1.Find equations for two lines that are both tangent to the curve y=x^3−3x^2+3x−3 and parallel to the line 3x−y=15. 2.At what point on the curve y=1+2c^2−3x is the tangent line parallel to the line 3x−y=5 ? Illustrate by graphing the curve and both lines. 3.Find an equation of the normal line to the curve y=√x that is parallel to the line 2x+y=1
Answers
1. Equations for two tangent lines parallel to the line 3x - y = 15: y = 3x - 3 and y = 3x - 5.
2. No point on the curve \(y = 1 + 2c^2 - 3x\) where the tangent line is parallel to 3x - y = 5.
3. Equation of the normal line to y = √x parallel to 2x + y = 1: 2√ax + y = 2a + 1.
1. To find equations for two lines that are both tangent to the curve \(\(y = x^3 - 3x^2 + 3x - 3\)\) and parallel to the line 3x - y = 15, we need to determine the points of tangency and the slope of the tangent lines.
First, let's find the derivative of the curve \(\(y = x^3 - 3x^2 + 3x - 3\)\). Taking the derivative with respect to \(x\), we get:
\(\(\frac{dy}{dx} = 3x^2 - 6x + 3\)\)
Setting the derivative equal to 3:
\(\(3x^2 - 6x + 3 = 3\)\)
\(\(3x^2 - 6x = 0\)\)
3x(x - 2) = 0
This equation gives us two possible values for x: x = 0 and x = 2.
For \(\(x = 0\), \(y = (0)^3 - 3(0)^2 + 3(0) - 3 = -3\)\), giving us the point (0, -3).
For \(\(x = 2\), \(y = (2)^3 - 3(2)^2 + 3(2) - 3 = 1\)\), giving us the point (2, 1).
Using point-slope form for the first line (tangent at point (0, -3)):
\(\(y - (-3) = 3(x - 0)\)\\\(y + 3 = 3x\)\\\(y = 3x - 3\)\)(equation for the first tangent line)
Using point-slope form for the second line (tangent at point (2, 1)):
\(\(y - 1 = 3(x - 2)\)\\\(y - 1 = 3x - 6\)\\\\\(y = 3x - 5\)\) (equation for the second tangent line)
Therefore, the equations for the two lines that are both tangent to the curve \(\(y = x^3 - 3x^2 + 3x - 3\)\)and parallel to the line \(\(3x - y = 15\) are \(y = 3x - 3\) and \(y = 3x - 5\).\)
2. To find the point on the curve \(\(y = 1 + 2c^2 - 3x\)\) where the tangent line is parallel to the line 3x - y = 5, we need to find the slope of the tangent line and equate it to the slope of the given line.
The slope of the given line is m = 3.
To find the slope of the tangent line, we take the derivative of the curve \(\(y = 1 + 2c^2 - 3x\)\) with respect to x:
\(\(\frac{dy}{dx} = -3\)\)
Since the tangent line is parallel to the given line, the slope of the tangent line is also m = 3.
Equating the slopes, we have:-3 = 3
This equation is not possible to solve, which means there is no point on the curve \(\(y = 1 + 2c^2 - 3x\)\) where the tangent line is parallel to the line 3x - y = 5.
To illustrate this graphically, we can plot the curve\(\(y = 1 + 2c^2 - 3x\)\) and the line 3x - y = 5 on a graph.
Let's choose c = 1. Plugging this value into the curve equation, we have \(\(y = 1 + 2(1)^2 - 3x\)\), which simplifies to y = 3 - 3x.
As we can see from the graph, the curve and the line do not intersect at any point, indicating that there is no point on the curve where the tangent line is parallel to the line 3x - y = 5.
3. To find the equation of the normal line to the curve \(\(y = \sqrt{x}\)\) that is parallel to the line 2x + y = 1, we need to determine the slope of the normal line and a point on the line.
The given line 2x + y = 1 can be rewritten in slope-intercept form as y = -2x + 1. Since the normal line is parallel to this line, it will have the same slope, which is m = -2.
The slope of the tangent line to the curve \(\(y = \sqrt{x}\)\) at any point can be found by taking the derivative of the curve with respect to x. The derivative of \(\(\sqrt{x}\) is \(\frac{1}{2\sqrt{x}}\)\). Evaluating this derivative at a specific x value will give us the slope of the tangent line at that point.
