The answer to the question is that \( A_{1} \) is smaller than \( A_{2} \)
To begin, it is important to note that the terms "emalier" and "5PRECALC7" are not relevant to the question and can be ignored. Additionally, there are several typos and extraneous information that can also be ignored. The main focus of the question is to determine the relationship between \( A_{1} \) and \( A_{2} \).
From the information provided, it is clear that \( A_{1} \) is smaller than \( A_{2} \). This is because the value of \( A_{1} \) is given as 2, while the values of \( b \) and \( c \) are 27 and 33, respectively. Since \( A_{2} \) is the sum of \( b \) and \( c \), it is clear that \( A_{2} \) is larger than \( A_{1} \).
Therefore, the answer to the question is that \( A_{1} \) is smaller than \( A_{2} \).
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use this triangle for problems 4 and 5
1. What is the length of AB
2. What is the area of this triangle
(1) The length of AB in triangle ABC 24.58 units.
(2) The area of the triangles is 77.94 sq. units.
What is the length of AB for triangle ABC?
The length of AB in triangle ABC given is calculated by applying cosine rule as shown below.
Length AB is opposite angle C, so will denote the length as c.
c² = a² + b² - 2ab cos(C)
where;
a is the length of side CBb is the length of side ACC is the angle Cc² = (18)² + (10)² - 2(18 x 10) cos(120)
c² = 604
c = √ 604
c = 24.58 units
The area of the triangles is calculated as follows;
A = ¹/₂ab sin C
A = ¹/₂ x 18 x 10 x sin (120)
A = 77.94 sq. units
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Graph f(x) = (x+1) (x-5)
The graph of the quadratic function is on the image at the end.
How to graph the quadratic function?Here we have the quadratic function:
f(x) = (x + 1)*(x - 5)
To graph this, we need to find some points of the parabola and then connect them.
So let's evaluate the function.
if x = -1
f(-1) = (-1 + 1)*(-1 - 5) = 0
if x = 0
f(0) = (0 + 1)*(0 - 5) = -5
if x = 1
f(1) = (1 + 1)*(1 - 5) = 2*-4 = -8
if x = 5 then:
f(5) = (5 + 1)*(5 - 5) = 0
So we have the points (-1, 0), (0, -5), (1, -8) and (5, 0).
With these we can graph the parabola (you can try to find more points to get a better graph).
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last year there were 129 pies baked for the bake sale. this year there were b pies baked. using b write an expression for the total numbers of ingredients and pies baked in the two years
Answer:
Step-by-step explanation:
Assuming that the number of ingredients per pie is constant, we can write an expression for the total number of ingredients and pies baked in the two years as:
Total number of ingredients = (129 x ingredients per pie) + (b x ingredients per pie)
Total number of pies baked = 129 + b
So, if we let "i" represent the number of ingredients per pie, we can write the expression as:
Total number of ingredients = (129 x i) + (b x i)
Total number of pies baked = 129 + b
Note that without knowing the value of "i," we cannot simplify this expression any further.
Evaluate the function f(x)=x²-3x - 8 at the given values of the independent variable and simplify. a. f(8) b. f(x+9) c. f(-x) a. f(8) = (Simplify your answer.) b. f(x + 9) = (Simplify your answer.) c. f(-x) = (Simplify your answer.)
Answer:
Step-by-step explanation:
Given: [tex]f(x)=x^{2} -3x - 8[/tex]
To find:
a) f(8)
To find f(8), replace x with 8 in f(x)
[tex]f(8) = 8^{2} -3(8) -8 = 32[/tex]
b) f(x+9)
To find f(x+9), replace x with x +9 in f(x)
[tex]f(x+9) = (x +9)^{2} -3(x +9) -8 = x^{2} +18x+81-3x-27-8=x^{2} +15x+46[/tex]
c) f(-x)
To find f(-x), replace x with -x in f(x)
[tex]f(x)=(-x)^{2} -3(-x) - 8 =x^{2} +3x-8[/tex]
This is how we simplify these expressions.
The difference between the digits of a two -digit number is 1. The number itself is one more than five times the sum of its digits. If the unit digit is greater than the tens digit, find the number.
The number is 63. The difference between the digits of a two-digit number is 1.
What is number?Number is a mathematical object used to count, measure, and label. Numbers can be represented in a variety of forms, such as numerals, symbols, or words. Numbers are fundamental to mathematics, and all other areas of science and technology. They are used to represent amounts of money, measurements, dates, and amounts of time. Numbers are also used to identify objects and people, and to create equations and formulas. Number is essential for understanding the world around us.
