Answer:
Question 1:
The sum of interior angles of a polygon can be found by the following formula:
(n-2) × 180
Where n is the no. of sides
A pentagon has 5 sides
So,
= (5-2) × 180
= (3) × 180
= 540 degrees
Question 2:
Since The sum of interior angles of a regular octagon is 1080 and the total interior angle are 8
So, Measure of interior angle = [tex]\frac{1080}{8}[/tex]
Measure of interior angle = 135 degrees
Question 3:
Since, one interior angle in a hexagon measures 120 degrees.
So,
The interior angle should be subtracted by 180 to get the exterior angle.
Exterior angle = 180-120
Exterior Angle = 60 degrees
7th grade math I need some help
Answer:
Step-by-step explanation:
[tex](-14+\frac{3}{2}b)-(1+\frac{8}{2}b)=-14-1+\frac{3}{2}b-4b[/tex]
= ([tex]-15-\frac{5}{2}b[/tex])
[tex](5+2b)+(2b+\frac{3}{2})=(5+\frac{3}{2})+(2b+2b)[/tex]
= [tex](4b+\frac{13}{2})[/tex]
[tex](\frac{7}{2}b-3)-(8+6b)[/tex] = [tex](\frac{7}{2}b-6b)-(3+8)[/tex]
= ([tex]-\frac{5}{2}b-11[/tex])
[tex](-10+b)+(7b-5)=(-10-5)+(b+7b)[/tex]
= [tex](8b-15)[/tex]
What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 52 college students were surveyed and r = 12 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05. (a) What is the level of significance?
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.24
For the alternative hypothesis,
p ≠ 0.24
This is a two tailed test
Considering the population proportion, probability of success, p = 0.24
q = probability of failure = 1 - p
q = 1 - 0.24 = 0.76
Considering the sample,
Sample proportion, P = r/n
Where
r = 12
n = 52
P = 12/52 = 0.23
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.23 - 0.24)/√(0.24 × 0.76)/52 = - 0.17
Recall, population proportion, P = 0.24
The difference between sample proportion and population proportion(p - P) is 0.24 - 0.23 = 0.01
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.24 - 0.01 = 0.23
the p for the right tail is 0.24 + 0.01 = 0.25
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area below the test z score in the left tail 0.43
We would double this area to include the area in the right tail of z = 0.17 Thus
p = 0.43 × 2 = 0.86
The level of significance is 5%
Since alpha, 0.05 < than the p value, 0.86, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, this information does not imply that the color preference of all college students is different (either way) from that of the general population.
The graph of a line goes through the points (-4,3) and (6,8). What is the equation
of the line in slope-intercept form?
Answer:
y = 1/2x+5
Step-by-step explanation:
You have two points so you can find the slope
m = (y2-y1)/(x2-x1)
m = (8-3)/(6 - -4)
(8-3)/(6+4)
5/10
1/2
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 1/2 x+b
Substitute a point into the equation
8 = 1/2(6)+b
8 = 3+b
b=8-3 = 5
y = 1/2x+5
Find a linear second-order differential equation F(x, y, y', y'') = 0 for which y = c1x + c2x4 is a two-parameter family of solutions. Make sure that your equation is free of the arbitrary parameters c1 and c2. (Use yp for y' and ypp for y''.)
Answer:
[tex]4y+ y"x^2-4y'x = 0[/tex]
↓
[tex]F(x, y, y', y'') = 0[/tex]
Step-by-step explanation:
From the information given:
[tex]y = c_1x + c_2x^4 \\ \\ y^1'= c_1 + 4c_2x^3 \\ \\ c_1 =y' - 4c_2x^3 \\ \\[/tex]
So;
[tex]y = y'x -4c_2x^4+c_2x^4 \\ \\ y - y'x - 3c_2x^4 \\ \\ y'= y"x+y'- 12c_2x^3 \\ \\ c_2= \dfrac{y"x}{12x^3} \\ \\ c_2= \dfrac{y"}{12x^2}[/tex]
∴
[tex]y = y'x- \dfrac{3x^4*y'' }{12x^2} \\ \\ \\ y = y'x - \dfrac{y" x^2}{4} \\ \\ \\ 4y+ y"x^2-4y'x = 0[/tex]
↓
[tex]F(x, y, y', y'') = 0[/tex]
The figure is reflected across line m and then across line n. What is the resulting transformation?
