Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
What are the domain and range?
The domain and range of a function are the set of all the inputs and outputs a function can give respectively. The domain and range are important aspects of a function. The domain takes all the possible input values from the set of real numbers and the range takes all the output values of the function.
We have the functions, f(x) = eˣ and g(x) = x+6
So, their composition will be g(f(x)).
Then, g(f(x)) = g(eˣ) = eˣ+6
Thus, g(f(x)) = eˣ+6.
Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.
Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.
Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
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Keisha reads a label on a measuring cup that shows 16 fluid ounces is the same as 2 cups. Using this information, how many fluid ounces are in 6 cups?
Salut/Hello!
Answer: 48 fluid ounces are in 6 cups
Step-by-step explanation:
We know there are 16 fluid ounces in 2 identical cups which results one cup is equal to 16 ÷ 2 = 8
After that we can find out how many fluid ounces are in 6 cups. 6 × 8 = 48
I hope it'll be useful! :]
At noon, a 36 foot building casts a 20 foot shadow. Find the shadow cast by a 6 foot tree. Set up a proportion and solve. Be sure to show all your work!
Answer:
3 1/3 ft
Step-by-step explanation:
Let SHADOW and HEIGHT pertain to the building, and let shadow and height pertain to the tree.
The proportion is:
HEIGHT/SHADOW = height/shadow
Now we fill in with the numbers we know, and "shadow" for the shadow of the tree.
(36 ft)/(20 ft) = (6 ft)/(shadow)
Cross multiply.
36 × shadow = 6 × 20
36 × shadow = 120
shadow = 120/36 = 10/3
shadow = 3 1/3
Answer: 3 1/3 ft
Is the point (-1, 6) on the lines below? y = 5x + 3 y = 2x + 4
The point (-1, 6) is on the lines y = 5x + 3 and y = 2x + 4
How to determine if the points is on the lineFrom the question, we have the following parameters that can be used in our computation:
Point = (-1, 6)
Also, we have
y = 5x + 3
y = 2x + 4
Substitute the known values in the above equation, so, we have the following representation
6 = 5(-1) + 3 = -2 -- false
6 = 2(-1) + 4 = 2 --- false
Hence, the point is not one the line
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If four people are chosen for a team out of a group of seven, how many possible combinations are there (order does
not matter)
Finding the Reflection Line On a coordinate plane, triangle 1 is reflected across the x-axis to form triangle 4, is reflected across a diagonal to form triangle 3, is reflected across the y-axis to form triangle 2. Use the figure to complete the statements. Triangle 1 is the image of triangle 2 reflected over the . Triangle 2 is the image of triangle 3 reflected over the . Reflecting triangle 4 over the y-axis results in triangle .
The statements are Triangle 1 is the image of triangle 2 reflected over the Y axis, Triangle 2 is the image of triangle 3 reflected over the X axis and Reflecting triangle 4 over the y-axis results in triangle 3.
What is Reflection?Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
We have four triangles in the figure given.
So reflection of a figure results in the mirror image of the figure.
Line of reflection is the line through which a figure is reflected.
Line of reflection of the triangles 1 and 2 is the Y axis.
So Triangle 1 is the image of triangle 2 reflected over the Y axis.
Line of reflection of triangles 2 and 3 is X axis.
So Triangle 2 is the image of triangle 3 reflected over the X axis.
Also line of reflection is y axis for triangles 4 and 3.
So Reflecting triangle 4 over the y-axis results in triangle 3.
Hence using the concept of line of reflections, Triangle 1 is the image of triangle 2 reflected over the Y axis, Triangle 2 is the image of triangle 3 reflected over the X axis and Reflecting triangle 4 over the y-axis results in triangle 3.
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Larry and Donna bought a sofa at the sale price of $1,152. The original price of the sofa was $1,920.
Find the amount of discount in dollars.
The discount in dollars is $768.
This is a question of simple subtraction.
A sale price is the discounted price at which goods or services are being sold. This price is usually offered for a limited period of time
Discounted Amount means an amount equal to the sum of the Offer Discount, Volume Discount and Payment Discount, applied to the List Price of all Eligible Products ordered by the Customer under these Terms.
Larry and Donna bought a sofa at the sale price of $1152.
The original price of the sofa was $1920.
So, Discounted amount of the sofa= (Original price of the sofa- Sale price of the sofa)
i.e, ($1920-$1152)= $768.
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When an object is dropped from above the ground the equation Y= 16x ^2 represents the number of feet y that the object falls in X seconds until it hits the ground a student claims that Y is not a function of X because X is squared is the student correct
The student is not correct. Y = 16x^2 is a function of X.