To solve this, the first thing to do is find the sum of the digits. Since the number is one more than five times the sum of its digits, the sum of the digits is (63/5)-1=12.5-1=11.5. This means that the tens digit is 11 and the unit digit is 11 + 1 = 12. Therefore, the two-digit number is 63.
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Two fire towers are located 5 miles apart on a straight road. They both spot the same fire on the north side of the road and report its location in terms of angles from the road. From the tower A, the fire is 22 degrees. From the tower B (5 miles east of tower A), the fire is 37 degree. How far from tower B is the point on the road closest to the fire? Please sketch and show the fire location. The point on the road closest to the fire will be on a line to the fire directly perpendicular to the road. Round to two decimal places
Tower B is 2.34 miles far from the point on the road closest to the fire.
The point on the road closest to the fire can be found by drawing a line perpendicular to the road that passes through the fire location. Let x be the distance from tower B to this point. Then, using trigonometry, we can find that the distance from tower A to the fire location is x/tan(22) and the distance from tower B to the fire location is (5 - x)/tan(37). Since the fire location is the same from both towers, these distances must be equal, so we can set up the equation x/tan(22) = (5 - x)/tan(37) and solve for x, which is approximately 2.34 miles.
To sketch the fire location, draw a straight road with two fire towers located 5 miles apart. From tower A, draw a line at an angle of 22 degrees towards the north side of the road to represent the direction of the fire location. From tower B, draw a line at an angle of 37 degrees towards the same side of the road. The point where these two lines intersect represents the location of the fire. Draw a line perpendicular to the road passing through this point to find the closest point on the road to the fire.
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What is the quotient of (−168) ÷ (−14) ÷ (−3)?
please help
Answer:
= -4
Step-by-step explanation:
To solve this expression, we need to perform the division in the correct order, following the rules of mathematical operations. We can simplify the expression as follows:
(-168) ÷ (-14) ÷ (-3) = (-168) ÷ [(-14) x (-3)] [dividing by a negative number is the same as multiplying by its reciprocal]
= (-168) ÷ 42
= -4
Therefore, the quotient of (-168) ÷ (-14) ÷ (-3) is -4.
Given the polynomial 3x^(3) - 4x^(2) + 9x - 12, rewrite the polynomial as a product of binomials.
The polynomial 3x³ - 4x² + 9x - 12 as a product of binomials is (3x - 4)(x² + 3).
To rewrite the polynomial 3x³ - 4x² + 9x - 12 as a product of binomials, we need to factor the polynomial. One method to do this is by grouping. Here are the steps:
1. Group the first two terms and the last two terms: (3x³ - 4x²) + (9x - 12)
2. Factor out the common factor from each group: x²(3x - 4) + 3(3x - 4)
3. Notice that (3x - 4) is a common factor in both groups, so we can factor it out: (3x - 4)(x² + 3)
4. Now we have the polynomial rewritten as a product of binomials: (3x - 4)(x² + 3)
Therefore, the polynomial 3x³ - 4x² + 9x - 12 can be rewritten as (3x - 4)(x² + 3).
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Help me, please. Please provide a clear answer
Answer:
see explanation
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
4x + 21 + x - 10 + 2x + 8 = 180
7x + 19 = 180 ( subtract 19 from both sides )
7x = 161 ( divide both sides by 7 )
x = 23
Then angles in triangle are
4x + 21 = 4(23) + 21 = 92 + 21 = 113°
x - 10 = 23 - 10 = 13°
7x + 8 = 7(23) + 8 = 161 + 8 = 169°
the only 2 possible angle measures are A and E
Use synthetic division to perform the division.
−8x^3+6x^2−9x+4 / x−2
Question content area bottom
Part 1
−8x^3+6x^2−9x+4 / x−2=enter your response here
(Simplify your answer.)
The final response is:
−8x^3+6x^2−9x+4 / x−2 = -8x^2 - 10x - 29 + (62/(x-2))
The synthetic division of −8x^3+6x^2−9x+4 / x−2 can be performed as follows:
Step 1: Write the coefficients of the dividend in a row: -8, 6, -9, 4
Step 2: Write the divisor in the form x-a, in this case x-2, so a=2
Step 3: Bring down the first coefficient, -8, to the bottom row
Step 4: Multiply the first number in the bottom row, -8, by a, 2, and write the result, -16, in the next column
Step 5: Add the numbers in the second column, 6 and -16, to get -10, and write the result in the bottom row
Step 6: Repeat steps 4 and 5 with the new number in the bottom row, -10, until all columns have been completed
Step 7: The last number in the bottom row is the remainder, and the other numbers in the bottom row are the coefficients of the quotient
The synthetic division table looks like this:
| 2 | | | | |
|---|---|---|---|---|
|-8 | 6 | -9| 4 | |
| |-16|-20| 58| |
|---|---|---|---|---|
|-8 |-10|-29| 62| |
The quotient is -8x^2 - 10x - 29 with a remainder of 62.