a. glide reflection
b. rotation
c. translation
d. reflection
There are 40 nickels in a roll. If you have 250 rolls of nickels, how many nickels do you have?pls help me
Answer:
10,000 nickles
Step-by-step explanation:
Since there are 40 nickles in a roll and you have 250, think that you have 250 sets of 40. This means that this question is a multiplication problem.
Multiply 40 x 250. This would give you 10,000.
Don't forget units.
The number of nickels in 250 rolls is 10000
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here, There are 40 nickels in a roll. If I have 250 rolls of nickels, then the number of nickels in total is = 250×40
= 10000
Hence, The number of nickels in 250 rolls is 10000
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Bryan’s golf coach suggested he take some golf lessons. The pro at windy fairways charges $20.00 per month plus $10.00 per lesson. The pro at sunny sands charges $100.00 per month for unlimited classes. How many classes does he have to take for both pros be the same price?
Answer:
8
Step-by-step explanation:
(100 - 20) / 10 = 8
Answer: He has to take a class per month from the both pros
Step-by-step explanation:
Purple paint is made by mixing red paint and blue paint in the ratio 2 : 3. If 15 litres of blue paint is used, how much red paint will be needed?
Answer:
Because they are in the ratio 2:3 we'll call red and blue paint 2x and 3x respectively. We know that there are 15 liters of blue paint which means that 3x = 15. Solving for x we get x = 5. Since red paint is denoted by 2x it would be 2 * x = 2 * 5 = 10.
Answer:
10 liters
Step-by-step explanation:
Red : Blue
2 3
We want 15 blue liters
15/3 = 5
Multiply each term by 5
Red : Blue
2*5 3*5
10 : 15
If p(y) = y^3+3 y^2-5y-6, then p (-3) = ------------------
Answer:
9
Step-by-step explanation:
[tex]p(y)=y^3+3y^2-5y-6 \\\\p(-3)=(-3)^3+3(-3)^2-5(-3)-6= \\\\-27+27+15-6= \\\\9[/tex]
Hope this helps!
Answer:
p(-3)=9
Step-by-step explanation:
This question ask us to find p(-3), or what p(y) is when y is equal to -3.
We know that:
p(y)= y^3+3 y^2-5y-6
We want to find p(-3), so substitute -3 in for every y.
p(-3)= (-3^3)+3(-3^2)-5(-3)-6
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Solve the exponents first (-3^3 and -3^2)
-3^3=-3*-3*-3= -27
-3^2= -3* -3= 9
p(-3)= -27+ 3(9) -5(-3) -6
Next, multiply 3 and 9
p(-3)= -27+27-5(-3)-6
Then, multiply -5 and -3
p(-3)= -27+27+15-6
-27 and 27 equal 0, so they cancel each other out.
p(-3)=15-6
p(-3)= 9
Factor the trinomial by grouping.
9x^3 - 3x^2 -30x
Answer:
3x(3x+5)(x-2)
Step-by-step explanation:
[tex]9x^3-3x^2-30x= \\\\3x(3x^2-x-10)= \\\\3x(3x^2+5x-6x-10)= \\\\3x(x(3x+5)-2(3x+5))= \\\\3x(3x+5)(x-2)[/tex]
Hope this helps!
Which square root is between 4 and 5?
Answer:
√24
Step-by-step explanation:
4.89897948 will be the answer. Which is a number in between 4 and 5. Hope this helps :)
Part 3
1. Be sure your work is shown and steps are in order.
2. List all the possible rational roots.
3. Use synthetic division to test the possible rational roots and factor possible.
4. Identify complex roots if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-intercepts
c. (if possible) anything you can learn by considering symmetry and transformations.
