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

A semi-circle with a diameter of 6 cm sits on top of an isosceles trapezoid. Find the area of the entire figure.

Answers

Answer:

                                     

Step-by-step explanation:

Which equation is a linear function?
Please answer within 5 minutes

Answers

Answer:

y= x/2-5

Step-by-step explanation:

Answer:

y=x²+7

Step-by-step explanation:

I'm pretty sure this is the answer

The blue dot is at what value on the number line?
I'm really desperate, please help me. I'll give the person who has the correct answer brainliest.

Answers

Answer:

-19

Step-by-step explanation:

It's going by three's

A bag with 8 marbles is shown below. (2 marbles are yellow, 3 are red, and 3 are blue.) A marble is chosen from the bag at random. What is the
probability that it is yellow or red?
Write your answer as a fraction or a whole number.

Answers

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Hi there!

We're given that there are 8 marbles in total. 2 marbles are yellow and 3 are red, making the number of red AND yellow marbles 5 (2+3=5)

Because 5 out of the 8 marbles are yellow or red, the probability of choosing one of them is [tex]\frac{5}{8}[/tex].

I hope this helps!

Answer:

P(Red or Yellow) = 5/8

Step-by-step explanation:

2 (yellow) + 3 (red) = 5

Hence, the probability is 5/8

Feel free to mark it as brainliest :D

Convert 69 g/cm to kilograms per meter (kg/m).

Answers

Answer:

69g/cm is 6.9kg/m

Step-by-step explanation:

[tex]1 g --> \frac{1}{1000}kg\\\\69g --> \frac{69}{1000}kg\\\\1cm --> \frac{1}{100}m\\\\\frac{69 g}{1cm} = \frac{\frac{69}{1000} }{\frac {1}{100}} = \frac{69}{1000} \times \frac{100}{1} = \frac{69}{10} = 6.9kg/m[/tex]

Answer:

[tex]69 \: g {cm}^{ - 1} \\ 69 \times {10}^{ - 3} \times ({10}^{ - 2} ) ^{ - 1} kg \: {m}^{ - 1} \\ 69 \times {10}^{ - 1} \: kg {m}^{ - 1} \\ 6.9 \: kg {m}^{ - 1} [/tex]

A carpet measures 7 meters 3 decimeters in length and 4 meters
decimeters in width. What is its area in square meters?

Answers

Answer:

29.2 metres squared

Step-by-step explanation:

because 3 decimetre equal 1 metre, 7 metres and 3 decimetre equal 7.3 metres.

now we just use the area formula to solve.

Area = Length × Width = 7.3 × 4 = 29.2 metres squared


I GIVE BRAINLIEST!!!
Margie needs to borrow $9,000 from a local bank. The loan has a 8.5% interest rate for 4 years. What will Margie's monthly payment be?

Answers

Answer: I'm sorry I don't know but il try and calculate the answer for you

Step-by-step explanation:

Look at the cylinder.

What is the total surface area?

Answers

D is the correct answer, 130 pie in squared.

The library surveyed 180 people about their favorite type of movie. If 40% of the people chose action, how many people chose action?

Answers

Answer:72

Step-by-step explanation:

I. B. Find the circumference of the following given data,
1. r= 15m
2. r = 25cm
3. d = 30m
4. d = 10m
5. r = 7cm​

Answers

CIRCUMFERENCES

1. 94.25 m
2. 157.08 cm
3. 94.25 m
4. 31.42 m
5. 21.99 cm

A distance of 400 km is represented in the map by 3 cm. What is the distance between two towns if they are 7.5 cm apart in the map?​

Answers

Answer:

The distance between the two towns is of 1000 km.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

We have that:

3 cm represents a distance of 400 km.

What is the distance represented by 7.5 cm?

3 cm - 400 km

7.5 cm - x km

Applying cross multiplication:

[tex]3x = 400*7.5[/tex]

[tex]x = \frac{400*7.5}{3}[/tex]

[tex]x = 1000[/tex]

The distance between the two towns is of 1000 km.

What is the area of the base of the cone below? 12ft v=90ft^3​

Answers

Answer: C 22.5 ft2!

Step-by-step explanation:

i took the test, have a great day:) <3

Answer:

right

Step-by-step explanation:

Please help me!!!

Find the measure of angle x in the figure below:

Answers

Answer:

Step-by-step explanation:

48° is the answer to the question

Need help fast please

Answers

Answer:

28

Step-by-step explanation:

Since this is a right triangle, we can use the pythagorean theorem

a^2 +b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + 45^2 = 53^2

a^2 +2025=2809

a^2 = 2809-2025

a^2 =784

Take the square root of each side

sqrt(a^2) = sqrt(784)

a =28

Reflect the following points over the
x-axis. (-5, -3) (-2,-6) (-4,-8)

Answers

Reflect over x-axis rule: (x,y) -> (x,-y)

(-5,3) --> (-5,-3)

(-2,-6) --> (-2,6)

(-4,-8) --> (-4,8)

WILL MARK BRAINLIEST!!!