Let's choose a value of x = a to represent the point where the normal line is parallel to the line 2x + y = 1. The slope of the tangent line at this point is \(\(\frac{1}{2\sqrt{a}}\).\)
Since the normal line is perpendicular to the tangent line, the slope of the normal line will be the negative reciprocal of the tangent line's slope. Therefore, the slope of the normal line is \(\(-2\sqrt{a}\)\).
Now, we have the slope \(\(-2\sqrt{a}\)\) and a point\(\((a, \sqrt{a})\)\)on the normal line. Using the point-slope form of a line, we can write the equation of the normal line:
\(\(y - \sqrt{a} = -2\sqrt{a}(x - a)\)\)
Expanding and simplifying:
\(\(y - \sqrt{a} = -2\sqrt{a}x + 2a\sqrt{a}\)\)
Rearranging the equation to match the standard form Ax + By = C:
\(\(2\sqrt{a}x + y = 2a\sqrt{a} + \sqrt{a}\)\\\\\(2\sqrt{a}x + y = (2a + 1)\sqrt{a}\)\)
Multiplying through by \(\(\frac{1}{\sqrt{a}}\)\) to rationalize the expression:
\(\(\frac{2}{\sqrt{a}}x + \frac{1}{\sqrt{a}}y = 2a + 1\)\)
Finally, simplifying the equation:
\(\(2\sqrt{a}x + y = (2a + 1)\)\)
Therefore, the equation of the normal line to the curve \(\(y = \sqrt{x}\)\) that is parallel to the line \(\(2x + y = 1\) is \(2\sqrt{a}x + y = 2a + 1\)\), where a is the chosen value of x on the curve.
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Related Questions
/\(\frac{x-9}{15} =\frac{2x-9}{10\\}\)
Answers
Step-by-step explanation:
\( \frac{x - 9}{15} = \frac{2x - 9}{10} \\ \)
\( \frac{x - 9}{3} = \frac{2x - 9}{2} \\ \)
\(2( x - 9) = 3(2x - 9) \\ \)
\(2x - 18 = 6x - 27\)
\(27 - 18 = 6x - 2x\)
\(9 = 4x\)
\(x = \frac{9}{4} \\ \)
(2) Joshua needed to put 5 cookies in each gift box. He had 16 chocolate chip cookies and 19 oatmeal cookies. How many boxes could he fill with cookies?
Answers
Answer:
7 boxes
Step-by-step explanation:
16+19 is 35. divide 35 by 5 and you get 7 boxes
allen and ben are painting a fence. the ratio of the amount of work allen does to the amount of work ben does is $3:5$. if the fence requires a total of $240$ square feet to be painted, how many square feet does ben paint?
Answers
The fence Ben paints is 150 square feet.
Given:
ratio of the amount of work allen does to the amount of work ben does is 3:5
allen : ben = 3:5
total work done in ratio = 3 + 5 = 8
Count the fence Ben paints
Since , fence requires a total of 240 square feet to be painted
Thus, ben = ratio of ben/ total ratio × total of works
ben = 5/8 × 240
ben = 1,200/8
ben = 150
Hence , The fence Ben paints is 150 square feet .
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compnay a charges $82 and allows unlimited mileage. company b has an intial fee of $55 and charges an additional $0.60 for every mile driven. for what mileage will company a charge less than company b
Answers
For distances of 45 miles or less, Company A is cheaper, while for distances greater than 45 miles, Company B is the cheaper option.
To determine at what mileage Company A charges less than Company B, we can set up an equation and solve for the variable, which in this case will represent the number of miles driven. Let x be the number of miles driven, and let C(x) represent the cost of renting a car from Company B after driving x miles.
We know that Company A charges a flat fee of $82 for unlimited mileage, so we can represent the cost of renting from Company A as a constant function C(x) = 82. For Company B, the cost function is given by:
C(x) = 55 + 0.60x
We want to find the value of x for which Company A charges less than Company B. In other words, we want to find the point at which the two cost functions intersect. To do this, we can set the two functions equal to each other and solve for x:
82 = 55 + 0.60x
27 = 0.60x
x = 45
Therefore, when the number of miles driven is 45 or less, Company A charges less than Company B. For any mileage greater than 45, it is cheaper to rent from Company B.