3a. p(x)= 2x^5 - 9x^4 + 6x^3 + 22x^2 - 20x - 25
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
p(x) = (x +1)^2(2x -5)(x^2 -4x +5)
complex roots: 2±i
see the last attachment for a graph
Step-by-step explanation:
2. The leading coefficient of p(x) is 2, and the constant term is 25. The Rational Root Theorem tells you possible rational roots will be of the form ...
±(divisor of 25)/(divisor of 2)
That is, they are ...
±1/2, ±1, ±5/2, ±5, ±25/2, ±25
__
3. Before we get into synthetic division, we choose to see if we can reduce this list any. We note that p(0) = -25. The value of p(1) is the sum of the coefficients:
p(1) = 2 -9 +6 +22 -20 -25 = 30 -54 = -24
Similarly, the value of p(-1) is the same sum with odd-degree coefficients negated:
p(-1) = -2 -9 -6 +22 +20 -25 = 42 -42 = 0
So, we found our first root: -1. Using synthetic division, we can reduce the polynomial and start over. See the first attachment for this division.
__
The reduced polynomial is ...
p1(x) = 2x^4 -11x^3 +17x^2 +5x -25
We already know that +1 is not a of it. Checking -1, we have ...
p1(-1) = 2 +11 +17 -5 -25 = 0
So, we found our second root: -1. Using synthetic division, we can reduce the polynomial and start over. See the second attachment for this division.
__
The reduced polynomial is ...
p2(x) = 2x^3 -13x^2 +30x -25
The alternating signs tell us there are no more negative real roots. They also tell us there are 1 or 3 positive real roots. We know p2(0) = -25. Then ...
p2(1) = 2 -13 +30 -25 = 32 -38 = -6
The average rate of change between these points is (-6 -(-25))/(1 -0) = 19. At this rate, we expect a root between x=1 and x=2. Testing x=2 using synthetic division, we get a remainder of -1. (See the 3rd attachment.) Then the rate of change between x=1 and x=2 is (-1 -(-6))/(2-1) = 5, suggesting x=5/2 might be a worthwhile test value.
The synthetic division is shown in the 4th attachment. You will note that we divide the polynomial p2(x) by its leading coefficient, so the coefficients used for p2(x) in the synthetic division are 1, -13/2, 15, -25/2. The remainder of 0 tells us that (x -5/2) is a factor of p2(x)/2, or (2x -5) is a factor of p2(x).
__
The reduced polynomial is ...
p3(x) = x^2 -4x +5
This can be written in vertex form as ...
p3(x) = (x -2)^2 +1
The positive leading coefficient means the graph opens upward, and the vertex at (2, 1) means there are no real solutions.
The real solutions to p(x) are x = -1, -1, and 5/2.
__
4. The complex solutions will be the solutions to ...
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i . . . . complex roots of p(x)
__
5. The graph is shown in the last attachment. The odd degree and positive leading coefficient of p(x) means the overall shape will be from lower left to upper right (/). That is, the sign of the end value of p(x) will match the sign of x.
The graph will touch the x-axis from below at x = -1, and will cross at x = 2.5. There is no particular symmetry.
The final quadratic factor is graphed and its vertex shown. The vertex matches that of the vertex-form equation for p3(x), above.
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
real solutions to p(x) are x = -1, -1, and 5/2.
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i complex roots
what is the slope-intercept equation of the line below?
Answer:
4
Step-by-step example
Slop is the
For the Black Panther Trip 420 students were scheduled to go. After collecting more parent surveys, 15% more students are going on the trip. Each admission ticket cost $22.75. What was the total amount paid for all the tickets purchased?
Answer: $ 10,988.25
Step-by-step explanation:
Hi, to answer this question, first we have to multiply the original number of students scheduled to go to the trip (420) by the added students’ percentage (15%) in decimal form (divided by 100)
420 x (15/100) = 420 x 0.15 = 63 students added
Adding the number of extra students to the original number:
420+63 = 483 students (total number of students)
Finally, we have to multiply the result by the cost of each admission ticket (22.75)
483 x 22.75 = $ 10,988.25
The graph shows the relationship between daily caffeine
consumption and resting heart rate for some adults.