Solve for the listed Angles of the circle. Question in the picture

Answers

Wollllllllyyyyy d-d-d-d-d-Dora

Find the common difference of the arithmetic sequence -16 -13 -10

Answers

Answer:

3

Step-by-step explanation:

-16+3= -13

-13+3= -10

the next number would be -7

Solve for the value of x. Round to the nearest tenth.

Answers

the answer would be 19.3

Once again, I'm asking for assistance in this problem. I thought it was 1/6 but I'm unsure. Someone help. The number next to 2/5 is 1/5.​

Answers

Answer:

Equation of the parabola:  or

Vertex form:

Intercept form:Step-by-step explanation:

Stuart throws a biased coin 10 times.
He gets 7 Tails.
Maxine throws the same coin 50 times.
She gets 30 Tails.
Prasha is going to throw the coin once.
(i) Whose results will give the better estimate for the probability that she will get Tails,
Stuart's or Maxine's?
You must give a reason for your answer.

Answers

Answer:

Below.

Step-by-step explanation:

1. Prasha's result is better as she tossed the coin the most times.

The result which gives a better estimate of obtaining tail is that which provides a greater probability, hence, Stuart's result is better.

Recall :

Probability = required outcome / Total possible outcomes

Stuart's throw:

Number of tails = 7Number of throws = 10

P(Tail) = 7/10 = 0.7

Maxine's throw :

Number of throws = 50Number of tails = 30

P(Tail) = 30 / 50 = 0.6

The result with higher probability gives the better estimate of obtaining tail.

Therefore, Stuart's result will be a better estimate.

Learn more : https://brainly.com/question/18153040

P(A and B)=P(A)•P(B) is used when two events are used when two events are

Answers

Answer:

Independent.

Step-by-step explanation:

Independent events:

Two events, A and B, are said to be independent if the probability of both happening is the same as the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Thus, P(A and B)=P(A)•P(B) is used when two events are independent.

Please help me with simplifying this equation? (-5)^5/ (-5)^-6
Thanks

Answers

I think so that the answer is -48828125

Which pair of functions are inverses of each other?
Wanting to make sure of answers in this pretest

Answers

Answer:

The only pair of functions that are inverses of each other are the ones for option D.

Step-by-step explanation:

Two functions, f(x) and g(x), are inverses if and only if:

f( g(x) ) = x

g( f(x) ) = x

So we need to check that with all the given options.

A)

[tex]f(x) = \frac{x}{7} + 10 \\g(x) = 7*x - 10\\[/tex]

then:

[tex]f(g(x)) = \frac{7*x + 10}{7} -10 = x + \frac{10}{7} - 10[/tex]

This is clearly different than x, so f(x) and g(x) are not inverses.

B)

[tex]f(x) = \sqrt[3]{11*x} \\g(x) = (\frac{x}{11} )^3[/tex]

Then:

[tex]f(g(x)) = \sqrt[3]{11*(\frac{x}{11})^3 } = \sqrt[3]{\frac{x^3}{11^2} } = \frac{x}{11^{2/3}}[/tex]

This is different than x, so f(x) and g(x) are not inverses.

C)

[tex]f(x) = \frac{7}{x} -2 \\g(x) = \frac{x + 2}{7}[/tex]

Then:

[tex]f(g(x)) = \frac{7}{\frac{x + 2}{7} } - 2 = \frac{7*7}{x + 2} - 2[/tex]

Obviously, this is different than x, so f(x) and g(x) are not inverses.

D)

[tex]f(x) = 9*x - 6\\g(x) = \frac{x + 6}{9}[/tex]

Then:

[tex]f(g(x)) = 9*\frac{x + 6}{9} - 6 = x + 6 - 6 = x\\g(f(x)) = \frac{(9*x - 6) + 6}{9} = x[/tex]

In this case we can conclude that f(x) and g(x) are inverses of each other.

Jack wants to abopt all kittens that weigh more than 4 ounces how many kittens will he abopt

Answers

Yea he will
Adopt that many kittens

convert 4/5 into percent​

Answers

the answer is 80% because percentage wise, 100 would be equivalent to 5 so 100divided by 5 would make it 20 every 1, so 20x4 is 80%

How many small cubes, with a side length of 1/2 cm, will fill the larger rectangular prism below?