A function is a mathematical relationship between two variables, where each value of the independent variable (in this case, X) corresponds to exactly one value of the dependent variable (in this case, Y). The equation Y = 16x^2 satisfies this definition.
The fact that X is squared in the equation does not mean that it is not a function of X. In this case, Y is a function of X because for each value of X, there is a unique value of Y determined by the equation Y = 16x^2.
This equation represent the distance an object falls (Y) in a certain amount of time (X) assuming that the only force acting on the object is gravity, and the acceleration due to gravity is constant (approximately 9.8 m/s^2 or 32 ft/s^2). The equation Y = 16x^2 is known as the equation of motion under gravity.
When you deposit your funds in a financial institution such as a bank, your
money is protected by:
A. Certificate of Deposit Insurance (CDI).
B. the Federal Bank Protection Act (FBPA).
OC. the Federal Deposit Insurance Corporation (FDIC).
OD. the security arrangement with your bank.
When you deposit your funds in a financial institution such as a bank, your money is protected by the Federal Deposit Insurance Corporation (FDIC).
What is deposit in bank ?
deposit in bank nothing but when we want to store the money and by depositing the money in the bank ensures us more security.
Deposit coverage is one of the sizable benefits of getting an account at an FDIC-insured bank—it’s how the FDIC protects your cash within the not going event of a bank failure. the usual insurance amount is $250,000 according to depositor, according to insured bank, for each account possession category. and you don’t need to purchase deposit insurance. in case you open a deposit account in an FDIC-insured bank, you're mechanically blanketed. test out the assets in this page to learn extra about deposit coverage.
Hence, When you deposit your funds in a financial institution such as a bank, your money is protected by the Federal Deposit Insurance Corporation (FDIC).
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Answer:
C. the Federal Deposit Insurance Corporation (FDIC)
Step-by-step explanation:
if a room dimension measures a lenght of 350m and width of 200m calculate the number of square tiles of lenght 5m would be needed to tile the entire room
Answer: 2800 Tiles
Step-by-step explanation: area of the room = l × b
= 350 × 200 = 70,000
Area covered by one tile = 5 × 5 = 25
No. of tiles required to cover entire room = 70,000/25
= 2,800
total 2,800 tiles would be needed to tile the complete room.
Answer:
Step-by-step explanation:
Just divide the two areas 350 x 200 /(5 x 5)
350 x 8 = 2800 tiles
Consider the sequence:
4, 12, 20, 28, 36, 44, 52,...
Find the nth term of the sequence.
Answer:
68
Step-by-step explanation:
52+8=60
60+8=68
each time I add 8
Answer: 8n+4
Step-by-step explanation:
The numbers go up in 8, so we know its 8n.
If you put the 8 times table above these set of numbers, yo would get this-
8, 16, 24, 32, 40, 48, 56...
4, 12, 20, 28, 36, 44, 52...
Therefore you must add 4 to get to 8.
List all the multiples of 2
Answer:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc.
Step-by-step explanation:
It's counting by two's.
On what interval is the following function increasing and negative?
The function is increasing and negative on (3п/2, 2п)
A and B are two cities.
a) Measure the bearing of B from A.
b) Measure the bearing of A from B.
Ax to Bx
a) Measure the bearing of B from A = 030
b) Measure the bearing of A from B = 210
What is bearing angle?The term bearing is used in the navigation. The bearing is the horizontal angle which is made between the direction of an object to the another object.
This angle is measure in the clockwise direction from the north direction.
To measure bearing of two cities:
Draw a straight line between point A and B upward. Now draw 2 lines vertically up going through both points as shown in attached image. Now measure the angle between the vertical line and the diagonal line. It's 030.
Hence, measure the bearing of B from A is 030.
To measure the bearing of A from B add 180 to the 030.
we get 210.
Hence, measure the bearing of A from B is 210.
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A new van is priced at $19,500. If the buyer chooses to finance, they will pay $5,000 as a down payment and $375 per month. After how many months will the buyer have paid more that $10,000 toward the van?
A. 19,500 — 375x < 10,000
B. 5,000x + 375 > 10,000
C. 19,500 — 5000x > 10,000
D. 5,000 + 375 > 10,000
The inequality that represents the situation is . 5,000x + 375 > 10,000
(option b)
What is the the inequality?
