Use the Singapore Bar Method, including drawings, to solve the following problem. Identify the unit value when appropriate, including labels. The sides of the triangle are in the ratio 5:7:8 and the longest side is 36 cm longer than the shortest side. Find the perimeter of the triangle.

The series converges for -1 < x < 1, and the interval of convergence is:

I = (-1, 1).

To find the radius of convergence, we can use the ratio test:

lim┬(n→∞)⁡|\(9(-1)^n n x^{2} /|9 (-1)^n nx^n\)| = lim┬(n→∞)⁡|x|/|1| = |x|

The series converges if the ratio is less than 1 and diverges if it is greater than 1.

So, we need to find the values of x such that |x| < 1:

|x| < 1

Thus, the radius of convergence is R = 1.

To find the interval of convergence, we need to test the endpoints x = -1 and x = 1:

When x = -1, the series becomes:

\(\sum 9 (-1)^n n(-1)^n = \sum -9n\)

which is divergent since it is a multiple of the harmonic series.

When x = 1, the series becomes:

\(\sum 9 (-1)^n n(1)^n = \sum 9n\)

which is also divergent since it is a multiple of the harmonic series.

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This means we are considering only a part of the ellipse that is centered at the point (0,0) and moves in the direction of the hands of a clock.

The given question is asking about a portion of an ellipse centered at the origin and oriented clockwise. Let's break down the question and provide a clear and concise answer.

An ellipse is a curved shape that looks like a stretched-out circle. It has two main properties:

a major axis and a minor axis. The major axis is the longer distance across the ellipse, and the minor axis is the shorter distance.

In the given question, we are specifically talking about a portion of the ellipse. This means we are considering only a part of the entire ellipse.

When we say the portion is centered at the origin, it means that the center of the portion lies at the point (0,0) on the coordinate plane.

Now, let's talk about the orientation. Clockwise orientation means that if you were to walk along the portion of the ellipse, you would move in the direction of the hands of a clock.

To summarize, the given question is asking about a portion of an ellipse centered at the origin and oriented clockwise.

This means we are considering only a part of the ellipse that is centered at the point (0,0) and moves in the direction of the hands of a clock.

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Answer: its B because an inequality is where you have a reater thn or less than sign

Step-by-step explanation:

6.1). the rate of depreciation, r, is approximately 10.77%.

6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2).  Ncominkosi borrowed approximately R 377,510.83 from the bank.

6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.

Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.

Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.

Therefore, the rate of depreciation, r, is approximately 10.77%.

6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:

\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)

Where:

P = Monthly payment

PV = Loan principal amount

r = Monthly interest rate

n = Total number of monthly payments

Let's calculate the monthly installment amount for Ncominkosi's loan:

Loan amount = Total amount paid to the bank - Interest

Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)

Number of monthly payments = 6 years * 12 months/year = 72 months

Using the formula mentioned above:

\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)

Substituting the values:

\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)

Calculating the value:

P≈R10,505.29

Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.

Total amount paid to the bank: R 596,458.10

Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.

Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:

\(A=P(1+r/n)(n*t)\)

Where:

A = Total amount paid

P = Loan principal amount

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

We can rearrange the formula to solve for the loan principal:

\(P=\frac{A}{(1+r/n)(n*t)}\)

Substituting the values:

Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)

Calculating the value:

Loan principal (P) ≈ R 377,510.83

Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.

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Answer:

would that be 12

Step-by-step explanation:

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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The temperature on the fifth day in January is -7°C.

It should be noted that a mean simply means the average of a set of numbers that are given.

Since the mean temperature for the first 4 days in January was 3°C. The rural temperature will be:

= 4 × 3°C

= 12°C

The mean temperature for the first 5 days in January was 1°C. The total temperature will be:

= 5 × 1°C

= 5°C

The temperature of the fifth day will be the difference between the temperature. This will be:

= 5°C - 12°C

= -7°C

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The patient underwent a three-stage surgical procedure to remove squamous cell carcinoma on the tip of their nose.

Based on the given information, the patient underwent a three-stage surgical procedure for the removal of squamous cell carcinoma on the tip of the nose. The tumor was initially removed (first stage) and divided into seven blocks for examination. However, positive margins were observed. Consequently, a second stage was performed, and the tumor was divided into five blocks, again revealing positive margins. Finally, a third stage was carried out, and the specimen was divided into three blocks, which were found to be clear of skin cancer.

The multiple stages of the surgical procedure indicate the physician's effort to ensure the complete removal of squamous cell carcinoma by progressively resecting the affected tissue until clear margins were achieved. This stepwise approach is common in cases where the tumor extends beyond the initial resection boundaries to ensure complete eradication of the cancer cells.

