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
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
Related Questions
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.
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!
Look at the cylinder.
What is the total surface area?
Answers
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
convert 4/5 into percent
Answers
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
1. 94.25 m
2. 157.08 cm
3. 94.25 m
4. 31.42 m
5. 21.99 cm
Jack wants to abopt all kittens that weigh more than 4 ounces how many kittens will he abopt
Answers
Adopt that many kittens
WILL MARK BRAINLIEST!!!
Solve for the listed Angles of the circle. Question in the picture
Answers
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]
Helppp please and thank you !
Answers
Answer:
209 (Sorry if wrong)
Step-by-step explanation:
12x12=144
13x5=65
144+65=209
==================================================
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".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 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
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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
Solve for the value of x. Round to the nearest tenth.
Answers
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
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:
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:
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
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
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 outcomesStuart's throw:
Number of tails = 7Number of throws = 10P(Tail) = 7/10 = 0.7Maxine's throw :
Number of throws = 50Number of tails = 30P(Tail) = 30 / 50 = 0.6The 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
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:
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
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.
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:
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)
Please help me!!!
Find the measure of angle x in the figure below:
Answers
Answer:
Step-by-step explanation:
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.
Please help me with simplifying this equation? (-5)^5/ (-5)^-6
Thanks
Answers
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
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
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