The inequality that can be used to determine after how many months he would have paid more than $10,000 has this form:
down payment + (monthly payment x number of months) > $10,000
$5,000 + ($375 x m) > $10,000
$5,000 + $375m > $10,000
In order to determine the value of m, take the following steps:
Combine similar terms together:
375m > 10,000 - 5,000
Add similar terms together:
375m > $5000
Divide both sides of the equation by 375
m > 5000 / 375
m > 13.3 days
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A hot air ballon is hovering 104 meters above the ground and begins to assend at a rate of 11 meters per second. Let
y be the height of the balloon in meters x seconds after it begins to assend.
Write an equation in slope-intercept form that models the height of the balloon.
How high is the balloon after 19 seconds?
Answer: The height of the balloon in meters x seconds after it begins to ascend can be represented by the equation y = mx + b, where m is the slope (the rate of change in height) and b is the y-intercept (the initial height of the balloon).
Given that the balloon is hovering 104 meters above the ground and begins to ascend at a rate of 11 meters per second, we can substitute these values into the equation:
y = 11x + 104
This equation is in slope-intercept form, the slope (m) is 11 and the y-intercept (b) is 104. This equation represents the height of the balloon in meters x seconds after it begins to ascend.
To find the height of the balloon after 19 seconds, we can substitute x = 19 into the equation:
y = 11(19) + 104 = 209 meters
So the hot air balloon is 209 meters high after 19 seconds.
Step-by-step explanation:
37 hundredths= ____ tenths + ____ hundredths
Show each inequality on a number line and then write all the one-digit integers that satisfy it. k ≥0
The one-digit integers that satisfy the inequality k>0 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A number is a line that is made up of positive and negative numbers with the distance between the preceding and succeeding unit to be 1.
The negative values on the number line are -1, -2, -3...-9 while the value greater than zero are 1, 2, 3, 4,...9
Hence the one-digit integers that satisfy the inequality k>0 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
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The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 600 people. By selling tickets, the members would like to raise $3,900 every night to cover all expenses. Let x represent the number of adult tickets sold at $8.50. Let y represent the number of student tickets sold at $5.50 each. If all 600 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3,900? At one performance there were times as many student tickets sold as adult tickets. If there were 400 tickets sold at that performance, how much below the goal of $3,900 did ticket sales fall?
By using simultaneous linear equation, it can be calculated that 200 adult tickets and 400 student tickets were sold and the ticket sale falls $1320 below the goal of $3300.
What is simultaneous linear equation?Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation. Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
The simultaneous linear equation needs to be solved
Let d represents the number of adult tickets and s represents the number of student tickets
Their auditorium holds 600 people
d + s = 600 ..... (1)
Price of adult ticket = $7.50
Price of student ticket = $4.50
Total price = $(7.50d + 4.50s)
Therefore,
7.50d + 4.50s = 3300
5d + 3s = 2200 ..... (2)
Multiplying (1) by 3
3d + 3s = 1800.... (3)
Subtracting (3) from (2)
2d = 400
d = 200
Putting the value of d in (1)
200 + s = 600
s = 600 - 200
s = 400
Now, Total tickets sold = d + 2d = 3d
d = 120
s = 240
Number of student ticket sold = 240
Number of adult ticket sold = 120
Total cost = 240 4.50 + 120 7.50
= $1980
Fall in ticket sale = $(3300 - 1980) = $1320
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M varies jointly as r² and as l. If M = 20 when I = 8 and r = 2, find: (a) the law connecting these variables, (b) r when M = 400 and l=10.
Answer:
(a) Law connecting the variables:
[tex]M = \frac{5}{8}Ir^{2}[/tex]
(b) r = 8 and r = -8
Step-by-step explanation:
(a) Equation for a joint variation is:
[tex]M = KIr^{2}[/tex] where K is the constant
Substituting the provided values of M, I and r:
= [tex]20 = K(8)(2^{2} )[/tex]
= [tex]20 = K(8)(4)[/tex]
= 20 = 32K
= [tex]K = \frac{20}{32}[/tex]
[Divide the numerator and the denominator by the highest common factor (i.e. 4)]
= [tex]K = \frac{5}{8}[/tex]
Therefore:
[tex]M = \frac{5}{8}Ir^{2}[/tex]
(b) [tex]M = \frac{5}{8} I r^{2}[/tex]
Substituting the values of M and I:
[tex]400 = \frac{5}{8} (10)r^{2}[/tex]
[tex]400 = \frac{5}{8} (10)r^{2}[/tex]
[tex]400 = \frac{50}{8} r^{2}[/tex]
[tex]\frac{(400)(8)}{500} =r^{2}[/tex]
[tex]\frac{3200}{50} = r^{2}[/tex]
[tex]64 =r^{2}[/tex]
Taking the square root on both sides of the equation:
[tex]r = \sqrt{64}[/tex]
[tex]r = 8[/tex] and [tex]r = -8[/tex]
find values of x where the horizontal asymptote cross the graph of function f(x)=x^2-1/x^3
The rational function should be set to p and x should be solved if there is a horizontal asymptote,
How do you determine the location where a graph reaches a horizontal asymptote?The rational function should be set to p and x should be solved if there is a horizontal asymptote, such as y=p. In the event that x is a real number, the line crosses the horizontal asymptote at (x,p).