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Answer:

Step-by-step explanation:

This is a quadrilateral. A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

The interior angles of a simple quadrilateral ABCD add up to 360 degrees of arc.

Answer:

Angle x = 40°

Step-by-step explanation:

All angles of any quadrilateral sum up to 360°.

So here, already measure of 3 angles are given.

So if we add up all angles + Angle x then it sums up to 360°.

So, the following steps will lead you to the answer:

73° + 157° + 90° + Angle x = 360°

(Now add up the measure of the three given angles)

320° + Angle x = 360°

(Now, through transposition moves 320° to the RHS) (Remember when transposing the signs change)

Angle x = 360° - 320°

Finally,

Angle x = 40°

Hope it helps!!!

The vector equation for the plane represented by 2x + 3y + z - 1 = 0 is:

r = [x₀, y₀, z₀] + t × [2, 3, 1]

To determine a vector equation for the plane represented by the equation 2x + 3y + z - 1 = 0, we can use the coefficients of x, y, and z in the equation as the components of a normal vector to the plane. The normal vector will be orthogonal (perpendicular) to the plane.

The coefficients of x, y, and z in the equation are 2, 3, and 1, respectively. Therefore, the normal vector to the plane is given by:

n = [2, 3, 1]

Now, let's denote a point on the plane as P(x, y, z) and the coordinates of the point as (x₀, y₀, z₀). The vector from the point P₀(x₀, y₀, z₀) to any point on the plane P(x, y, z) will lie in the plane.

Using the vector equation of a plane, the equation becomes:

r - r₀ = t ×n

where r = [x, y, z] represents a general position vector in the plane, r₀ = [x₀, y₀, z₀] represents a position vector of a specific point on the plane, t is a scalar parameter, and n = [2, 3, 1] represents the normal vector to the plane.

Rearranging the equation, we get:

r = r₀ + t × n

Substituting the coordinates of the point P₀(x₀, y₀, z₀) and the normal vector n = [2, 3, 1], we obtain the vector equation for the plane:

r = [x₀, y₀, z₀] + t × [2, 3, 1]

So, the vector equation for the plane represented by 2x + 3y + z - 1 = 0 is:

r = [x₀, y₀, z₀] + t × [2, 3, 1]

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Answer:

5/12

Step-by-step explanation:

Answer:

D) -47/36

Step-by-step explanation:

Trust me.

we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

To compute n, we can use the formula:
n = ((zα/2)^2 * 2p*(1-p*)) / (ε^2)
Where zα/2 is the z-score associated with a confidence level of 1-α, p* is the probability of success for a binomial distribution, and ε is the margin of error.
Since we are given that the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 is at least 0.80, we can set α = 0.20 to find the corresponding z-score of 1.28.
Using p* = 1/2 as an upper bound for both P1 and P2, we can calculate the margin of error as:
ε = zα/2 * sqrt((p*(1-p*)) / n)
Plugging in the values, we get:
0.05 = 1.28 * sqrt((0.25) / n)
Solving for n, we get:
n = 501.76
Therefore, we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

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Answer: yes, it does fall at a constant rate. for each hour there is one inch of rainfall.

Step-by-step explanation:

if the line goes the the origin (0,0) then that means that it is a constant rate. if you look at the chart, there is number on every other line. This means that there is an odd number on the other lines. If you then go up the line for 1 hour, then you will meet at lines intersecting to get 1 inch of rainfall per hour

The error percentage is 4.13%.

The amount of mistakes is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Given

Annie estimates that the height of a bookcase is 78.25 in.

The actual height is 75.50 in.

The error percentage.

We know the formula for the error percentage.

\(\rm \% Error = \dfrac{Measured \ value- Actual\ value}{Actual\ value} * 100\\\\ \% Error = \dfrac{78.25 - 75.50}{78.75}*100\\\\ \% Error = \dfrac{3.25}{78.75}*100\\\\ \% Error = 0.0413*100\\\\ \% Error = 4.13 \%\)

The error percentage is 4.13%.

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The principal argument of z is tan⁻¹(2/3), the required principal argument of z is tan⁻¹(-2/3), the required principal argument of z is -1.249 + π, Cartesian form of the given exponential form is 4.34 + 3.03i, Cartesian form of the given exponential form is -1 - i√3, Polar form of a - z is (2√2, -π/4) and Polar form of b - z is (2, 0).