So the final response is:
−8x^3+6x^2−9x+4 / x−2 = -8x^2 - 10x - 29 + (62/(x-2))
I hope this synthetic division explanation was helpful!
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A circle moves through 145 degrees in 25 seconds. If the radius
of the circle is 21 cm, find the linear and angular speeds.
The linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.
The linear speed of the circle can be found by calculating the length of the arc traveled in 25 seconds. The length of an arc is given by the formula L = rθ, where r is the radius of the circle and θ is the central angle in radians. Converting the given angle from degrees to radians, we have:
θ = 145 degrees * π/180 = 2.53 radians
Substituting the values into the formula, we get:
L = 21 cm * 2.53 = 53.13 cm
Therefore, the linear speed of the circle is:
v = L/t = 53.13 cm/25 s = 2.125 cm/s
The angular speed of the circle can be found by dividing the central angle by the time taken to travel that angle. Therefore, the angular speed of the circle is:
ω = θ/t = 2.53 radians/25 s = 0.1012 rad/s
Hence, the linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.
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A tractor cost $9250 and depreciates in value by 12% per year. How much will the tractor be worth after 5 years?
Please answer ASAP!
Answer:
$3,700
Step-by-step explanation:
12% of 9,250 is 1,110
so each year 1,110 is subtracted from the original price of the tractor.
So if you subtract 1,110 five times from 9,250 you get 3,700.
pls answer this question only even numbers like 2,4,6....
Answer:
image is blur dear!!!
Step-by-step explanation:
Jill's gym class lasted 50 minutes. She walked around the school track for the first 15 minutes. Then, she played kickball for 25 minutes. She got to play on the playground for the rest of class. After kickball, how long did Jill get to play on the playground?
Jill played for 10 mins. 25+15=40 50-40=10
Identify and explain any restrictions on the variablex in the expression √6x-2
The restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.
The restrictions on the variablex in the expression √6x-2 are determined by the fact that the square root of a negative number is not a real number. Therefore, the expression under the square root must be greater than or equal to zero. This gives us the following inequality:
6x-2 ≥ 0
Solving for x, we get:
6x ≥ 2
x ≥ 2/6
x ≥ 1/3
So the restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.
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Three dices are rolled, what is your random variable x for the number of times "2" is rolled? What are the probabilities for each instance?
The required probability for the three dices to be rolled for the given condition is equal to ,
probability 0.579 when X=0,
probability 0.347 when X =1
probability 0.069 for X = 2
probability 0.005 when X = 3.
The random variable X represents the number of times the number '2' is rolled when three dices are rolled.
X represents the values from 0 (when no '2' is rolled) to 3 (when all three dices show '2'.
Probabilities for each case, use the binomial probability formula, we, have,
P(X = a) =ⁿCₐ × pᵃ × (1-p)ⁿ⁻ᵃ
n = Number of trials (in this case, n = 3)
a = Number of successes (here, 'a' ranges from 0 to 3).
p = Probability of success (rolling a '2' on a single die)
p = 1/6
Required probabilities for each possibility is,
P(X = 0) = (³C₀) × (1/6)^0 × (5/6)^3
= 125/216
≈ 0.579
P(X = 1) = ((³C₁) × (1/6)¹ × (5/6)²
= 75/216
≈ 0.347
P(X = 2) = ³C₂× (1/6)²× (5/6)¹
= 15/216
≈ 0.069
P(X = 3) = (³C₃) × (1/6)³× (5/6)⁰
= 1/216
= 0.004629
≈ 0.005
Therefore, the random variable X for the number of times 2 is rolled for three dices are rolled represents probability distribution,
X = 0 with probability 0.579
X = 1 with probability 0.347
X = 2 with probability 0.069
X = 3 with probability 0.005
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98. A blue whale weighs up to \( 1.8 \times 10^{6} \mathrm{~kg} \). How much will 12 blue whales weigh?
12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex].
