Write three quadratic equations that are NOT equivalent, each forming a graph with vertex
(−2,3).
Please explain it
Answers
When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).
The vertex of a quadratic equation:
a[tex]x^{2}[/tex]+bx + c = y
is located at :
x = -b/2a.
In this case, x = -2
Then,
-b/2a = -2
And we also have that:
a[tex](-2)^2[/tex] -2b + c = 3
Then we have two equations:
-b/2a = -2
a[tex](-2)^2[/tex] -2b + c = 3
We have only equations and 3 variables, So we can just give the variable c different values and we will find different quadratic equations that are not equivalent.
Let's begin with c = 0 ,Our equations are:
-b/2a = -2
a[tex](-2)^2[/tex] -2b + 0 = 3
In the first equation we can isolate b and get :
b = 4a
Now we can replace this in the other equation and solve this for a.
4a + 4a x -2 = 3
-4a = 3
a = -3/4
then:
b = 4a = 4 x -3/4 = -3
The first quadratic equation is:
(-3/4)[tex]x^{2}[/tex] - 3x = y
Now, To find the second let's use a different value of c.
c = 1
b = 4a
a[tex](-2)^2[/tex] -2b + 1 = 3
Let's solve in the same way as before:
4a + 4a x -2 + 1= 3
-4a = 2
a = 2/-4 = 1/-2
b = 4 x -1/2 = -2
Then our equation is :
(-1/2)[tex]x^{2}[/tex] -2x + 1 = y
For the last equation, let's use c = 2
then our equation are:
b = 4a
a(-2)^2 - 2b +2 = 3
Same as before, replace the first equation in the second
4a + 4a x-2 +2 = 3
-4a +2 = 3
-4a = 1
a = -1/4
Then:
b = 4 x (-1/4) = -1
Our third equation is :
(-1/4)x^2 - x + 2 = y
Now, Below you can see all of them graphed.
When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).
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Related Questions
Select the correct answer from each drop-down menu. Using the image below, select the best answer from each pull-down to complete the statements. The measure of ∠FED is ? °. ∠CBD and ∠ ? are complementary angles. Please help. thank you
Answers
The value of ∠FED is 120° and ∠CBD is complementary to ∠FDE
What are complementary angles?Complementary angles are two angles that sum up to 90°
For example 60° and 30° are complementary.
Either angle is called the complement of the other angle.
∠FED, ∠FDE and ∠DFE are in a triangle.
so,
∠FED + ∠FDE + ∠DFE = 180°
16x - 8 + 2x + 9 + 35 = 180 ( sum of angles in a triangle)
18x +36 = 180
18x = 180 - 36
18x = 144
x = 144/18
x = 8
so ∠FED = 16x - 8
Substitute x = 8 into the equation above we have
16(8) - 8 = 128 - 8 = 120°
∠FDE = 2x + 9
∠FDE = 2(8) + 9 = 25°
∠BED = 6x + 12
∠BED = 6(8) + 12
∠BED = 48 + 12
∠BED = 60°
∠CBD = -2x + 81
∠CBD = -2(8) + 81
∠CBD = 65°
so since ∠CBD = 65° and 90 - 65 = 25°
∠CBD is complementary to ∠FDE
In conclusion, ∠FED is 120° and ∠CBD is complementary to ∠FDE
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what is (x+5)……………
……….:…………
Answers
Answer:
x+5
Step-by-step explanation:
there are no like terms
If X = 32 yards, Y = 60 yards, and Z = 68 yards, what is the sine of ZA?
Answers
The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The given triangle is a right-angled triangle
As Z² = X²+Y²
So sin (x) = 60/68=0.88
and sin(y) = 32/68=0.47
Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.
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Determine whether the percent of change is a percent of increase or a
percent of decrease. Then find the percent of change.
%
original: 20
new: 18
by
Answers
Answer:
the change is in %age of decrease of 10%
Step-by-step explanation:
original value = 20
new value = 18
decrease = 2
%age decrease = decrease/original value * 100
= 2/20 * 100
= 10%
In the following expression, n is a rational number: Which expression below is equivalent to this expression?
Answers
Answer:
none of them
Step-by-step explanation:
I need help asap thank you..
Answers
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
Help with this math problem
Answers
The value of the investment after 3.25 years is $434.93.
What is the interest rate?The amount a lender charges a borrower, expressed as a percentage of the principle, is known as the interest rate.
Given that, the initial investment is P₀ = $400, the interest rate is n = 2.6%, and the time is x = 3.25 years.
