LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (-100,0) and (100,0), where unit distance on the coordinate plane is measured in miles
A receiver is located somewhere in the first quadrant. The receiver computes that the difference in the distances from the receiver to these transmitters is 180 miles.
What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the
hyperbola?
Answer:
Answers
The differences between the distances from the receiver to the two
transmitters is a constant.
[tex]\mathrm{The \ equation \ of \ the \ hyperbola\ is}\displaystyle \ \underline{\frac{y^2}{90^2} - \frac{x^2}{10\left(\sqrt{19} \right)^2} = 1}[/tex]Reasons:
The location of the transmitters = (-100, 0) and (100, 0)
The difference in the distance from the receiver to the transmitters = 180 miles.
Let the distances from the receiver to the transmitters be d₁ and d₂, we have;
|d₂ - d₁| = 180 = 2·a
[tex]\displaystyle a = \frac{180}{2} = 90[/tex]
c = The x-coordinates of the transmitters = 100
b² = c² - a²
∴ b² = 100² - 90² = 1900
b = √(1900) = 10·√(19)
Therefore;
The general form of the equation of an hyperbola is presented as follows;
[tex]\displaystyle \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1[/tex]
The standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola is; [tex]\displaystyle \underline{\frac{y^2}{90^2} - \frac{x^2}{10\left(\sqrt{19} \right)^2} = 1}[/tex]
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Related Questions
x ÷ 2 = 50
x = ?
Question Easy
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[tex]x \div 2 = 50 \\ = > x = 50 \times 2 \\ = > x = 100[/tex]
Answer:x = 100
Hope it helps.
Do comment if you have any query.
[tex]x = 100[/tex]
hope it helpssee the attachment for explanation!
3. Use the vertical line test to determine whether the relation graphed below is a function
(1 point)
Oyes
Ono
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Answer:yes
Step-by-step explanation:
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3. Write Math Two factors that make a product are sometimes called a factor
pair. Describe how using factor pairs helped you solve the problems.
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Is the value of the factor yes yes
Find 6 / 2(9) . Express your answer as a fraction in simplest form.
Answers
Answer:
3 or 3/1
Step-by-step explanation.
since 9 is in parenthuses, do 2x9, then you have the fraction 6/18, and 6 does into 18 3 times evenly, so the answer is 3.
The simplification form of the fraction 6/2(9) is 1/3 after using the concept of fraction and basic arithmetic operation.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The fraction is:
= 6/2(9)
From the definition of the fraction, the top of the fraction number is called the numerator and the second is the bottom of the fraction number which is called the denominator.
In the given fraction the number 6 is in the numerator and 2(9) is in the denominator.
= 6/18 (after the multiplication of 2 and 9)
= 1/3 (divide by 6 on the numerator and denominator)
Thus, the simplification form of the fraction 6/2(9) is 1/3 after using the concept of fraction and basic arithmetic operation.
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5 divided by 3/4 in simplest form
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Answer:
improper form: 20/3
Mix Number: 6 2/3
Step-by-step explanation:
5/3/4
Can be simplified into 5 * 4/3
Which is 20/3
Hope this helps!
Answer:
e
Step-by-step explanation:e
120 miles in 1 3/4 hours as a unit rate
Answers
9514 1404 393
Answer:
68 4/7 miles/hour
Step-by-step explanation:
The unit rate is found by dividing miles by hours:
(120 miles)/(7/4 hours) = 480/7 miles/hour = 68 4/7 miles/hour
tickets to a fair cost $4 for children and $10 for adults. You are unsure of how many tickets were sold, but know that $200 was collected. define your variables. What would be my variables??
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Answer:
4=
10=
200=
I dont actully know this i wanted to give it a try n all i got was this
The triangles shown below must be congruent.
25°
55-7
100"
100
55"
25°
0
о
A. True
о
B. False
Answers
9514 1404 393
Answer:
B. False
Step-by-step explanation:
The three pairs of corresponding angles have the same measures, so the triangles are similar by AA similarity. However, at least one pair of corresponding sides must be shown congruent before the triangles can be declared congruent.
There is nothing in the diagram to require the triangles be congruent.
With three corresponding equal angles triangles are not congruent. Therefore, the given statement is false.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
The three pairs of corresponding angles have the same measures, so the triangles are similar by AA similarity. However, at least one pair of corresponding sides must be shown congruent before the triangles can be declared congruent.
With three corresponding equal angles triangles are not congruent. Therefore, the given statement is false.