Which phrases describe the relationship between heart
rate and daily intake of caffeine? Select two options.
Effects of Caffeine
negative correlation
180
increasing heart rate
constant correlation
Resting Heart Rate (bpm
positive correlation
decreasing heart rate
1 2 3 4 5 6 7 8 9 10
Total Coffee Intake (Cups)
Answer:
A and B. increasing heart rate and positive correlation
Step-by-step explanation:
The heart rate increases as they drink more cups of coffee and because the both sets of data are increasing in the same direction, it's positive correlation.
Hope my answer helps and isn't too short <3
Answer: B AND D
Step-by-step explanation:
What is the volume of the prism? 1080 cm 2700 cm 3240 cm 6480 cm
Answer:
Volume of prism = 3,240 cm³
Step-by-step explanation:
GIven.
Hexagonal prism.
Side of base(b) = 12cm
Height of prism = 9cm
Height of base (h)= 10cm
Find:
The volume of the prism.
Computation:
Area of base of hexagonal prism = n/2[bh]
Area of base of hexagonal prism = 6/2[(12)(10)]
Area of base of hexagonal prism = 360 cm²
The volume of prism = Area of base of hexagonal prism × Height of prism
The volume of prism = 360 × 9
Volume of prism = 3,240 cm³
Can you please help me
Answer:
complementary angle: 63
supplementary angle: 153
Step-by-step explanation:
Complementary angles mean angles that add up to 90. Therefore 90-27=63
Supplementary angles are angles that add up to 180. Therefore 180-27=153
HOW DO I FIND THE AREA OF DEF?
Answer:
169.7
Step-by-step explanation:
first lets find the other side of the small triangle
cos(30 degrees)=(7*sqrt (3))/x
x*cos(30 degrees)=7*sqrt (3)
x=(7*sqrt (3))/cos(30 degrees)
x=14
14/14=1
so proportion is 1/1
thus the bottom the outer part of the triangle is also 7*sqrt(3)
now, for the area
lets find the 2 side length of the triangle we need
DE: 14+14=28
DF: 7*sqrt(3)+7*sqrt(3)=14*sqrt(3)
let's find EF,
sin(30 degrees)=x/28
x/28=sin( 30 degrees)
x=28*sin( 30 degrees)
x=14
A=(14*sqrt(3))*14*0.5
A=(14*sqrt(3))*7
A= around 169.7
Answer:
≈169.7
Step-by-step explanation:
cos30 = (7[tex]\sqrt{3}[/tex])/x
x= (7[tex]\sqrt{3}[/tex])/cos30 = 14
h = 14+14 = 28
sin30 = EF/28
EF = sin30 * 28 = 14
tan30 = 14/DF
DF = 14/tan30 ≈ 24.248
Area = 24.248*14/2 ≈ 169.74 ≈ 169.7
46+9a=-5a+74 solve for a
Answer: a=2
Step-by-step explanation:
-14a=-28
divide both sides by -14
a=2
help pls tysm
What are two examples of financial institutions?
Answer:
The major categories of financial institutions include central banks, retail and commercial banks, internet banks, credit unions, savings, and loans associations, investment banks, investment companies, brokerage firms, insurance companies, and mortgage companies
Step-by-step explanation:
sorry i did not put 2 examples, i put too many examples lollll
Answer:
There are two primary types of financial institutions non-depository and depository.
Step-by-step explanation:
an insurance company would fall under the non-depository group, and a credit union would be defined as a depository institution.
Let the polynomials A = 7x² + 3xy e B = -3xy.
Determine A + B
a) 7x²
b) 3xy
c) 7x² + 6xy
d) 14x² + 6xy
e) -3xy
Answer:
The answer is A.