The formula for the future value in continuous compounding is:
P(x) = P₀eⁿˣ
Substitute P₀ = 400, n = 2.6%, and x = 3.25 into the equation:
[tex]P(3.25) = (400)e^{2.6\%(3.25)}\\[/tex]
= 434.93
Hence, the value of the investment after 3.25 years is $434.93.
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A famous leaning tower was originally 180.5 feet high At a distance of 125 feet from the base of the tower, the angle of olevation to the top of the tower is found to be 56° Find ZRPQ indicated in the figure. Also find the perpendicular distance from R to PQ
Answers
The perpendicular distance from R to PQ is 346 feet.
What are the trigonometric functions?
The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
We have,
consider the sides of leaning tower are,
opposite side of the angle 56° (x) = 180.5 feet.
Adjacent side of the angle 56° (y) = 125 feet.
We know,
[tex]tan\theta =\frac{ opposite \ side}{ adjacent \ side} = \frac{x}{y}[/tex]
[tex]\theta = \ tan^{-1} \left(\frac{ opposite \ side}{ adjacent \ side} \right)[/tex]
The angle of elevation is [tex]\theta = \ tan^{-1} \left(\frac{180.5 }{125} \right)[/tex]
θ = 56°
The perpendicular distance from R to PQ is RQ
[tex]sin\theta = \frac{opposite side}{hypotanous} = \frac{180.5}{y}[/tex]
sin(56) = 180.5/PQ
RQ = 180.5/sin(56)
RQ = - 346.08
RQ = 346 (distance never be negative),
Hence, the perpendicular distance from R to PQ is 346 feet.
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Select the correct answer from the drop-down menu.
A new park is adding two new walking paths, as indicated by and , which are measured in meters. The park resembles an isosceles trapezoid.
Figure shows a trapezium ABCD. AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
Determine the length of each path.
A.
The length of each path is
130
meters.
B.
The length of each path is
140
meters.
C.
The length of each path is
120
meters.
D.
The length of each path is
150
meters.
Answers
A.The length of each path is 130 meters.
Given:
The park resembles an isosceles trapezoid.
Figure shows a trapezium . AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
we know that:
Diagonals are equal in isosceles trapezoid.
14x + 4 = 11x + 31
14x - 11x = 31 - 4
3x = 27
divide by 3 on both sides
3x/3 = 27/3
x = 9
Diagonal length = 14x + 4.
= 14*9 + 4
= 126 + 4
= 130 meters.
Therefore The length of each path is 130 meters.
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Creating a Function from a Mapping
The mapping shows a relationship between input and
output values.
Input
Activity
-5
SAING
2
40 Intro
Output
T? 7 NO
-3
-2
2
Which ordered pair could be removed to make this
relation a function?
O (-5,0)
-O (-1, -3)
O (4,-2)
O (6,-1)
Done
Answers
The ordered pair could be removed to make this relation a function is (4,-2).
What is an ordered pair?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
The numeric values in an ordered pair can be integers or fractions.
Here,
A function is when each input has one output. So, for every x there is one y. The x values can not repeat.
But in the given value x is repeating so the ordered pair (4, -2) can be removed.
Hence, the ordered pair could be removed to make this relation a function is (4,-2).
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Solve each equation for x. Show all steps.
A) log base 4 (x^2 -12x+48) =2
B) 27^(4x-6) =(1/9)^(2x-7)
Answers
A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8
B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2
Solving equations: Determining the value of xFrom the question, we are to solve the given equations
The given equation is log₄(x² - 12x + 48) = 2
From one of the laws of logarithm, we have that
logₐ x = n ⇒ x = aⁿ
Thus,
log₄(x² - 12x + 48) = 2 becomes
(x² - 12x + 48) = 4²
x² - 12x + 48 = 16
x² - 12x + 48 - 16 = 0
x² - 12x + 32 = 0
Solve the quadratic equation
x² - 12x + 32 = 0
x² - 8x - 4x + 32 = 0
x(x - 8) -4(x - 8) = 0
(x - 4)(x - 8) = 0
x - 4 = 0 OR x - 8 = 0
x = 4 OR x = 8
B) 27^(4x-6) =(1/9)^(2x-7)
Solve for x
27^(4x-6) =(1/9)^(2x-7)
Express the bases in index form
3^3(4x-6) =(3)^-2(2x-7)
Equate the powers
3(4x - 6) = -2(2x - 7)
12x - 18 = -4x + 14
12x + 4x = 14 + 18
16x = 32
Divide both sides by 16
16x/16 = 32/16
x = 2
Hence, the value of x is 2
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2x-4y=4
x-2y = 8
Helppppp
Solve for y and graph example;(number,number)
Answers
The system of equations has no solutions, meaning that the two lines never intersect, as shown by the image at the end of the answer.