Given that z = 3 + 2i and we need to find z + z*

Conjugate of z = 3 + 2i is z* = 3 - 2i

On adding z and z* we get, z + z* = (3 + 2i) + (3 - 2i)  = 6

Exponential form of z = 3 + 2i can be found as follows:

r = |z|

  = tan⁻¹(2/3)

Thus, z = r(cosΘ + isinΘ)

             = sqrt(13)[cos(tan⁻¹(2/3)) + isin(tan⁻¹(2/3))]

Now, we need to find the principal argument.

The principal argument is the value of Θ that lies between -π and π.

So, the principal argument of z is given by:

tanΘ = 2/3. ⇒ Θ = tan⁻¹(2/3)

We have already found the exponential form of z.

So, the principal argument of z = tan⁻¹(2/3).

Given that z = 3 - 2i and we need to find zz*

Conjugate of z = 3 - 2i is z* = 3 + 2i

On multiplying z and z* we get, zz* = (3 - 2i)(3 + 2i)

                                                           = 9 + 4

                                                           = 13

Exponential form of z = 3 - 2i can be found as follows:

r = |z|

  = sqrt(3^2 + (-2)^2)

   = tan⁻¹(-2/3)

Thus, z = r(cosΘ + isinΘ)

             = sqrt(13)[cos(tan⁻¹(-2/3)) + isin(tan⁻¹(-2/3))]

Now, we need to find the principal argument.

The principal argument is the value of Θ that lies between -π and π.

So, the principal argument of z is given by:

tanΘ = -2/3. ⇒ Θ = tan⁻¹(-2/3)

We have already found the exponential form of z.

So, the principal argument of z = tan⁻¹(-2/3).

Given that z = -1 + 3i and we need to find zz*.

Conjugate of z = -1 - 3i is z* = -1 + 3i

On multiplying z and z* we get, zz* = (-1 + 3i)(-1 - 3i) = 10

Exponential form of z = -1 + 3i can be found as follows:

r = |z|

  = sqrt((-1)^2 + 3^2)

  = tan⁻¹(3/-1)

Thus, z = r(cosΘ + isinΘ)

             = sqrt(10)[cos(tan⁻¹(3/-1)) + isin(tan⁻¹(3/-1))]

The principal argument is the value of Θ that lies between -π and π.

So, the principal argument of z is given by:

tanΘ = 3/-1. ⇒ Θ = tan⁻¹(-3) + π = -1.249 + π

So, the principal argument of z = -1.249 + π.

Given that z = 4 - 3i and we need to find |z|

Magnitude of z = |z|

                          = sqrt(4^2 + (-3)^2)

                           = 5.

Cartesian form of z can be found as follows:

Re(z) = 4 and Im(z) = -3.

So, z = 4 - 3i.

Thus, |z| = 5.

Given that a - z = 5(cos20° + isin20°)

We know that cos⁡θ = Re⁡(ejθ) and sin⁡θ = Im⁡(ejθ).

So, the given complex number can be written as, a - z = 5ej20°

Using Euler's formula, ejθ = cosθ + isinθ

Substituting θ = 20°, we get,ej20° = cos20° + isin20°On

Substituting this value in the given expression, we get,

a - z = 5(cos20° + isin20°)

        = 5(cos20° + isin20°)

        = 4.34 + 3.03i.

Cartesian form of the given exponential form is 4.34 + 3.03i.

Given that b - z = 2e i4π/3 and we need to write in Cartesian form.

We know that cos⁡θ = Re⁡(ejθ) and sin⁡θ = Im⁡(ejθ).

So, the given complex number can be written as, b - z = 2ej4π/3

Here, we need to express the exponential form in Cartesian form.

Using Euler's formula, ejθ = cosθ + isinθ

Substituting θ = 4π/3, we get,

ej4π/3 = cos4π/3 + isin4π/3

           = -1/2 + i√3/2

On substituting this value in the given expression, we get,

b - z = 2ej4π/3

        = 2(cos4π/3 + isin4π/3)

        = -1 - i√3.

Cartesian form of the given exponential form is -1 - i√3.

Given that 3 + 4i and we need to write in polar form.

We know that

r = |z|

  = √(3^2 + 4^2)

  = 5Θ

  = tan^-1(4/3)

Thus, z = 5(cos(tan^-1(4/3)) + isin(tan^-1(4/3)))

Given that z = 3 - i and w = 1 + 3i, and we need to find (2z + 3w) / (2z - 3w)

Using the formula for the division of two complex numbers, we get:

(2z + 3w) / (2z - 3w) = [(2)(3 - i) + (3)(1 + 3i)] / [(2)(3 - i) - (3)(1 + 3i)]

                                 = (6 + i + 9 + 9i) / (6 - 2i - 9 - 9i)

                                 = (15i + 15) / (-2 - 7i)

Rationalizing the denominator, we get

(15i + 15) / (-2 - 7i) = [(15i + 15)(-2 + 7i)] / [(-2 - 7i)(-2 + 7i)]

                             = (75 + 15i) / 53

The final result is (75 + 15i) / 53.