In summary, Company A charges a flat rate of $82 for unlimited mileage, while Company B charges an initial fee of $55 and an additional $0.60 for every mile driven. To find the point at which Company A charges less than Company B, we set the two cost functions equal to each other and solve for the number of miles driven. The result is 45 miles, meaning that for any distance of 45 miles or less, it is cheaper to rent from Company A, while for any distance greater than 45 miles, Company B is the cheaper option.
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Kareem is trying to decide which college to attend full time next year. Kareem believes there is a 55% chance that he will attend State College and a 33% chance that he will attend Northern University. The probability that Kareem will attend either State or Northern is (state your answer as a decimal and round your answer to two decimal places).
Answers
The probability that Kareem will attend either State or Northern is 0.88, which is 88% as a percentage. Rounded to two decimal places, the answer is 0.88.
The probability that Kareem will attend either State or Northern is the sum of the individual probabilities of attending each college.
Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain.
The probability of an event A is calculated as the number of outcomes that result in A divided by the total number of possible outcomes. This is known as the classical definition of probability.
P(State or Northern) = P(State) + P(Northern) = 0.55 + 0.33 = 0.88
So the probability that Kareem will attend either State or Northern is 0.88, which is 88% as a percentage. Rounded to two decimal places, the answer is 0.88.
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A horizontally thrown dart falls 5 cm before it travels 2. 5 m to hit the dart board. how fast was it thrown?
Answers
The dart player throws a dart horizontally at a speed of 24.75 m/s.
In this question,
The horizontal distance traveled by the dart, x = 2.5 m
The dart hits the board 5 cm below the height from which it was thrown.
⇒ 5 cm = 0.05 m
Let the time taken by the dart to hit the board is t.
The time taken can be calculated using the Newton's second law of motion,
\(y = ut+\frac{1}{2}at^{2}\)
Put, u = 0, a = -g and g = 9.8
On substituting the above values, we get
⇒ \(-0.05 = 0-\frac{1}{2}(9.8)t^{2}\)
⇒ \(0.05(\frac{2}{9.8}) = t^{2}\)
⇒ \(t^{2} =0.0102\)
⇒ \(t=\sqrt{0.0102}\)
⇒ t = 0.1010 s
Now, the velocity (speed) can be calculated as
displacement = speed × time
⇒ 2.5 = speed × 0.1010
⇒ speed = \(\frac{2.5}{0.1010}\)
⇒ speed = 24.7524 m/s
Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.
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PLSSSSS!!!!!! HELP ME!!!! I WIL MARK U!!!!!
Answers
Answer:
-44
Step-by-step explanation:
You multiply 11 times 2 to the second power then multiply negative 1
That is bro it’s easy
A motorcycle has a maximum power of 72 kilowatts. The motorcycle and its rider are travelling along a straight horizontal road. When they are moving at a speed of Vm s 1, they experience a total resistance force of magnitude kV newtons, where k is a constant The maximum speed of the motorcycle and its rider is 60 m s- Show that k = 20
Answers
To show that k = 20, we need to use the given information about the motorcycle's maximum power and maximum speed.
We know that the maximum power of the motorcycle is 72 kilowatts. We can convert this to watts by multiplying by 1000, giving us 72,000 watts.
We also know that the maximum speed of the motorcycle and its rider is 60 m/s. At this speed, the resistance force is equal to kV newtons.
We can use the formula for power to relate the maximum power to the resistance force and speed:
Power = Force x Velocity
Since the motorcycle is moving at its maximum speed, we can use the maximum power to find the maximum force:
72,000 = Force x 60
Solving for the force, we get:
Force = 1,200 newtons
Now we can use this maximum force and the maximum speed to find the value of k:
1,200 = k x 60
Solving for k, we get:
k = 20
Therefore, we have shown that k = 20, as required.
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4x + y = 4
2x + 6y = 24
Which action creates an equivalent system that will eliminate one variable when they are combined?
Group of answer choices
Multiply the first equation by −4 to get −16x − 4y = −16.
Multiply the second equation by −4 to get −8x − 24y = −96.
Multiply the first equation by −2 to get −8x − 2y = −8.
Multiply the second equation by −2 to get −4x − 12y = −48.