What is a system of equations?A system of equations is a set of equations in the context of a problem, and these equations are solved to find the numeric value of each variable of the problem.
When the system involves linear equations, such as is the case in this problem, the solution is given by the intersection point between these two lines.
In this problem, the equations are given as follows:
2x - 4y = 4.x - 2y = 8.From the second equation, it is found that:
x = 8 + 2y.
Replacing on the first equation, the solution for y can be obtained as follows:
2(8 + 2y) - 4y = 4
16 + 4y - 4y = 4
0y = -12
Which is a contradiction, hence the system has no solutions and the two lines do not intersect.
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Emmett is planning a party at an escape room. The escape room will charge Emmett a
booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
Answers
Answer:
B. After the booking fee the party will cost $20 per person
A harbor seal dives 35 meters below the ocean's surface. Then it dives down an additional 12 meters Determine the seal's new position relative to the surface of the ocean
Answers
The seal's new position relative to the surface of the ocean is 47 meters below.
How to calculate the value?It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.
In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres
The new position will be;
= -35 - 12
= -47
This implies that it's 47 meters below the ocean surface.
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3.
A circular pool of oil grew so that its radius increased by 2 feet. The formula shown can
be used to determine the area of the circle.
A = π (r + 2)²
Which equation is equivalent to the formula solved for r in terms of A?
Or=√1-2
Or=√√√+2
Or=√√4+2
Or-√4-2
Answers
Equation which is equivalent to the formula solved for r in term of A is [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex].
What is circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A circle is also termed as the locus of the points drawn at an equidistant from the centre.
What is radius?
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.
What is circumference?
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.
Given that;
[tex]A = \pi{({r+2})^{2}}[/tex]
[tex](r+2)^{2} =\frac{A}{\pi}[/tex] (equivalent transformation)
[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex]
[tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]
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Find the X-intercept for this please .
Answers
Answer: I believe both the x and y- intercepts are “(0,0)”
Step-by-step explanation: there is only one intercept and it is at the origin (0,0) making both the x and y - intercepts (0,0) :)
Last year, Ivanna opened an investment account with $7500. At the end of the year, the amount in the account had decreased by 7.8%. How much is this
decrease in dollars? How much money was in her account at the end of last year?
Answers
0.065=x/5800
x=$377; that is the dollar value of the decrease
The account is now worth $5423.
Dave’s Furniture Store is having a 35% off sale on tables. Robert paid $195 for a table that was on sale. What was the original price of the table?
Answers
Answer:
557.143
Step-by-step explanation:
195 / 35% = 557.14
At the end of an amusement park ride, a boat lands in a pool, splashing out a lot of water. Three inlet pipes, each working alone, can fill the pool in 8 seconds, 12 seconds, and 16 seconds, respectively. How long would it take to fill the pool if all three inlet pipes are used?
Answers
The three inlet pipes, each working alone can fill the pool in 8 seconds, 12 seconds, and 16 seconds, respectively. it will take them 3.69 seconds fill the pool
How to determine how long it takes it fill the poolThe problem requires to determine how long it takes to fill the pool when the three pipes are working simultaneously
let the time to fill the the pool when the three pipes are working simultaneously be y, such that
8 seconds pipe fills the pool in y/8 seconds
12 seconds pipe fills the pool in y/12 seconds
16 seconds pipe fills the pool in y/16 seconds
Adding the times together
y/8 + y/12 + y/16 = 1
13y/48 = 1
y = 48/13
y = 3.69 seconds
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Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
Answers
The values of y and x are -7 and 2 respectively, completing the ordered pairs: (6,-7) and (2,1).
What are the values of y and x?Given the equation in the question;
y = −2x + 5Ordered pairs: (6,y) and (x,1)To find the y-value that completes the ordered pair ( 6,y ), replace all occurrence of x with 6 in the equation and solve for y.
y = −2x + 5
y = −2( 6 ) + 5
Multiply -2 and 6
y = -12 + 5
y = -7
Hence, the output value is -7, this forms an ordered pair of (6,-7).