Although your function ultimately reaches for the H.A., it doesn't mean it never touches the line. Set the equation equal to that value and solve to determine which values of x, if any, allow the function to touch the H.A. to determine if it does.
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There are no values of x where the horizontal asymptote crosses the graph of the function.
How do you determine the location where a graph reaches a horizontal asymptote?The rational function should be set to p and x should be solved if there is a horizontal asymptote, such as y=p. In the event that x is a real number, the line crosses the horizontal asymptote at (x,p).
A horizontal asymptote occurs when the function approaches a constant value as the input goes towards positive or negative infinity.
For the graph of the function f(x) = x² - 1/x³, there are no horizontal asymptotes.
A horizontal asymptote would occur if the highest power of x in the numerator of f(x) was equal to the highest power of x in the denominator, but the denominator of f(x) doesn't have any powers of x, so there is no horizontal asymptote.
Therefore, there are no values of x where the horizontal asymptote crosses the graph of the function.
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5 tan x -3 = 1 solve this equation for 0° ≤ x ≤ 360° make a sketch of the graph and indicate all the solutions.
Answer: 38.66 degrees and 218.66 degrees
Step-by-step explanation:
which exponential function decreases faster
100(.2661)^t
100(.1593)^t
The exponential function that decreases faster is given as follows:
100(.1593)^t.
How to model an exponential function?A decaying exponential function is modeled as follows:
y = a(1 - r)^x.
In which the parameters are given as follows:
a is the initial value.r is the decay rate, as a decimal.The decay rate of each exponential function in this problem is given as follows:
100(.2661)^t: 1 - r = 0.2661 -> r = 0.7339.100(0.1593)^t: 1 - r = 0.1593 -> r = 0.8407.The function with the higher decay rate is the one that decays faster.
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Describe the graph of the quadratic function
Quadratic equations is another name for them. ax² + bx + c = 0 is the quadratic equation's general form.
What is meant by quadratic function?A polynomial of degree two in one or more variables is referred to as a quadratic polynomial in mathematics. A polynomial function that is defined by a quadratic polynomial is known as a quadratic function.
A second-degree polynomial equation, which must contain at least one squared component, is what is known as a quadratic. Quadratic equations is another name for them. ax² + bx + c = 0 is the quadratic equation's general form.
A parabola is a curved form that represents the graph of a quadratic function. A parabola's vertex is one of its focal points. Its graph's highest or lowest point is where it is. Consider it similar to the parabola's endpoint.
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How much would you need to invest in a money market account if you would like to have $5,000 in the account at the end of 3 years? The account provides an APR of 5% compounded monthly.
Answer:
To calculate the amount you would need to invest in a money market account to have $5,000 at the end of 3 years, we can use the formula for future value of an investment:
FV = PV(1+r)^n
where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), and n is the number of compounding periods.
In this case,
FV = $5,000 (future value)
r = 5% (APR) = 0.05 (as a decimal)
n = 3 years * 12 (months) = 36
So we can use the formula:
PV = FV / (1 + r)^n
PV = $5,000 / (1 + 0.05)^36
PV ≈ $3,716.76
So you would need to invest $3,716.76 in the money market account to have $5,000 in the account at the end of 3 years.
The sum of the present ages of Kathy and Samantha is 60 years. In 8 years, Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago. How old are they now? Write it in a equation
Answer:
Kathy is 48 years old and Samantha is 12.
Step-by-step explanation:
This is a challenging question that requires some interpretation. Let K and S stand for the current ages of Kathy and Samatha.
We are told that: K+S = 60
And, in 8 years: K+8 and S+8
"Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago" ["3 years ago:" from now or in 8 years. I'll interpret it as from now, or (S-3)]
(K+8) = 3(S+8-3)+5 ["5 years older than 3 times as old as Samantha was 3 years ago"]
(K+8) = 3(S+5)+5
K+8 = 3S+20
K = 3S+12
---
Rearrange the firts equation to isolate K
K = 60-S
Now use this definition of K in the previous equation:
K = 3S+12
60-S = 3S+12
4S = 48
S = 12
K+S = 60
K+12 = 60
K = 48
=====
CHECK
Does K + S = 60? 48+12 = 60 YES
In 8 years, will Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago?
