac{78}{100}[/tex]

Required

Probability that a [tex]customer[/tex] does [tex]not[/tex] live [tex]within[/tex] [tex]50[/tex] miles

To do this, we make use of complement rule;

Which states that:

[tex]p + p' = 1[/tex]

Make p' the subject

[tex]p' = 1 - p[/tex]

So, we have:

[tex]p' = 1 - \frac{78}{100}[/tex]

Express fraction as decimal

[tex]p' = 1 - 0.78[/tex]

[tex]p' = 0.22[/tex]

FREE BRANLEIST URGENT WITH EQUATION!! WILL REPORT AND GET BANNED IF LINKS AND INCORRECT ANSWERS

Answers

Answer:

ok so a it' probabily 21 or a number between 1-10

Step-by-step explanation:

Answer:

q.10 142 degree

q.11 x=11

q.12 complementary angles

The weight of laboratory grasshoppers follows a Normal distribution, with a mean of 90 grams and a standard deviation of 2 grams. What percentage of the grasshoppers weigh between 86 grams and 94 grams

Answers

Answer:

95.44% of the grasshoppers weigh between 86 grams and 94 grams.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 90 grams and a standard deviation of 2 grams.

This means that [tex]\mu = 90, \sigma = 2[/tex]

What percentage of the grasshoppers weigh between 86 grams and 94 grams?

The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 86. So

X = 94

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{94 - 90}{2}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

X = 86

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{86 - 90}{2}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544*100% = 95.44%

95.44% of the grasshoppers weigh between 86 grams and 94 grams.

Other Questions
NEED HELP ASAP!!!.....Which is not true about the ionic compound sodium chloride (NaCl)? A.)it was formed when electrons were shared B.)it is electrically neutral C.)it has properties different from the atoms from which it is formed D.)it is a white crystalline solid How do you convert from grabs to moles of a substance1. Divide by the molar mass2. Subtract the molar mass3. Add the molar mass4. Multiple by the molar massPLEASE HELP !!! A review is a type of Persuasive Writing.TrueFalse -Quel bus est-ce qu'on prend?- Le____O A. blanchesO B. blancheO c. blancsO D. blanc How do steroids cause death 13. Federico tiene un examen maana. O Tiene que estudiarO Tiene sedO Tienen hambreO Tiene prisaO Tienen ganas de ver una pelcula Waterway Industries Recorded operating data for its Cheap division for the year. Waterway requires its return to be 10%. Sales $1600000 Controllable margin 88000 Total average assets 4400000 Fixed costs 100000 What is the ROI for the year (10 points) How did the United States raise most of the funds needed to pay for the war? ( 1) through taxes on income and certain goods 2) through the sale of war bonds O 3) through loans from Allied powers 4) through mass production in industries. Whats 2-4 plz helppppp the number of digits in the square root of 36000000 is Type the pronoun and the noun it replaces.Sarah did not go to work because she was ill.Pronoun: Noun: Slipper Company sold a productive asset, a machine, for cash. It originally cost Slipper $29,000. The accumulated depreciation at the date of disposal was $24,000. A gain on the disposal of $2,900 was reported. What was the asset's selling price Which expressions are equivalent to (59 + 3h + 4) - 2? In the sentence below, the underlined portion is a clause. Identify the type of clause.I can't go to the movies since I don't have anymoney.Independent clauseDependent clauseNon essential clause None of the choices what is 20% of 90??? Brendan made a diagram to compare and contrast the benefits of two types of social behavior. The diagram shows 2 overlapping circles labeled Flocking and Herding. There is a z in Herding.Which description belongs in the area marked "Z"?reproductionprotectionforaginghydrodynamic efficiencyplease help this is an exam and its timeddddd How is waste (and the accumulation of it) not only harming wildlife, but ourselves? F r e e points if you can answers these questions. Get 4 or the most question correct and ill mark Brainliest.After everyone post their answers ill reveal the true answers. #1: Find the area of the triangle shown below.*6 ft14 ft Find measure angle GJK (5x + 8) (7x - 16)