Step-by-step explanation:
You have to add up both polynomials together :
A = 7x² + 3xy
B = -3xy
A + B = 7x² + 3xy + (-3xy)
= 7x² + 3xy - 3xy
= 7x²
What is the solution to the division problem below? (You can use long division
or synthetic division.)
2x - 3x2 -5x - 12
X-3
A. 2x2 + x + 4
B. 2x2 + 3x + 4
C. 2x2 + 7x + 4
O D. 2x2 + 5x + 4
SUBMIT
Answer:
I would say B.
Step-by-step explanation:
I used synthetic division for this, so I'm unsure if this is right. I have yet to learn exponents with it. Here's how I wrote it : 3] 2 -3 -5 -12. I bring down the 2 and multiply it by three to get six. After that, I multiply the sum of it (3) and got 9. I do the same, get -4 and multiply it another time, getting positive 12. I add the twelves together, get zero, and put it together as 2x^2+3x+4.
Hope this helps!
Which point is not in the solution set of the equation 3y + 2 = x2 − 5x + 17?
A) (-2,10) or
D) (5,5)
B and C where wrong.
Answer:
A (-2, 10)
Step-by-step explanation:
If you plug in the point into x and y you should get "false" on a calculator, or the answer won't make sense, meaning that it's not a part of the set
(-2,10) is not the solution set of the given equation [tex]3y+2 =x^{2} -5x+17[/tex].
What is solution to the equation?The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.
According to the given question
We have an equation
[tex]3y + 2 =x^{2} -5x+17[/tex]
The above equation can be written as
[tex]x^{2} -5x +17-3y-2=0...(i)[/tex]
For finding the point which is not the solution set of the equation, first we will substitute the given points in the above equation and check whether it making the equation true or not.
For point (-2, 10)
Substitute, x = -2 and y = 10 in the equation (i)
[tex](-2)^{2} -5(-2) + 17 - 3(10) -2\\=4+10+17-30-2\\= -1\neq 0[/tex]
Hence, (-2, 10) is not the solution of the given equation.
For point (5, 5)
Substitute, x = 5, and y = 5 in equation (i)
[tex](5)^{2} -5(5)+17-3(5)-2\\=25-25+17-15-2\\=0[/tex]
Hence, (5, 5) is the solution of the given equation.
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Martha has $10,000 saved and wants to attend a college with a current tuition of $10,000 a year. She will graduate from high school in five years. Roughly how much more will Martha need to save for one-year's tuition to account for an annual rate of inflation of 3%?
Answer:
$1,592.74
Martha will need to pay $1,592.74 more
Step-by-step explanation:
Using the compound interest/inflation formula;
A = P(1+r)^(t)
Where;
A = final value
P = initial value = $10,000
r = inflation rate = 3% = 0.03
t = time = 5 years
Substituting the values;
A = $10,000(1+0.03)^(5)
A = $11592.740743
A = $11,592.74
How much more will Martha need to save;
C = final value - initial value = A - P
C = $11,592.74 - $10,000
C = $1,592.74
Martha will need to pay $1,592.74 more
Answer:
1,590.00
Step-by-step explanation: I took the test
Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP Statement Reason 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given 2. m∠H + m∠J + m∠K = 180° 2. ? 3. 30° + 50° + m∠K = 180° 3. substitution property 4. 80° + m∠K = 180° 4. addition 5. m∠K = 100° 5. subtraction property of equality 6. m∠J = m∠P; m∠K = m∠N 6. substitution 7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent 8. △HKJ ~ △LNP 8. AA similarity theorem Which reason is missing in step 2?
Answer:
[tex]2. m\angle H+m\angle J +m\angle K =180^{\circ}[/tex]
Reason: the sum of all interior angles of any triangle is equal to 180º.