The weight of 12 blue whales will be the product of the weight of a single blue whale and the number of blue whales. To find the product, we simply multiply the weight of a single blue whale by the number of blue whales.
So, the weight of 12 blue whales will be:
[tex]\( 1.8 \times 10^{6} \mathrm{~kg} \) × 12 = \( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]
Therefore, 12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]
Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.
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prisim A is similar to prisim B. The volume prisim a is 2080 cm3. what is the volume of prisim B?
Answer:
2080cm^3
Step-by-step explanation:
Simplify: 27 − 3 exponent 3 + 4 x 2 exponent 2 − 6.
Answer:
10
Step-by-step explanation:
27-[tex]3x^{3}[/tex]+(4 x [tex]2x^{2}[/tex]) - 6
= 27 - 27 + (4 x 4) - 6
= 0 + 16 - 6
= 10
Answer: 10
Step-by-step explanation:
27 - 3^3 + 4 × 2^2 - 6
= 27 - 27 + 4 × 4 - 6 (since 3^3 = 27 and 2^2 = 4)
= 0 + 16 - 6= 10
Therefore, the simplified value of the expression is 10.
given trinomial. If the trinomial cannot be factored, indicate "Not Factorable". x^(2)+12x+35 to enter your answer (opens in new window ) 2 Points
The given trinomial x^(2)+12x+35 is factorable. It's factors would be (x+7)(x+5).
To factor this trinomial, we need to find two numbers that multiply to 35 and add to 12. The two numbers that satisfy this condition are 7 and 5. Therefore, we can factor the trinomial as follows:
x^(2)+12x+35 = (x+7)(x+5)
So, the factored form of the given trinomial is (x+7)(x+5).
Therefore, the answer is (x+7)(x+5).
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values of x : -6-(4x)/(x+2)=(8)/(x+2)
There are no values of x that satisfy the equation -6-(4x)/(x+2)=(8)/(x+2).
To find the values of x for the equation -6-(4x)/(x+2)=(8)/(x+2), we need to follow the following steps:
Multiply both sides of the equation by (x+2) to eliminate the fractions:
(x+2)(-6-(4x)/(x+2))=(x+2)(8)/(x+2)
Simplify the equation:
-6(x+2)-4x=8
Distribute the -6:
-6x-12-4x=8
Combine like terms:
-10x-12=8
Add 12 to both sides:
-10x=20
Divide both sides by -10:
x=-2
However, we need to check our answer to make sure it does not result in a zero denominator in the original equation. If we plug in x=-2 into the original equation, we get a zero denominator, which is not allowed. Therefore, there are no values of x that satisfy the equation.
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Kaylin buys a greeting card for 3.79. She then buys 4 postcards that all cost the same amount. The total cost is 5.11. How much is each postcard? Show your work.
Answer:
0.33
Step-by-step explanation:
5.11-3.79= total for 4 postcards
then answer divided by 4 postcards
3. What is the relationship between <8 and <4?
7
1 2
3 4
6
8
Ocorresponding angles
Oalternate exterior angles
Osame-side interior angles
Oalternate interior angles
(1 point)
The relationship between ∠8 and ∠4 include the following: A. corresponding angles.
What are corresponding angles?In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.
By applying corresponding angles theorem to lines l and m, we have the following:
8 ≅ ∠4
3 ≅ ∠7
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College enrollment of 41,000 increases by 7% every year.
The exponential function showing the relationship between y and t is y = 41,000 x (1.07)^t
How to determine the exponential functionFrom the question, we have the following parameters that can be used in our computation:
Initial value, a = 41,000
Rate = 7% increment
The exponential function for the college enrollment y of the college, in dollars, after t years can be expressed as:
y = a(1 + r)^t
Substitute the known values in the above equation, so, we have the following representation
y = 41,000 x (1 + 7%)^t
Evaluate
y = 41,000 x (1.07)^t
Where 1.07 is the factor by which the college enrolment increases
Hence, the function is y = 41,000 x (1.07)^t
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7.1 Bellwork
1 of 31 of 3 Items
Question
Classify each polygon by the number of sides. Then say whether it is convex or concave, regular or not regular.
shape:
, convex or concave:
, regular or not regular:
.
The polygons are classified as :-
1.CONVEX
2.CONCAVE
3.CONCAVE
4.REGULAR
5.CONCAVE
6.IRREGULAR
What are polygons?A polygon is a geometrical figure, with finite sides and angles, they can be regular and irregular.
Regular Polygon
A regular polygon is that which has all its sides and angles equal, for example an equilateral triangle and a square.
