The sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.
The formula for the sum of the first n consecutive odd numbers is n^2. This can be proven by induction.
Let n = 2k – 1.
Base case: When k = 1, then n = 2k – 1 = 1. The sum of the first 1 consecutive odd numbers is 1^2 = 1.
Inductive step: Assume that for some k = p, the sum of the first 2p – 1 consecutive odd numbers is (2p – 1)^2.
Now, consider the case when k = p + 1. The sum of the first 2(p + 1) – 1 consecutive odd numbers is:
(2p – 1)^2 + (2p + 1) + (2p + 3) + … + (4p + 1).
This can be written as (2p – 1)^2 + 2(1 + 2 + … + (p + 1)) (2p + 1).
By the sum of an arithmetic sequence, the expression in the parentheses is equal to (p + 1)(2p + 2).
Therefore, the sum of the first 2(p + 1) – 1 consecutive odd numbers is (2p – 1)^2 + 2(p + 1)(2p + 2).
Simplifying, this is equal to (2p + 1)^2.
Therefore, the statement holds for k = p + 1, and by induction, it holds for all positive integers k.
Therefore, the sum of the first 2k – 1 consecutive odd numbers is (2k – 1)^2.
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Jackson invested $320 in an account paying an interest rate of 3. 2% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $410?
If Jackson invested $320 in an account paying an interest rate of 3. 2% compounded continuously, assuming no deposits or withdrawals are made, it would take: 3.37 years
for the value of the account to reach $410
To solve this problem, we can use the formula for continuously compounded interest:
A = P * e^(rt)where A is the final amount, P is the initial amount (320), r is the interest rate (3.2%), and t is the time in years.
Solving for t, we get:
t = (ln(A/P)) / (r)Plugging in the values, we get:
t = (ln(410/320)) / (0.032)Approximating this, we get:
t = 3.37 years, rounded to the nearest tenth of a year.So it would take about 3.4 years for the value of the account to reach $410.
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which of the following is the midpoint riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width?
The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is 9980
The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is calculated by summing the area of each subinterval under the midpoint of the interval.
The formula for the midpoint Riemann sum is given by:
Sum = (width of interval) * (height of midpoint)
For this problem, since the width of each interval is 16/4 = 4, the midpoint Riemann sum is calculated by:
Sum = 4 * (1 + (16/4)^3 + (32/4)^3 + (48/4)^3)
Substituting the values for each midpoint, we get the following equation:
Sum = 4 * (1 + 4^3 + 8^3 + 12^3)
This simplifies to:
Sum = 4 * (1 + 64 + 512 + 1728)
Therefore, the midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is:
Sum = 4 * (2495)
Sum = 9980
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2/3 - 5/9=
in simplest form
Answer:
Step-by-step explanation:
2/3 - 5/9 = 1/
9
≅ 0.1111111
Answer: 1/9
Step-by-step explanation:
When Kyle doesn't study for his tests, he has a 45% chance of passing. If Kyle didn't study for15 tests this semester, what is the probability he passed at this semester?
The probability that Kyle will pass all 15 tests if he does not study for them is approximately 0.0017.
This is because the probability of passing each individual test without studying is 0.45, and the probability of passing all tests without studying is equal to 0.45 multiplied by itself 15 times, which is 0.0017. This means that the odds of Kyle passing all 15 tests without studying are very slim.
Even if he has a good understanding of the material and has been able to recall the information without studying, it is very unlikely that he will be able to do so for all 15 tests. It is therefore recommended that Kyle studies for his tests in order to increase his chances of passing them.
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sandeep, hee, sara, and mohammad play euchre with a standard deck consisting of 24 cards (a, k, q, j, 10 , and 9 from each of the four suits of a regular deck of playing cards). in how many ways can the deck be dealt so that each player receives 5 cards, with 4 cards left in the middle, one of which is turned face-up? the order of the 3 cards that are left face-down in the middle does not matter, but who receives a particular set of 5 cards (for example, sara or sandeep) does matter.
There are 23,311,945,600 possible ways to deal the cards to the four players and choose one card to be turned face-up in the middle.
We can calculate the number of ways to deal the cards to the four players and then multiply by the number of ways to choose which card is turned face-up in the middle.
First, there are 24 choose 5 ways to deal the first hand, since each player receives 5 cards. Then, there are 19 choose 5 ways to deal the second hand, since there are now 19 cards left. Similarly, there are 14 choose 5 ways to deal the third hand and 9 choose 5 ways to deal the fourth hand.