K = 48+8 = 56
S = 12+8 = 20
Three years ago S was 9.
(K+8) = 3(S+8-3)+5
(K+8) = 3(12+8-3)+5
K + 8 = 3(17)+5
K = 48
===
Kathy is 48 years old and Samantha is 12.
find the derivative by first principle rule f(x)=3÷x+2
Answer:
The derivative of f(x) = 3 ÷ x + 2 is f'(x) = -3 ÷ (x+2)².
Step-by-step explanation:
This is found by using the first principle method of differentiation, which states that the derivative of a function is the rate of change of the function with respect to the indepedent variable. In other words, the derivative of a function measures how much the output of the function changes with respect to a small change in the input.
To find the derivative of f(x) = 3 ÷ x + 2, we start by taking the limit as h approaches 0 of the difference quotient (f(x + h) - f(x)) ÷ h.
The difference quotient is (3 ÷ (x + h + 2) - 3 ÷ (x + 2)) ÷ h. Simplified, this becomes 3h ÷ (x + h + 2)(x + 2).
When h approaches 0, the difference quotient becomes 3 ÷ (x + 2)², which is the derivative of f(x).
What is
equal to? (5 points)
3^3/2
3^√9
2^√9
3^√27
2^√27
The expression 3^(3/2) is equal to ²√27. The 4th option is the answer
How to find what is equal to 3^(3/2)?
Index is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.
The expression 3^(3/2) can be written in form of root and power. That is:
3^(3/2) = ²√3³
3^(3/2) = ²√27
Therefore, the expression 3^(3/2) is equal to ²√27
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Write 6/7 as a decimal rounded to three decimal places.
Show step by step long division please :)
Answer:
0.857
Step-by-step explanation:
----------------
7 | 6
7 goes 0 times into 6, so we write a 0.
0.
----------------
7 | 6.0
Add .0 to 6 to get 6.0
7 goes 8 times into 60.
8 × 7 = 56
0.8
----------------
7 | 6.0
- 5.6
------------
60 - 56 = 4
Write another 0, 6.00, and bring down a zero.
0.8
----------------
7 | 6.00
- 5.6
------------
40
7 goes 5 times into 40.
0.85
----------------
7 | 6.00
- 5.6
------------
40
- 35
---------
40 - 35 = 5
Add another 0 to 6.00 to get 6.000; bring down that zero.
Now you have 50.
0.857
----------------
7 | 6.000
- 5.6
------------
40
- 35
---------
50
7 goes 7 times into 50.
7 × 7 = 49
Add a zero, bring down a zero,
0.857
----------------
7 | 6.0000
- 5.6
------------
40
- 35
---------
50
- 49
-----------
10
7 goes 1 time into 10.
You end up with 0.8571
0.8571
----------------
7 | 6.0000
- 5.6
------------
40
- 35
---------
50
- 49
-----------
10
- 7
-----------
3
0.8571 rounds to 0.857
Find the sum of the first 5 terms of a G.P whose first term is 3 and its common ration ¼ to four Significant figure.
Answer:85
Step-by-step explanation:
PLEASE HELP I NEED WORK SHOWN DONT UNDERSTAND
3. A radio station has a tower that is 25 miles east and 32 miles north of downtown Squirrel
Hills. The tower emits a signal that reaches receivers that are within 45 miles of its
location.
A) Write an equation in general form that describes the locations within the receiving
distance of the tower.
B) Determine if Squirrel Hills is within the receiving distance of the signal.
I
An equation in general form that describes the locations within the receiving distance of the tower is (x - 25)² + (y - 32)² = (45)².
And Squirrel Hills is within the receiving distance of the signal.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Given:
A radio station has a tower that is 25 miles east and 32 miles north of downtown Squirrel Hills.
The tower emits a signal that reaches receivers that are within 45 miles of its location.
From the attached image,
(25, 32) is the location of the tower.
And (0, 0) is the location of Hill.
So, equation,
(x - 25)² + (y - 32)² = (45)²
To determine if Squirrel Hills is within the receiving distance of the signal:
That means,
when (x, y) = (0, 0),
(0 - 25)² + (0 - 32)² = (45)²
1649 < 2025
That means, the Squirrel Hills is within the receiving distance of the signal.
Therefore, the Squirrel Hills is within the receiving distance of the signal.
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