To find the x-value that completes the ordered pair ( x,1 ), replace all occurrence of y with 1 in the equation and solve for x.
y = −2x + 5
1 = −2x + 5
Add 2x to both sides
1 + 2x = −2x + 2x + 5
1 + 2x = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2
Hence, the input value is 2, this forms an ordered pair of (2,1).
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A fair six-sided die is rolled twice. What is the theoretical probability that the first number that comes up is greater than or equal to the second number?
OA. 1
6
OB. 1
2
O c. 7
12
O
D. 5
Answers
Answer:
c. 7/12
Step-by-step explanation:
There are 36 possible outcomes when you roll a die twice.
11, 12, 13, 14, 15, 16
21, 22, 23, 24, 25, 26
31, 32, 33, 34, 35, 36
41, 42, 43, 44, 45, 46
51, 52, 53, 54, 55, 56
61, 62, 63, 64, 65, 66
The desired outcomes are the ones whose first number is greater than or equal to the second number. They are shown in bold and underline above.
There are 21 desired outcomes.
p(first number ≥ second number) = 21/36 = 7/12
Answer: c. 7/12
What do you observe? What do you wonder? What are 2 things you know and 1 thing that you're missing?
Answers
The observation of the graphing speed versus time is given below.
What is acceleration?The rate at which the speed is changing is known as acceleration.
From the graph, the line segment OA and DE have linear acceleration which increases the velocity.
Similarly, from the graph, the line segment BC and EF have linear deacceleration which decreases the velocity.
From the graph, line segment AB has constant acceleration which increases the velocity.
And from the graph, the line segment CD has zero acceleration which makes the velocity to be constant.
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4/7
of a square is painted green.5/6 of the remainder is painted red. If the green
part is 36 cm² more than the red. find the area of the square.
Answers
Answer:
168
Step-by-step explanation:
Let the area of the square be [tex]x[/tex].
[tex]\frac{4}{7}x-\frac{5}{6}\left(\frac{3}{7}x \right)=36 \\ \\ \frac{4}{7}x-\frac{5}{14}x=36 \\ \\ \frac{8}{14}x-\frac{5}{14}x=36 \\ \\ \frac{3}{14}x=36 \\ \\ \frac{1}{14}x=12 \\ \\ x=168[/tex]
a recipe requires 3/4 cup of water. Nora has a 1 1/2 cup measuring cup. how much of the measuring cup is filled with water?
Answers
Answer:
i think it is 15/20
Step-by-step explanation:
because 6/8,9/12,12/16
(x2 + 3x –9) ÷ (x – 2).
Answers
Answer:
Step-by-step explanation:
Determine the length of the line segment shown. graph of line segment from negative 6 comma negative 5 to 0 comma 3 100 units 25 units 10 units 8 units
Answers
The length of the line segment will be 10 units.
What is Distance?
The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;
D = √( y₂ - y₁)² + (x₂ - x₁)²
Given that;
Two endpoints of the line segment are (6, -5) and (0, 3).
Now,
The length of the line segment is distance between two endpoints (6, -5) and (0, 3).
So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;
D = √(0 - 6)² + (3 - (-5))²
D = √36 + 64
D = √100
D = 10 units
Thus, The length of the line segment will be 10 units.
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Distance in Feet
1. Earlier this week the famous "Live Cannonball” - Gunter Money was shot from a cannon at the Austin Expo.
Gunter flew to a height of 70 feet and traveled a distance of 160 feet only to land perfectly in a safety net.
Assume (0, 0) was the starting point for Gunter's flight and that he landed in the net at (160, 0).
(a) Use matrices to find the equation for Gunter Money's path.
(b) Write the equation for Gunter Money's path in vertex form.
(c) device a method to estimate the angle at which Gunter money takes off
Answers
The 160 feet range and 70 feet height of the path of Gunter Money which can be described with a quadratic equation, gives;
(a) The path is; y = -1.09375×10²·x² + 1.75·x
(b) The vertex form of the equation is; y = -1.09375·(x - 80)² + 70
(c) The angle at the start is approximately 60.3°
What is quadratic equation?A quadratic equation is a single variable polynomial equation of the second degree.