So, the number of ways to deal the cards to the four players is:
24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!))
Now, we need to multiply this result by 4, since there are 4 possible cards to turn face-up in the middle. So, the final answer is:
4 * 24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = 4 * (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!)) = 4 * 5,827,986,400 = 23,311,945,600.
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What goes on the X and y-axis of a graph?
The x-axis should contain the independent variable (also known as the "explanatory variable"), and the y-axis should contain the dependent variable (also known as the "response variable").
Definition of X and Y Graph?
The x-axis and the y-axis, which together make up a graph's coordinate plane, can be used to define an x and y graph.
The y-axis and the x-axis each stand in for one of the two axes: the horizontal or horizontally oriented. The origin, or point of reference for the plane, is the intersection of the x- and y-axes.
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The x-axis (horizontal line) of the graph should have the independent variable, and the y-axis should have the dependent variable (vertical line). At the origin, the location of the coordinates, the x and y axes intersect (0,0).
What is represented by the x-axis? The x-axis (horizontal line) of the graph should have the independent variable, and the y-axis should have the dependent variable (vertical line).At the origin, the location of the coordinates, the x and y axes intersect (0,0).A point's horizontal location is shown by the x-axis; its vertical position is indicated by the y-axis; and its exact center point is referred to as the origin.The line that runs vertically from bottom to top on a graph is known as the y-axis.The coordinate measurement axis is parallel to this axis.Y-coordinates are the numerical values plotted along the y-axis.The x-coordinate comes first in ordered pairs, followed by the y-coordinate, and is written in parentheses: (x, y).To learn more about X and y-axis refer
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Explain why each of the following expressions makes no sense. (dot product )(a) u\bullet(v\bulletw)(b) (u\bulletv)+w(c) ?u\bulletv?(d) k\bullet(u+v)
All the given statements does not make sense by the definition of dot product.
(a) (dot product)(a): The dot product is a mathematical operation and doesn't take any arguments or values, so this expression doesn't make sense as written.
(b) u\bullet(v\bulletw): The dot product is associative, meaning that u\bullet(v\bulletw) = (u\bullet v)\bullet w. However, the expression itself is not well defined, since the inner expression v\bullet w doesn't specify what values v and w represent.
(c) (u\bullet v) + w: The dot product is an scalar product, meaning it results in a scalar value, and adding a scalar to a vector does not make sense mathematically.
(d) k\bullet(u+v): The dot product is between two vectors, and the expression k\bullet(u+v) implies that the dot product is between a scalar (k) and a vector (u+v). This does not make mathematical sense, as the dot product is only defined between two vectors of the same dimension.
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if you must use a 1/4 inch diameter mill, then the best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius with the minimum requirement of: (a) < 0.25 inch (b) > 0.125 inch (c) < 0.125 inch (d)
The best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius of (b) > 0.125 inches.
The choice of fillet radius is an important factor in determining the surface tolerance and finish of a machined part. A fillet radius is a rounded corner between two flat surfaces. A fillet radius that is too small can result in a rough surface, while a fillet radius that is too large can weaken the part.
In this scenario, a 1/4 inch diameter mill is being used, so the best surface tolerance and finish would be achieved if the fillet radius is greater than 0.125 inch, but less than 0.25 inch. This will ensure that the part is not weakened and the surface is smooth. The exact value of the fillet radius will depend on the specific requirements of the machining process.
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Complete Question:
If you must use a 1/4 inch diameter mill, then the best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius with the minimum requirement of:
(a) < 0.25 inch
(b) > 0.125 inch
(c) > 0.25 inch
(d) = 0.25 inch
(e) = 0.125 inch
(f) < 0.125 inch
Whats the slope and y-intercept
2x-6y=24
I think I know the intercept I just don't know the slope.
Answer:
x-6y=-24
Step-by-step explanation:
do it
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope and y-intercept of the equation 2x - 6y = 24, you can first isolate y by adding 6y to both sides and then dividing both sides by -6. This gives you: y = (-1/3)x + 4
So, the slope is -1/3 and the y-intercept is 4.