Answers
The correct option is the last one, multiply the second equation by −2 to get −4x − 12y = −48.
Which action creates an equivalent system that will eliminate one variable when they are combined?Here we have the system:
4x + y = 4
2x + 6y = 24
One way to eliminate one of the variables is:
Adding the first equation and -2times the second one, then we will get:
4x + y + -2*(2x + 6y) = 4 + -2*24
4x + y - 4x - 12y = -44
-11y = -44
And we removed variable x, so the correct option is the last one.
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Is the graph increasing, decreasing, or constant?
O A. Increasing
• B. Decreasing
C. Constant
Answers
Answer:
b decreasing its korrect now
If (3.46)²-(1.54 ) 2 = 10x
find the value of x
Answers
Answer:
x = 0.96
Step-by-step explanation:
Given
(3.46)² - (1.54)² = 10x, evaluate left side
11.9716 - 2.3716 = 10x
9.6 = 10x ( divide both sides by 10 )
0.96 = x
Answer:
\(x = 0.88916\)
Step-by-step explanation:
\(If \: (3.46)² \: - \: (1.54 ) 2 = 10x \\ 11.9716\: - \: 3.08 = 10x \\10x = 11.9716\: - \: 3.08 \\ 10x = 8.8916 \\ x = \frac{8.8916}{10} = 0.88916\)
In a greenhouse, basil is grown in planters that have a base of 5 1/2 in by 1 2/3 in. If there is a 3 x 3 array of these planters with no space between them, what is the area covered by the planters?
Answers
Answer: 82.5 inches
Step-by-step explanation: We know that each plantar has a base of 5.5 by 1 2/3. So if we multiply 5.5 by 1 2/3 we can get 9.166666667. However, there is 9 planters because 3 times 3 is 9. So if we multiply 9.166666667 by 9 we will get 82.5 inches
The table how the participation in a chool’ debate club during the lat four year. Year 1 2 3 4 Student 14 19 25 33 Between which to year did the club ee the greatet growth? By what percent did it grow?
Answers
The greatest growth was between years 1 and 2. The growth between those years was about 36%.
What is the greatest growth?
The process of developing; progressive expansion; the act or process of growing. size or developmental stage: It hasn't yet grown to its full potential. finished with development. growth of ritual forms: transition from a simpler to a more complex stage.
Here, we have
Given: Year 1 2 3 4, Student 14 19 25 33.
We have to calculate which year the club has the greatest growth.
19 - 14 = 5 / 14 x 100
= 35.714 > 36%
The other values by calculating the percent increase were
(from 2-3) = 31.57%
(from 3-4) = 32%
Hence, the greatest growth was between years 1 and 2. The growth between those years was about 36%.
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What are “holes” in algebra 2?
Answers
Answer:
Step-by-step explanation:
A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.
It is 2.5 to LR and another hour to Dallas
If I am traveling to Little
Rock for a flight, I have to
drive 2.5 hours. I am
flying to Dallas. To fly to
Dallas it takes
approximately an hour
from Little Rock. What
fraction of my trip is the
drive to Little Rock?
Round to the nearest
hundreth.
Answers
Answer:
Step-by-step explanation:
First make sure everything is in hours, yes everything is in hours !
So the fraction of little Rock to the rest is little Rock over the total.
2.5 hour/ 3.5 hours
0.714
Without using a calculator, fill all the solutions of sin(t)=-1
Where -pi is less than t less than or equal to pi
Answers
The solution to the equation sin(t) = -1 is t = -π/2 in the interval -π < t < π
How to calculate the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
sin(t) = -1
Take the arc sin of both sides
So, we have
t = sin⁻¹(1)
The interval is given as -π < t < π
When evaluated, we have
t = -π/2
Hence, the solution to the equation is t = -π/2
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Ramiro is also a college student. He has a credit card balance of $500.00. The APR on his card is 18.24%. His minimum payment is $10.00. (do not use commas or dollar signs in the answers)
How much will he pay in all?
Answers
Answer:
No of Monthly payments it would take to pay off his credit card = $94.601 per month
Step-by-step explanation:
If Ramiro made monthly payments at the end of each month, how long would it take to pay off his credit card?