Irregular Polygon
A irregular polygon is that which has all its sides and angles unequal,
For example, a scalene triangle, a rectangle, a kite, etc.
Convex Polygon
A Convex polygon is that which has all its angles less than 180 degrees,
Concave Polygon
A Concave polygon is that which has its angles greater than 180 degrees,
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The complete question attached
A vector u and a set S are given. If possible, write u as a linear combination of the vectors in S.
U = [1]. S = {[1}, [0}}
[1] {[0] [1]}
vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.
To write vector u as a linear combination of the vectors in set S, we need to find scalars a and b such that:
u = a[1] + b[0]
Substituting the values of vector u and the vectors in set S into this equation, we get:
[1] = a[1] + b[0]
This equation can be simplified to:
[1] = [a] + [0]
Since the scalar b is being multiplied by the zero vector, it will always equal the zero vector, and can therefore be eliminated from the equation. This leaves us with:
[1] = [a]
We can see that the scalar a must equal 1 in order for this equation to be true. Therefore, vector u can be written as a linear combination of the vectors in set S as follows:
u = 1[1] + 0[0]
In conclusion, vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.
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Help!! please answer asap
Express as a trigonometric function of one angle.
cos 9 sin(−6) − cos 6 sin 9
The expression can be explained as the trigonometric function of an angle as follows sin(15).
The given expression can be simplified using the trigonometric identity for the sine of the difference of two angles:
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
Substituting the given values for a and b, we get:
sin(9 - (-6)) = sin(9)cos(-6) - cos(9)sin(-6)
Simplifying further, we get:
sin(15) = sin(9)cos(6) - cos(9)sin(-6)
Therefore, the given expression can be expressed as a trigonometric function of one angle as follows:
sin(15) = sin(9)cos(6) - cos(9)sin(-6)
-sin(15) = cos(9)sin(-6) - sin(9)cos(6)
So the final answer is -sin(15).
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RETIREMENT INCOME A retiree deposits S dollars into an account that earns interest at an annual rate r compounded continuously, and annually withdraws W dollars. a. Explain why the account changes at the rate dt/dV=rV−W where V(t) is the value of the account t years after the account is started. Solve this separable differential equation to find V(t). Your answer will involve r,W, and S. b. Frank and Jessie Jones deposit $500,000 in an account that pays 5\% interest compounded continuously. If they withdraw $50,000 annually, what is their account worth at the end of 10 years? c. What annual amount W can the couple in part (b) withdraw if their goal is to keep their account unchanged at $500,000 ?
V(t)=S ert-W/r
a. The rate at which the account changes (dt/dV) is equal to the interest rate (r) times the value of the account (V) minus the amount withdrawn (W). This can be written mathematically as dt/dV=rV-W. This is a separable differential equation, which can be solved by integrating both sides of the equation with respect to time. The solution is V(t)=S ert-W/r.
b. The value of the Jones' account at the end of 10 years can be found using the solution V(t) from part a: V(10)=500,000 e5%x10-50,000/5% = $387,468.51.
c. To keep their account unchanged at $500,000, the Jones' must withdraw an annual amount W such that V(t)=500,000. From the solution V(t)=S ert-W/r, we can solve for W: W = 500,000e5%x10 - 500,000/5% = $47,613.30.
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y = -4x+6
find the perpendicular line that passes through (-7,5)
find equation of parallel line that passes through (-7,5)
The equation of the parallel line is y = -4x - 23.
To find the equation of the perpendicular line that passes through (-7, 5), we need to first find the slope of the given line y = -4x + 6. The slope of this line is -4. The slope of a perpendicular line is the negative reciprocal of the original slope, so the slope of the perpendicular line is 1/4.
Next, we can use the point-slope form of an equation to find the equation of the perpendicular line:
y - y1 = m(x - x1)
y - 5 = (1/4)(x - (-7))
y - 5 = (1/4)(x + 7)
y = (1/4)x + 9/4 + 5
y = (1/4)x + 29/4
The equation of the perpendicular line is y = (1/4)x + 29/4.
To find the equation of the parallel line that passes through (-7, 5), we can use the same slope as the original line, -4, and the point-slope form of an equation:
y - y1 = m(x - x1)
y - 5 = -4(x - (-7))
y - 5 = -4(x + 7)
y = -4x - 28 + 5
y = -4x - 23
The equation of the parallel line is y = -4x - 23.
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The diameter of a circle is 4 m. Find its area to the nearest whole number.