Given that z^2 + z + 1 = 0, and we need to give all the roots of the equation.

We know that the roots of a quadratic equation are given by the formula z = [-b ± √(b^2 - 4ac)] / 2a

On comparing the given equation with the standard form of the quadratic equation ax^2 + bx + c = 0, we get a = 1, b = 1, and c = 1.

Substituting these values in the formula, we get,

z = [-1 ± √(-3)] / 2

Since there is no real number whose square is negative, the roots are complex numbers.

The roots of the equation are given by z = (-1 ± i√3) / 2.

Given that a - z = 2 - 2i, and we need to write in polar form.

We know that

r = |z|

  = √(2^2 + (-2)^2)

  = 2√2Θ

  = tan^-1(y/x)

  = tan^-1(-2/2)

  = -π/4

Thus, z = 2√2(cos(-π/4) + isin(-π/4)) = 2√2(-√2/2 - i√2/2)

            = -2 - 2i

Polar form of a - z is (2√2, -π/4).

Given that b - z = 2i, and we need to write in polar form.

We know that

r = |z|

  = 2Θ

  = tan^-1(y/x)

  = tan^-1(0/2)

  = 0

Thus, z = 2(cos0 + isin0) = 2

Polar form of b - z is (2, 0).

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Answer:

it should be (5,4)

Step-by-step explanation:

♊♊♊

Answer:

A would be reflected across to (5,-4), so, the bottom answer.

Step-by-step explanation:

For reflections across an axis, all I really do is count how many units a point is from the axis you are reflecting across, and then count the many on the other side of the axis. On this problem, A was 4 units above the x-axis, and 5 from the y-axis. I just counted 8 units down, or, 4 units down from the x-axis, and since I didn't change where my point was on the y-axis, it landed on the point (5,-4).

Answer:

3,8

Step-by-step explanation:

Answer:

You have to multiply the last number by 3. So 9 times 3 equals 27 and 27 times 3 equals 81 and so on. The answer would be 59,049

Step-by-step explanation:

I hope this helps!!

Answer:

$70 for 5 DVDs  one dvd costs $14

Step-by-step explanation:

Answer:

5 cd's is 70 dollars

Step-by-step explanation:

28 divided by 2 = 14

Therefore 1 cd = 14 dollars

14 x 5 = 70$=5 CD's

The probability distribution at each point x along the horizontal axis.

For a Normal distribution with mean 0 and standard deviation 1,

the following Python line outputs the probability p(-0.15 < x < 1.88):

print(st.norm.cdf(1.88, 0, 1) - st.norm.cdf(-0.15, 0, 1))

Probability is the likelihood or chance that an event will occur. It is a number between 0 and 1, with 0 indicating that an event will never occur and 1 indicating that an event will always occur.

Probability values range from 0 to 1, with a value of 0 indicating that the event will never occur and a value of 1 indicating that the event will always occur.

The probability is the value between 0 and 1 that indicates the likelihood of an event occurring. The probability is obtained by dividing the number of ways an event can occur by the total number of possible outcomes.

Scipy.stats.norm is the normal distribution's probability density function (pdf) in SciPy.

The PDF function is a part of the scipy.stats library in Python. The probability density function of the normal distribution is the function scipy.stats.norm.pdf(x, loc=0, scale=1). It is the height of the probability distribution at each point x along the horizontal axis.

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Answer:

y = -5/7x - 2

Step-by-step explanation:

The slope intercept form is y = mx + b

5x + 7y = -14

Subtract 5x both sides

7y = -5x - 14

Divided by 7 both sides

y = -5/7x - 2

So, the answer is y = -5/7x - 2

Answer:

1

Step-by-step explanation:

3.2/0.4=8

8×2=16

16×0.4=6.4

6.4÷0.1=64

Answer:

24

Step-by-step explanation:

She visits 3 temples one by one

She offers 1/2 of what she has in the baske

She is left with 3 flowers

If she gave 1/2 of what she had left to the 3rd, and the other half was 3

Then it means she gave the 3rd 3 flowers

So 3 is 1/8th of what she had at the beginning

Multiply 3*8 and you get 24

Hope this helps ^_^

To solve the given differential equation (6x+1)y^2 dy/dx + 4x^2 + 2y^3 = 0, we can rearrange the terms to make it an explicit equation for dy/dx: dy/dx = -(4x^2 + 2y^3) / ((6x+1)y^2)