Se conoce el peso ideal de un niño de 5 años en Colombia es de 20Kg. Escriba una frase que indique a cuántos kilogramos está cada niño, por debajo, por encima del peso ideal.
a. Juan pesa 22kg b. Mario pesa 18Kg c. Pedro pesa 26kg d. Alfredo pesa 20Kg
a) Juan, 2 kg de encima
b) Mario, 2 kg por debajo
c) Pedro, 5 kg por encima
d) Alfredo, Tiene el peso preciso
Qué se entiende por diferencia en matemáticasOperaciones aritméticas incluyen suma, resta, multiplicación y división
La diferencia en matemáticas es una operación aritmética de resta entre dos números grandes con un número pequeño para que el resultado sea siempre positivo.
La diferencia en matemáticas es también la diferencia de valor entre dos números
Ejemploa) la edad de Dewi = 25 años
edad de Adi = 51 años
entonces
Diferencia de edad entre A y B
= (51 – 25) años
= 26 años
Entonces la diferencia en sus edades es 26 años
b) El dinero de A = IDR 13,000.00
Dinero de B = IDR 10,500.00
entonces diferencia en su dinero es
= 13.000,00 IDR – 10.500,00 IDR
= 2.500,00 IDR
Entonces, la diferencia o la diferencia en su dinero es IDR 2,500.00
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Determine the value of the variable that makes the equation true.
1=-10c
The value of the variable that makes the equation true -1/10
What is an equation?An equation is a mathematical statement that shows the equality of two or more things. that is An equation is a mathematical statement that shows that two mathematical expressions are equal
The given equation is 1=-10c
To make the statement true, we have to determine the value of the variable c
this is done by making the variable c the subject of the relation
Now, 1/-10 = -10c/-10
Therefore c = -1/10 makes the equation true
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solve for x: x 2a-b=3(x a)-2(2a-b)
The expression x 2a-b=3(x a)-2(2a-b) has the result x = 2a / (2a + 3).
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.
Here,
To solve for x, we can simplify the equation first:
x * 2a - b = 3(x + a) - 2(2a - b)
Expanding the right side:
x * 2a - b = 3x + 3a - 2 * 2a + 2b
Combining like terms:
x * 2a - b = 3x + 3a - 4a + 2b
x * 2a - b = 3x - a + 2b
Now, we can isolate x on one side of the equation:
x * 2a - 3x = a - b + 2b
x * 2a - 3x = a + b
Multiplying both sides by -1:
-x * 2a + 3x = -a - b
Adding 2a to both sides:
x * 2a + 3x + 2a = -a - b + 2a
Combining like terms:
x * 2a + 3x + 2a = -a + 2a
x * 2a + 3x + 2a = 2a
Finally, collecting all x terms on one side:
x * (2a + 3) = 2a
Dividing both sides by (2a + 3):
x = 2a / (2a + 3)
The value of x for the expression x 2a-b=3(x a)-2(2a-b) is x = 2a / (2a + 3).
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What is the value of x in this triangle?
Enter your answer in the box.
Answer:102+31-180 = 47
so x = 47
Step-by-step explanation:
this is very simple
Tramaine is using a carton of chicken stock that contains 4 1/2 pints of chicken stock. He will use the 3/5 carton to make a stew and he will use the rest of the carton to make rice. How many pints of chicken
stock with Tramaine use for each dish?
Using the given fractions, we can see that for the stew they use (27/10) pints and for the rice (18/10) pints.
How many pints of chicken stock with Tramaine use for each dish?
We know that the carton has a volume of:
(4 + 1/2) pints of chicken stock.
He uses 3/5 of the carton to make a stew, so he uses:
(3/5)*(4 + 1/2) pints = (12/5 + 3/10) pints
= (27/10) pints.
And the rest, (2/5) of the carton, is used to make rice, then:
(2/5)*(4 + 1/2) pints = (8/5 + 2/10) pints = (18/10) pints.
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How do you solve quadratic equations with answers?
Answer:
Step-by-step explanation:
How to solve a quadratic equation using the Quadratic Formula.
Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, c.
Write the Quadratic Formula. Then substitute in the values of a, b, c.
Simplify.
Check the solutions.
The four methods for solving a quadratic issue are the quadratic formula, using square roots, factoring, and completing the square.
What is meant by quadratic equations?A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a ≠ 0.
Problems involving squares and quadrangles and quadratic equations are closely related. In actuality, the word quadratic comes from the Latin word quadratus, which means square.
The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem. An overview of all the many approaches to solving a quadratic equation is what I'd want to discuss right now.
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we plan to turn over the first 3 cards in a well-shuffled deck of 52 cards. compute the probability that both the second and third cards are the same suit.