The points in the path which is a path of a projectile and has a shape of a parabola are;
(0, 0), (80, 70), and (160, 0)
The equations are;
y₁ = a·x₁² + b·x₁ + c
y₂ = a·x₂² + b·x₂ + c
y₃ = a·x₃² + b·x₃ + c
Plugging in the coordinates of the three points in the path gives;
0 = a·0² + b·0 + 1·c70 = a·80² + b·80 + 1·c0 = a·160² + b·160 + 1·cThe matrix becomes;
[tex]A = \begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}[/tex]
[tex]X = \begin{bmatrix}a \\b \\c\end{bmatrix}[/tex]
[tex]Y = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]
We have;
A·X = Y, which gives;
[tex]\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}\cdot \begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]
[tex]X = \dfrac{Y}{A} = A^{-1}\cdot Y[/tex]
Where;
A⁻¹ = The inverse of the matrix A
[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \frac{ \begin{bmatrix}0 \\70 \\0\end{bmatrix}}{\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}} = \begin{bmatrix}\dfrac{1}{12800} & -\dfrac{1}{6400} & \dfrac{1}{12800} \\\\-\dfrac{3}{160} &\dfrac{1}{40} & -\dfrac{1}{160} \\\\1 &0 &0 \\\end{bmatrix}\bullet \begin{bmatrix}0\\ \\70\\ \\0\end{bmatrix}=\begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]
[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]
[tex]a = -\dfrac{7}{640}[/tex]
[tex]b = \dfrac{7}{4}[/tex]
c = 0
The equation for Gunter Money's path is therefore;
[tex]y = -\dfrac{7}{640} \cdot x^2 + 1\dfrac{3}{4} \cdot x + 0 = -1.09375\times 10^2 \cdot x^2 + 1.75\cdot x[/tex]
(b) The vertex of the path is (h, k) = (80, 70)
The vertex form of a quadratic equation is; y = a·(x - h)² + k
The equation of Gunter Money's path in vertex form is therefore;
[tex]y = -\dfrac{7}{640} \cdot \left(x - 80)^2 + 70 = -1.09375\times 10^2\cdot (x - 80)^2+70[/tex]
(c) The angle of the parabolic path of Gunter Money's motion at a point is given by the value of the arctangent of the differentiation of the function for the motion at the point as follows;
[tex]y' = -\dfrac{7\times 2}{640} \cdot x + 1\dfrac{3}{4}[/tex]
At the point Gunter Money takes off, (0, 0), we have;
[tex]tan(\theta) = y' = -\dfrac{7\times 2}{640} \times 0 + 1\dfrac{3}{4} = 1\dfrac{3}{4} = 1.75[/tex]
[tex]\theta = arctan(1.75) \approx 60.3^{\circ}[/tex]
The angle is approximately 60.3°
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Find the perimeter of the shape below. Each grey square has a side
length of 1.
Answers
The perimeter of the shape is 38 total unit.
Perimeter of plane shapesThe perimeter of a shape is a measure of the distance round the boundary or edge of the shape.
The given shape comprises of squares of 1 length each, hence to calculate for the perimeter of the shape, we add up each boundary of 1 unit length which will amount to 39 in total.
Therefore by careful observation, the perimeter of the plane shape is calculated to give us 39 total perimeter length.
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In chapters 5-8 of Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm. What causes these feelings
A. A visit from his father
B. A letter from Elizabeth
C. The arrival of Henry Clerval
D. An award for creating the monster
Answers
Answer:
C______________4_⁴________
$6000 are invested in a bank account at an interest rate of 6 percent per year.
Find the amount in the bank after 11 years if interest is compounded annually.
Find the amount in the bank after 11 years if interest is compounded quarterly.
Find the amount in the bank after 11 years if interest is compounded monthly.
Finally, find the amount in the bank after 11 years if interest is compounded continuously.
Answers
The value after 11 years with annual compounding is $11,389.79
The value after 11 years with quarterly compounding is $11,552
The value after 11 years with monthly compounding is $11,589.68
The value after 11 years with continous compounding is $70,080.78.
What is the future value?When an amount is compounded annually, it increases in value once a year. When an amount is compounded quarterly, it increases in value four times a year. When an amount is compounded monthly, it increases in value twelve times a year. When an amount is compounded continuously, it increases continuously over the investment period.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate - annual rate / number of compounding m = number of compoundingN = number of yearsValue after 11 years with annual compounding: $6,000 x (1.06)^11 = $11,389.79
Value after 11 years with quarterly compounding: $6,000 x (1 + 0.06 /4)^(11 x 4) = $11,552
Value after 11 years with monthly compounding: $6,000 x (1 + 0.06 /12)^(11 x 12) = $11,589.68
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateValue after 11 years: 6,000 x (2.718^0.06) x 11 = $70,080.78
To learn more about continuous compounding, please check: https://brainly.com/question/26476328
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