Answers

Answer:

15 cubes

Step-by-step explanation:

The volume of a rectangular prism is given as :

V = Lenght * width * height

V = 3/2 * 5/2 * 1/2

V = 15 / 8 cm³

Volume of a cube = a³

Where, a = side length of cube

a = 1/2 cm

V = a³ = (1/2)³ = (1/2 * 1/2 * 1/2) = 1/8

Volume of pyramid / volume of cube

15 / 8 ÷ 1 / 8

15 / 8 * 8 / 1

= 15

Helppp please and thank you !

Answers

Answer:

209 (Sorry if wrong)

Step-by-step explanation:

12x12=144

13x5=65

144+65=209

Answer:  174 square meters

==================================================

How to get that answer:

We have a 12 by 12 square of area 12*12 = 144 square meters.

Then on top of this we have a triangle with base 12 and height 5, so its area is base*height/2 = 12*5/2 = 60/2 = 30 square meters

Overall, the two areas combine to 144+30 = 174 square meters

---------

Side notes:

The missing side of the triangle can be found through the pythagorean theorem. You could use the trapezoid area formula as an alternative path, instead of finding the area of each smaller piece.We can condense the unit "square meters" into "sq m" or "m^2".

If h is positive, move h units

Answers

Answer:

what's your question mean I don't understand it

Step-by-step explanation:

Have a great day

Which expression is equivalent to 4(2x + 5) ? Replace the x with a 2

Answers

Answer:

8x+20

36

Step-by-step explanation:

4(2x) + 4(5)

= 8x +20

Hence,

Substituting 2 into 8x+20:

8(2)+20

= 36

Feel free to mark it as brainliest :D

8x+20, i'm guessing. i think i'm right too

round to the nearest hundredth . 7.428

Answers

Answer:

7.43

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

7.43

Step-by-step explanation:

So lets go over a few things:

In decimal form, you start of in the tenths.

So in this case that is 4.

After tenths, is hundreths, thousandths, ten thousandths, etc.

Since hundreths comes after the tenths, that will be 2.

Any number 5 or greater will be rounded up, and any number below 5 is rounde down.

Now, to find if we raise or lower the hundreths(which is 2), we must see if the thousandth splace is above or lower than 5.

We can see that our thousandths is 8.

Since 8 is higher than 5, the 2 in our hundreths place will go up to 3.

So we get:

7.43

Hope this helps!

Other Questions
Someone please help me answer this, I need help An antonym for translucent is opaque.What is the best definition of translucent?increasing light in open spacesblocking all lightlighting solid objectsallowing light to pass through Write a friendly letter to future 8th graders. A 330.-ohm resistor is connected to a 5.00-volt battery. What is the current through the resistor? PART A: What is the meaning of "culmination" in paragraph 1?A. complete collapseB. a disagreementC. final resultD. violent incident What does the business cycle shown on this graph suggest about the condition of the economy at point A? A. the economy is getting worse and will continue to climb in for another quarter B. the economy has struggled for some time but is preparing to recover C. the economy has been well for a while and is at its highest point of the cycle D. The economy is in a period of growth that will continue for some time How would I say "....with my mom and now I know that when...." in french? please someone help!!! i have no clue how to do this Kiran runs along a straight road of length 150 m. Afterreaching at end of the road he runs back to his initialposition along the same straight path. If he takes a totaltime of 1 minute for completing his running, find theaverage speed and average velocity of Kiran. I kilogram massDefine Find the volume of the cone using 3.14 for pi. Please help asap i need it! 4,7,2,x,2,9,6: the median is 5 A movie theater is giving snack coupons with every ticket that is purchased. The table shows the type of snack coupon that was requested by 25 randomly selected customers during one day. Based on the date from the table, how many soda coupons will most likely be requested when 450 tickets are purchased? no links :( What types of changes occur during the erosion and deposition of sediments in a river? The project managers for TechBooks are demonstrating to the marketing team the new features of the site that deliver personalized content to the user. When a user clicks on a web ad offering a 25% discount, it goes directly to a web page with information about the offer. What method of user personalization does this describe? 9.Identify the vertex of the graph. Tell whether it is a minimum or maximum.A. (2, 1); minimumB. (2, 1); maximumC. (1, 2); minimumD. (1, 2); maximum Hannah ordered a pizza. it was divided in 8 equal slices. Hannah ate two slices right away and another slice before bed. what friction of the pizza did she eat? medical research team is conducting a study to determine whether there is a relationships between aerobic walking and cholesterol levels. A random sample of 315 subjects is selected and represented in the table below. Test the claim that walking and cholesterol levels are related. Include appropriate statistical evidence to support your findings. What is a definition for ergonomics? Plz help me well mark brainliest if correct ....????.