Answer is 1/104. Probability is a branch of mathematics that deals with numerical descriptions of the probability of an event occurring or the probability that a statement is true.
What is the probability that both the second and third cards are the same suit?
Probability that the first card is a club = 1/4. (There are 13 club cards in the deck, and 13/52 = 1/4). Probability that the second card is a 3 = 1/13. (There are four 3 cards in the deck, and 4/52 = 1/13). Probability that the third card is red = 1/2. (There are 26 red cards in the deck, and 26/52 = 1/2). The probability of an event is a number between 0 and 1, where 0 represents approximately an impossibility and 1 represents a certainty. The higher the probability of an event, the more likely the event will occur. A simple example is mining a fair (impartial) coin. Since the coin is fair, both outcomes ("heads" and "tails") are equally likely; the probability of heads is equal to the probability of heads; and since no other outcome is possible, the probability of "heads" or "heads" is 1/2 (which can also be written as 0.5 or 50%).
Probability that the first card is a club, the second card is a 3, and the third card is red = 1/4 * 1/13 * 1/2
= 1/104
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How do I find the measure of angle ABE?? 43
The required measure of supplementary angle ∠ABE is 137°.
What are the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
The measure of a supplementary angle to an angle with measure x is defined as 180°-x. Therefore, the measure of the supplementary angle ∠ABE to an angle with a measure 43° is:
∠ABE = 180° - 43° = 137°
Thus, the required measure of supplementary angle ∠ABE is 137°.
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On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (2.4, negative 51) and a maximum value of (negative 0.75, 6), crosses the x-axis at (negative 2, 0), (0, 0), and (3.5, 0), and crosses the y-axis at (0, 0).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to negative infinity, the function's values go to positive infinity.
The truth about the end behavior of the graph is
D. As the x-values go to negative infinity, the function's values go to positive infinity.What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionExamining the given graph it can be deduced that end behavior is described as
x ⇒ -∞ f(x) ⇒ ∞
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Answer:
Step-by-step explanation:
The truth about the end behavior of the graph is
D. As the x-values go to negative infinity, the function's values go to positive infinity.
three sandwiches were given to each adult and two sandwiches were given to each child that went on the field trip. there were 40 people on the bus and a total of 89 sandwiches were given out. how many adults and how many children were on the trip ? (PLEASE HELP)
Answer:
the number of children on the trip=31
The number of adult=9
Step-by-step explanation:
Let's call the number of adults on the trip "a" and the number of children on the trip "c".
We know that:
a + c = 40 (the total number of people on the trip)
And:
3a + 2c = 89 (the total number of sandwiches given out)
We can use the first equation to solve for one variable in terms of the other:
a = 40 - c
And substitute this into the second equation:
3(40 - c) + 2c = 89
Expanding and simplifying:
120 - 3c + 2c = 89
120 - c = 89
Subtracting 120 from both sides:
-c = -31
So c = 31, the number of children on the trip.
And the number of adults on the trip, a = 40 - c = 40 - 31 = 9.
Laurie sold a house and made a commission of $14,050. She charges her customers a commission fee of 2. 5% on the selling price of the house. How much was the selling price of the house Laurie sold?
The selling price of the house that Laurie sold was $562,000.
The selling price is the amount paid by the customer to purchase the goods. The actual selling price is the amount paid by the customer for a product or service. This is the price that is more than the cost of products and includes a proportion of profit.
The cost price of an item is the amount spent to buy it or the price at which it is manufactured.
Let's call the selling price of the house "P".
The commission fee of 2.5% on the selling price of the house is equal to 0.025 * P.
Since Laurie made a commission of $14,050, we can set up the following equation:
0.025 * P = 14050
Dividing both sides by 0.025:
P = 14050 / 0.025 = 562000
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Mr chua bought a vanguard sheet with dimension 75 cm by 90 cm . He cut squares of identical size from the vanguard sheet such that there was no wastage
(a) What was the largest possible length of the side of each square he cut out?
(b) What was the total number of squares he cut out?
write an equivalent expression to the following: 5y + 35 HINT: think distributive property.
Answer:
5(y+7)
Step-by-step explanation:
Answer:
5(y + 7)
Step-by-step explanation:
Write an equation for this line.