Now, separate the variables by moving all the x terms to one side and y terms to the other side: (dy / (y^2 - 2y^3)) = - (4x dx / (6x + 1))

Next, integrate both sides of the equation: (dy / (y^2 - 2y^3)) = -∫(4x dx / (6x + 1))

To solve the given differential equation (6x+1) y^2 dy/dx + 4x^2 + 2y^3 = 0, we can rearrange the terms to get:

(6x+1) y^2 dy = - (4x^2 + 2y^3) dx

Now, we can integrate both sides:

∫ (6x+1) y^2 dy = - ∫ (4x^2 + 2y^3) dx

Integrating the left-hand side with respect to y and the right-hand side with respect to x, we get:

2y^3 (3x + 1) = - (4/3)x^3 - y^4 + C

where C is the constant of integration.

To solve for y, we can isolate y^4 on one side of the equation and take the fourth root:

y^4 = (4/3)x^3 - 2y^3 (3x + 1) + C

y^4 + 6y^3 x + (4/3)x^3 - C = 0

This is a quartic equation in y^4, which can be difficult to solve. However, if we substitute z = y^3, we can rewrite the equation as:

z^2 + 6xz + (4/3)x^3 - C = 0

This is a quadratic equation in z, which can be solved using the quadratic formula:

z = (-6x ± sqrt(36x^2 - 4(4/3)x^3 + 4C)) / 2

Simplifying and substituting back for y, we get:

y = (z)^(1/3)

y = [(-6x ± sqrt(36x^2 - 4(4/3)x^3 + 4C)) / 2]^(1/3)

This is the general solution to the given differential equation. To find a particular solution, we need to know the initial condition, such as y(0) = 1.

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Answer:

5.2

Step-by-step explanation:

The value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

The expression is given as:

(3x^5 + y^2)^2

Expand the expression

So, we have

(3x^5 + y^2)^2 = (3x^5 + y^2)(3x^5 + y^2)

Expand the bracket

(3x^5 + y^2)^2 = 9x^10 + 3x^5y^2 + 3x^5y^2 + y^4

Evaluate the sum

(3x^5 + y^2)^2 = 9x^10 + 6x^5y^2 + y^4

Hence, the value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

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Answer:

Step-by-step explanation:

-40

−20−8-12

−28−12

-40

Using the concepts of arithmetic and geometric progression, Maria's total land will exceed Lucia's amount of land in the 7th year.

An arithmetic progression is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

whereas, a geometric progression is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Lucia is increasing her land by arithmetic progression. She bought a 11 hectare land and increases it by 5 hectares every year.

Land in:

year 1 = 11

year 2 = 11+5 = 16

year 3 = 16+5 =21

year 4 =  21+5 = 26

year 5 = 26+5 = 31

year 6 = 31 + 5 =36

year 7 = 36+5 = 41

year 8 = 41+5 = 46

Maria is increasing her land by geometric progression. She bought 6 hectares land in first year. Multiplied the amount by 1.4 each year.

Land in:

year 1 = 6

year 2 = 6*1.4= 8.4

year 3 = 8.4*1.4 = 11.76

year 4 =  11.76*1.4 =16.46

year 5 = 16.46 *1.4 = 23

year 6 = 23 * 1.4 = 32.2

year 7 = 32.2 * 1.4 = 45.08

Learn more about arithmetic progression here

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The complete question is given below:

Lucia and Maria are business women who decided to invest money by buying farm land in Brazil. They started their investments at the same time, and each year they buy more land. Lucia bought 11 hectares of land in the first year, and each year afterwards she buys 5 additional hectares. Maria bought 6 hectares of land in the first year, and each year afterwards her total number of hectares increases by a factor of 1.4. In which year will Maria's amount of land first exceed Lucia's amount of land?

Answer:

\(\frac{6}{7}\)

y = \(\frac{6}{7}\) x

Step-by-step explanation:

Leave your answer as a fraction and do not change it into a decimal.

Your y is changing by 6 as your x is changing by 7

Take into accoun that the Pythagorean theorme is given by:

c² = a² + b²

8.

a = ?, b = 18, c = 30

solve the equation for a:

c² = a² + b²

a² = c² - b²

a = √(c² - b²) replace the values of c and b

a = √(30² - 18²)

a = √(900 - 324)

a = √(576)

a = 24

9.

c= ?, a = 5, b = 12

replace the values of b and a:

c = √(a² + b²)

c = √(5² + 12²)

c = √(25 + 144)

c = √(169)

c = 13

10.

b = ?, a = 6, c = 10

solve the equation for b:

b = √(c² - a²)

b = √(10² - 6²)

b = √(100 - 36)

b = √(64)

b = 8