No of Monthly payment it would take to pay off his credit card = nper(rate,pmt,pv,fv)
No of Monthly payment it would take to pay off his credit card = nper(18.24%/12,10,-500,0)
No of Monthly payment it would take to pay off his credit card = $94.601 per month.
a 13-ft ladder rests against a vertical wall. if the bottom of the ladder slides away at 1 ft/s, at what rate is the top of the ladder sliding down the wall when the bottom of the ladder is 5 ft from the wall? g
Answers
The given situation can be solved using the differential equation and the top of the ladder slides downward at 0.417 ft/s.
Let:
x be the distance from the bottom of the ladder to the base of the wall
y be the distance from the top of the ladder to the bottom of the wall
When the ladder is still, apply the Pythagorean Theorem,
x² + y² = 13²
5² + y² = 13²
y² = 169 - 25 = 144
y = 12 ft
When the ladder slides, apply the differential equation:
x² + y² = 13²
2x . dx/dt + 2y . dy/dt = 0
Substitute x = 5, dx/dt = 1, y = 12
2 . 5 . 1 + 2 . 12 . dy/dt = 0
24 dy/dt = -10
dy/dt = -5/12 = - 0.417 ft/s
The minus sign indicates that the ladder is sliding downward.
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Work out and simplify where possible
Answers
I hope it helps you ❤️❤️❤️
Answer:
a= 13/18 and b=5/16
Step-by-step explanation:
in A, multiply 4/9 by 2, you get 8/18 then add to it 5/18 you get 13/18
in B, multiply 3/8 by 2, you get 6/16 then subtract it by 1/16, you get 5/16
The ratio of the male and female teachers is 3:4 in Aadarsh H.S. School. If the number
of male teachers is 12, find the number of female teachers.
d)
7
Answers
Answer:
there is 16 female teachers because 4 * 4 is 14
male is eqaul to 12
so therefore female is eqaul to 3/4*12=9
A student states that −x is always equal to a negative integer. Complete the following statement to determine if the student is correct.
Answers
Answer:
iF X IS POSITIVE THEN -X IS ALWAYS NEGATIVE
IF X IS NEGATIVE, THEN -X IS ALWAYS POSITIVE
THE NEGATIVE OF A POSITIVE IS ALWAYS POSITIV
THE NEGATIVE OF A NEGATIVE IS ALWAYS POSITIVE
Step-by-step explanation:YS
−x is always equal to a negative integer is an incorrect statement.
The student is not correct.
What is Number system?A number system is defined as a system of writing to express numbers.
−x is always equal to a negative integer when x is positive integer
−x is always equal to a positive integer when x is negative integer
Which means the value of -x changes on the integer of x.
If x is positive then -x will be always negative, If x is negative then -x is positive.
The negative of a negative integer is positive and the negative of positive integer is negative.
Hence −x is always equal to a negative integer is an incorrect statement.
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10. A study of workplace benefits found that 56% of all American workers have a retirement plan, 68% have health insurances, and 49% have both. a) What is the probability that a randomly selected worker has a retirement plan or health insurance
Answers
To find the probability that a randomly selected worker has a retirement plan or health insurance, we need to add the probabilities of having a retirement plan and having health insurance and then subtract the probability of having both,
Since we don't want to count those workers twice. P(retirement plan or health insurance) = P(retirement plan) + P(health insurance) - P(both), P(retirement plan or health insurance) = 0.56 + 0.68 - 0.49, P(retirement plan or health insurance) = 0.75.
Therefore, the probability that a randomly selected worker has a retirement plan or health insurance is 0.75. we'll use the formula: P(A or B) = P(A) + P(B) - P(A and B), where A represents having a retirement plan, B represents having health insurance, and P(A and B) represents having both.
Given:
P(A) = 56% (retirement plan)
P(B) = 68% (health insurance)
P(A and B) = 49% (both)
Now we can plug these values into the formula: P(A or B) = 0.56 + 0.68 - 0.49 = 0.75, The probability that a randomly selected worker has a retirement plan or health insurance is 75%.
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only 0.02% of credit card holders of a company report the loss or theft of their credit cards each month. the company has 15,000 credit cards in the city of memphis. what is the probability that during the next month in the city of memphis a. no one reports the loss or theft of his or her credit cards? b. every credit card is lost or stolen? c. six people report the loss or theft of their cards? d. at least nine people report the loss or theft of their cards?