Step-by-step explanation:
1) Organizing
Statement 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. Reason: given
2) Since the sum of all internal angles of any triangle is equal to 180º, just like the formula. N the number of sides of a triangle:
[tex]S_{i}=180^{\circ}(n-2)\rightarrow 180(3-2) \therefore S_{i}=180^{\circ}[/tex]
3) We can also say
[tex]m\angle K=180^{\circ}-(m\angle H+m\angle J)\\m\angle K=180^{\circ}-\left ( 30^{\circ}+50^{\circ} \right )\\m\angle K=100^{\circ}[/tex]
Similarly to the other triangle:
[tex]m\angle L=180^{\circ}-(m\angle N+m\angle P)\\m\angle L=180^{\circ}-\left ( 100^{\circ}+50^{\circ} \right )\\m\angle L=30^{\circ}[/tex]
4) Hence,
[tex]2. m\angle H+m\angle J +m\angle K =180[/tex]
Reason: The sum of interior angles is equal to 180º.
Answer:
B
Step-by-step explanation:
Please help! Correct answer only!
Belle got a summer job at a movie theater cleaning the aisles after each film. This Sunday, 9 movies are scheduled to show, 7 of which feature an alien as the one main protagonist.
If Belle is randomly assigned to clean up after 6 movies, what is the probability that all of them feature an alien as the one main protagonist?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0833
Step-by-step explanation:
Consider steps below;
[tex]Total Possible Outcomes - 9C6,\\\\9! / 6! ( 9 - 6 )!,\\1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 / ( 1 * 2 * 3 * 4 * 5 * 6)( 1 * 2 * 3 ),\\\\362,880 / 720 * 6 = Combinations - 84,\\\\[/tex]
[tex]Number Of Outcomes - 7C6,\\\\7! / 6! ( 7 - 6 )!,\\1 * 2 * 3 * 4 * 5 * 6 *7/ ( 1 * 2 * 3 * 4 * 5 * 6 ) ( 1 ),\\\\Outcomes - 7[/tex]
[tex]Conclusion ; Solution - 7 / 84 = ( About ) 0.0833\\Hope That Helps![/tex]
Solution; Probability ≈ 0.0833
Is parallel to ? Explain. Yes, because both lines have a slope of . Yes, because both lines have a slope of . No, because the slopes of the lines are not equal. No, because the slopes of the lines are not opposite reciprocals of each other.
Answer:
I'd need to see the lines but basically, parallel lines have to be directly across from each other and they have to be the same size, I put a pic so you can see what I mean
Hope this helps you
Answer:
C) yes, because both lines have a slope of 2/3
Step-by-step explanation:
edg2020
i need help pls, asap pls !!
Answer:
B
Step-by-step explanation:
in a wood there are 420 silver birch trees, 160 oak tees and 300 wild cherry trees. what is the percentage of the oak trees give your answer to 1 decimal place
Answer:
18.2%
Step-by-step explanation:
The total number of trees in the wood = 420 + 160 + 300
= 880 trees
∴ The percentage of the oak trees = [tex]\frac{160}{880} * \frac{100}{1}[/tex]
= [tex]\frac{2 * 100}{11}[/tex]%
= [tex]\frac{200}{11}[/tex]%
= 18.181818...%
In 1 decimal place = 18.2%
Hope this helps!!
Explain how to solve this problem by writing down the steps. The grass on the field erodes by -1 1/2% every year. If the total length of grass on the field was 220 feet long 3 years ago, how long is the length of grass on the field now?
Answer:
Step-by-step explanation:
Since the grass on the field erodes by -1 1/2% every year, it means that the rate of erosion is exponential. It is therefore eroding in geometric progression. We would apply the formula for determining the sum of n terms of a geometric sequence which is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of terms(number of years) in the sequence.
a represents the first term in the sequence(the length 3 years ago)
r represents the common ratio(rate of erosion)
From the information given,
a = 220 feet
r = - 1.5/100 = - 0.015
n = 3
Therefore, the length of the field after 3 years, S3(length of the field now) would be
Sn = a(1 - r^n)/(1 - r)
S3 = 220(1 - (- 0.015^3)/(1 - - 0.015)
S3 = 220.0007425/1.015
S3 = 216.7495 feet