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Please help with this equation
Solving for b.
r=(b+a)m
Answers
Step-by-step explanation:
r = (b + a)m
Solve for b
r = bm + am
r/(am) = bm
r/(am) × 1/m = b
r/(am²) = b
b = r/(am²)
4x-5y=12, 6x+10y=18: solve by addition method
Answers
Answer:
x = 3 , y= 0
Step-by-step explanation:
Answer:
[tex]x=3[/tex];[tex]y=0[/tex]
Step-by-step explanation:
Double the first one, and add it to the second, to get rid of y
[tex]2I + II :8x -10y +6x -10y = 24+18\\14x = 42 \rightarrow x=3\\[/tex]
For the second value, let's take 3 times the first, subtract twice the second, and solve:
[tex]3I-2II: 12x-15y-(12x+20y)=36-36\\-15y-20y=0 \rightarrow -45y=0 \rightarrow y=0[/tex]
Write 1/ 5 √ 7 in index form
Answers
Your answer is long see it check correctly.
The index form of the fraction [tex]\frac{1}{(7^{(\frac{1}{5})}) }[/tex] is written as [tex]7^{(\frac{-1}{5})}[/tex] where the exponent notation is [tex]7^{(\frac{-1}{5})}[/tex].
Given data:
In index form, the expression [tex]\frac{1}{(7^{(\frac{1}{5})}) }[/tex] is written as [tex]7^{(\frac{-1}{5})}[/tex] , where the base is 7 and the exponent is -1/5. This means that we are taking the reciprocal of the fifth root of 7. The exponent of -1/5 indicates that we are essentially finding the inverse of the fifth root of 7.
When dealing with fractional exponents, the denominator of the fraction becomes the root, and the numerator becomes the power to which the base is raised. In this case, the base is 7, the denominator is 5, and the numerator is -1. So, [tex]7^{(\frac{-1}{5})}[/tex] represents the reciprocal of the fifth root of 7, which can also be expressed as the fifth root of 7 raised to the power of -1.
Hence, the exponent notation is [tex]7^{(\frac{-1}{5})}[/tex].
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The complete question is attached below:
Write [tex]\frac{1}{\sqrt[5]{7} }[/tex] in the index form.
An exponential function in the form y=2401(b)^x contains the point (4,1). What is the value of b?
Answers
equation with a variable on both sides that equal 27
Answers
Answer:
x +20 = 20 + 4 -x +10 (x =7)Step-by-step explanation:
equation with a variable on both sides that equal 27
x +20 = 20 + 4 -x +10
4 plates and 3 cups cost 20.90 dollars. 5 plates and 4 cups cost 26.50 dollars. Each plate costs the same amount as the other plates, and each cup costs the same amount as the other cups. What is the cost of 1 plate? What is the cost of 1 cup?
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Answer:
Hope this helps you understand...
Which sums and/or differences equal 14? Check all that apply.
Answers
Answer:
What's the choices??
Step-by-step explanation:
g(x) = -x + 2, find g(5)
Answers
Answer:
-3
Step-by-step explanation:
-(5)+2 = -3
Emiliano thinks x=40 is the solution 1/2x=80 explain why he is wrong
Answers
Emiliano divided by two instead of multiplying. To solve the equation, he had to multiply both sides by two so that he could see what x equals when it's alone (if half of x is 80, x, or two halves, is 160).
The solution of the given equation is 160. Emiliano wrong because instead of multiplying he must have divided 80 by 2.
The given equation is 1/2 x=80.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of the given equation is
1/2 x=80
⇒ x =80×2
⇒ x =160
The solution of the given equation is 160. Emiliano wrong because instead of multiplying he must have divided 80 by 2.
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Simon bought a $48 table on sale at 30% off.
Select from the drop-down menu to correctly complete the sentence.
The best estimate for the discount can be found using the expression
A)0.003(50)
B)0.3(50)
C)3(50)
D)30(50)
Explain, please!
Answers
Answer:
The answer is B. Hope this helps!
4 Find a formula for the exponential function passing through the points (-2, 4/9) and (3, 108)
Answers
9514 1404 393
Answer:
f(x) = 4·3^x
Step-by-step explanation:
We assume the function will be of the form ...
f(x) = a·b^x
Substituting the given values, we can find 'a' and 'b'.
4/9 = a·b^(-2)
108 = a·b^3
Dividing the second equation by the first gives ...
108/(4/9) = b^(3 -(-2))
243 = b^5
b = 3 . . . . . . 5th root
Using the second equation, we can find 'a':
108 = a·3^3 = 27a
a = 108/27 = 4
The formula for the exponential function is ...
f(x) = 4·3^x
This is K12 in sixth grade
The committee is planning a party and 150 guests are expected. Each table seats 12 people.
How many tables will be needed to seat all 150 guests?