Answers
a) The probability that no one reports the loss or theft of their credit cards is 0.0498.
b) The probability that every credit card is lost or stolen is practically zero.
c) The probability that exactly six people report the loss or theft of their cards is 0.1042
d) The probability that at least nine people report the loss or theft of their cards is 0.2142
a. To calculate the probability that no one reports the loss or theft of their credit cards, we can use the Poisson distribution with an average of λ = 0.02% * 15,000 = 3.
The probability that no one reports the loss or theft of their credit cards is:
P(X = 0) = e^(-λ) * (λ^0 / 0!) = e^(-3) * (1 / 1) = 0.0498 or approximately 5%.
b. The probability that every credit card is lost or stolen is:
P(X = 15000) = e^(-λ) * (λ^15000 / 15000!)
Since λ is very small, the probability of all 15000 credit cards being lost or stolen in a month is practically zero.
c. To calculate the probability that six people report the loss or theft of their cards, we again use the Poisson distribution with an average of λ = 3.
The probability that exactly six people report the loss or theft of their cards is:
P(X = 6) = e^(-λ) * (λ^6 / 6!) = e^(-3) * (3^6 / 720) = 0.1042 or approximately 10.4%.
d. To calculate the probability that at least nine people report the loss or theft of their cards, we need to sum the probabilities for X = 9, 10, 11, ..., 15, since there are only 15,000 credit cards in total.
The probability that at least nine people report the loss or theft of their cards is:
P(X >= 9) = Σ(i=9 to 15) P(X = i) = Σ(i=9 to 15) e^(-λ) * (λ^i / i!)
This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(X >= 9) is approximately 0.2142 or 21.42%.
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what is 2.1x10 to the 3rd power in standard form?
Answers
Answer:
2.1 x 10^3
Step-by-step explanation: To write a linear expression in standard form, rearrange the terms in alphabetical order. It is already in its standard form.
HELP GIVING BRAINLIEST (NO LINKS) 50 POINTS
Expression A: 2(x + 1)
Expression B: 2x + 2
which statement does not show that these expressions are equivalent
A.subsitiuting any value of x makes the expressions equivalent
B. Both expressions involve addition
C. The expressions name the same number regardless of the value of x
D. 2(x +1) can be rewritten as 2x + 2 using the distributive property
Answers
a 14 oz bottle of hair gel lasts Emily 21 weeks. how long will and 18 oz bottle last her?
Answers
Answer:
27 weeks
Step-by-step explanation:
first you would figure out how long one oz. of hair gel would last her. You would do this by dividing 21 by 14. 21/14 is 1.5. Next, if 1 oz. lasts 1.5 weeks, and there is a 18 oz bottle, then all you need to do is multiply 18 by 1.5. 18 times 1.5 is 27. Therefore, an 18 oz. bottle of hair gel would last Emily 27 weeks.
Y=-3x+1
10x + 2y = -6
Find x and y
Answers
The solution to the system of equation y = -3x + 1 and 10x + 2y = -6 is x = -2 and y = 7.
What is the solution to the system of equation?Given the equation in the question
y = -3x + 110x + 2y = -6To solve for the values of x and y.
First, plug the first equation into the second equation and solve for x.
10x + 2y = -6
Plug in y = -3x + 1
10x + 2( -3x + 1 ) = -6
Solve for x
10x - 6x + 2 = -6
4x + 2 = -6
4x = -6 - 2
4x = -8
x = -8/4
x = -2
Now, plug x = -2 into the first equation and solve for y.
y = -3x + 1
Plug in x = -2
y = -3( -2 ) + 1
y = 6 + 1
y = 7
Therefore, the solution is (-2,7).
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Help please giving brainliest
Answers
244×6=4×....
Yukarıdaki matematiksel ifade de eşitliğin sağlanabilmesi için noktalı yere hangi sayı gelmelidir ? acil
Answers
Answer:
a)366
Step-by-step explanation:
244×6=1464÷4=366
please solve quickly
Answers
Area of a circle = πr^2
Area of a sector with angle x° = (x/360) πr^2
for the larger sector,
x = 255°
r = 13.4 miles
Required area of sector = (255/360) × π × 13.4^2 = 399.57 miles^2
To the nearest tenth, Area = 399.6 miles^2