12
13
162
1800
Answers
Answer:
13
Step-by-step explanation:
divide 150 by 12
the answer is 12.5
round 12.5
;)
1/4 equals how many eighths
Answers
Answer:
The answer = 0.25
A random sample of 500 adult residents of Maricopa County found that 361 were in favor of increasing the highway speed limit to 75 mph, while another sample of 400 adult residents of Pima County found that 270 were in favor of the increased speed limit. Construct a 95% confidence interval on the difference in the two proportions. Round your answer to four decimal places (e.g. 98.7654).
Answers
Answer:
5.006
Step-by-step explanation:
3x+2=198
Solve it as Soon as possible!
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's solve for x ~
[tex]3x + 2 = 198[/tex][tex]3x = 198 - 2[/tex][tex]3x = 196[/tex][tex] \boxed{ \boxed{x = \dfrac{196}{3} } \: \: or \: \: \boxed{ x = 65.33}}[/tex]Answer:
[tex]\boxed{\blue{ = \frac{196}{3}}} [/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
3x+2=198
Step 1: Subtract 2 from both sides.
3x+2−2=198−2
3x=196
Step 2: Divide both sides by 3.
[tex] \tt \: \frac{3x}{3} = \frac{196}{3} [/tex]
Result:
[tex]\boxed{\underline{ x = \frac{196}{3}}} [/tex]
A man covers a distance of 150m in 1.5mins. Find the average speed in km per hour
Answers
Answer:
6 Km / hour
Step-by-step explanation:
Convert distance to Km ( 1 Km = 1000 m )
150 m = 150 ÷ 1000 = 0.15 Km
Convert 1.5 mins to hours ( 1 hour = 60 minutes )
1.5 = 1.5 ÷ 60 = 0.025 hours
average speed = [tex]\frac{distance}{time}[/tex] = [tex]\frac{0.15}{0.025}[/tex] = 6 Km / hour
The average speed in km per hour is 6 kilometers per hour
How to determine the average speed?The given parameters are:
Distance = 150 mTime = 1.5 minsConvert meters to kilometers
Distance = 150/1000 km
Distance = 0.15 km
Convert minutes to hours
Time = 1.5/60 hour
Time = 0.025 hour
The average speed is then calculated as:
Speed = Distance/Time
This gives
Speed = 0.15 km/0.025 hour
Evaluate
Speed = 6 kilometers per hour
Hence, the average speed in km per hour is 6 kilometers per hour
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The box plots shown represent the average mileage of two different types of cars. Use the box plots to compare the data sets. Drag each value to show if it is greater for SUVs, greater for sedans, or if there is not enough information to tell.
Answers
Answer:
Parallel box and whisker plots are regular box and whisker plots, but drawn "one-above-the other" on the piece of paper. To enable to do this easily, draw an x-axis which is big enough for the largest value in the data, and small enough for the smallest value in the data (in the entire collection of data). Plot each box-and-whisker diagram below each other.
Step-by-step explanation:
pls mark
Answer:
Parallel box and whisker plots are regular box and whisker plots, but drawn "one-above-the other" on the piece of paper.
Step-by-step explanation:
What value of x makes the equation true?
Answers
Answer:
x = 9/4
Step-by-step explanation:
-3x + 10 = 5x - 8
Add 3x to both sides
10 = 8x - 8
Add 8 to both sides
18 = 8x
Divide both sides by 8
18/8 = x
Reduce
9/4 = x
x = 9/4
Use the discriminant formula to find the number of x-intercepts in the graph of the equation.
x2 – 3x + 2 =y
b2 - 4ac
Answers
Answer:
2
Step-by-step explanation:
The values of a, b, c are ...
a = 1, b = -3, c = 2
Then the discriminant is ...
d = b^2 -4ac
d = (-3)^2 -4(1)(2) = 9 -8 = 1
The discriminant is positive, so there are two x-intercepts.
_____
Additional comment
The indications given by the discriminant are ...
d > 0, 2 real roots (2 x-intercepts)
d = 0, 1 real root (1 x-intercept)
d < 0, 2 complex roots (0 x-intercepts)
What is the sum of the numbers
1*2+2*3+.....n(n+1)
Answers
Answer:
8+n²+n
Step-by-step explanation:
Simplfy the expression
Find the area of the polynomial:
A.) 6a^3 + 12a^2 − 15a
B.) 6a^3 + 12a − 15
C.) 6a^2 + 12a − 15
D.) 5a^2 + 7a − 2
Answers
Answer:
A.) 6a^3 + 12a^2 - 15a
Step-by-step explanation:
Area = w * l
Area = 3a(2a^2 + 4a - 5)
Area = 6a^3 + 12a^2 - 15a
If Dylan does a job in 50 hours and Kristen does a job in 75 hours, how long will it take them to do the job
together?