Answer:
y = -2
Step-by-step explanation:
The equation is y = mx + b
But this line has no slope, but it has a y-intercept at (0,-2), so the equation is
y = -2
flip a coin. if you have flipped t tails, you need to flip t 1 consecutive heads to win the game. what is the probability to win the game?
The probability of winning the game, given t tails, is equal to [tex]0.5^t[/tex] .It's important to note that the outcome of each flip is independent.
The probability of winning the game in which you have flipped t tails and need to flip t consecutive heads can be calculated as follows:
Each flip of the coin has a probability of 0.5 of landing heads and 0.5 of landing tails. So, for the first flip, the probability of flipping a head is 0.5. For the second flip, the probability of flipping two heads in a row is
[tex]0.5 * 0.5 = 0.25[/tex]
For the third flip, the probability of flipping three heads in a row is
[tex]0.5 * 0.5 * 0.5 = 0.125[/tex] , and so on.
Therefore, the probability of winning the game, given t tails, is equal to 0.5^t. For example, if you have flipped 2 tails, the probability of winning the game by flipping 2 consecutive heads is
[tex]0.5 * 0.5 = 0.25.[/tex]
It's important to note that the outcome of each flip is independent, so the probability of winning the game given t tails is constant regardless of the number of tails flipped prior to the current flip.
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how many turning points does -3x^{3} 2 have
The polynomial -3x^3 + 2 has only one turning point.
A turning point is a point on a curve where the curve changes direction, either from going up to going down or vice versa. In other words, it is a point where the first derivative of the curve changes sign.
For the polynomial -3x^3 + 2, the first derivative is given by:
d/dx (-3x^3 + 2) = -9x^2
Since the first derivative is a monotonically decreasing function (that is, its slope is always negative), the polynomial -3x^3 + 2 has only one turning point.
Slope of first derivative
d²(-3x^3 + 2)/dx² = -18x
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Trapezoid HRNB is shown with midsegment MS.
HM = (5x-3),
MB = (x + 5)
HR=(2y+3).
MS (4y - 3). and
BN= (10x+1)
What is the value of a?
What is the value of y?
the value of x=2 and y =5, for the given trapezoid.
What is trapezoid?
A trapezoid, commonly referred to as a trapezium, is a quadrilateral or polygon with four sides. It has a set of parallel opposite sides as well as a set of non-parallel sides. The bases and legs of the trapezoid are referred to as parallel and non-parallel sides, respectively. A trapezoid is a four-sided closed 2D figure with a perimeter and an area. The bases of the trapezoid are two of the shape's sides that are parallel to one another. The legs or lateral sides of a trapezoid are its non-parallel sides. The altitude is the shortest distance between any two parallel sides.
Given, HM =5x-3
BM = x+5
So 5x-3 = x+5
4x = 8
x = 2.
and (4y - 3) =(2y+3)+(10x+1) /2
8y-6 = 2y+3 + 10x+1
6y = 10+20
y =5
Hence the value of x=2 and y =5, for the given trapezoid.
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as an architect, you are designing a new house. a window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. what are the smallest and largest areas that the window could be?
The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
This problem is based on the area of rectangle .
Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.
Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.
The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .
So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.
Similarly the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.
Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
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The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
This problem is based on the area of a rectangle.
Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.
Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.
The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .
So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.
Similarly, the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.
Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
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pls help Use your response to question 1 to write a recursive definition for the amount of medication in Aldi’s bloodstream after each dose of medication. Is your definition arithmetic, geometric, or neither? Explain.
The sequence is neither arithmetic nor geometric.
What does mathematical sequence mean?Informally, a sequence in mathematics is a list of items that are in some order (or events). It possesses members, much like a set (also called elements, or terms). The length of the series is the number of ordered elements in the sequence, which could be unlimited.
Also, Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
Squares, rectangles, circles, cones, cubes, and other shapes that can be created using geometry are known as geometric forms. In structural, civil, and architectural engineering, geometric forms are frequently used.
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The sequence from response to question 1 is neither arithmetic nor geometric.
How to identify the type of sequence ?The sequence in mathematics is the order of value of items or events. Usually, it contains a number or a series of numbers with a length of series that can be unlimited.
If the sequence has common differences from one value to another it can be considered as an arithmetic sequence, for example, 2,4,6,8. If the sequence has common ratios from one value to another it can be considered as a geometric sequence, for example, 2,4,8,16.
Since the response in question 1 doesn't have either common differences or common ratios, so it is neither arithmetic nor geometric.
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(exercise 2: find the critical points of the gompertz equation (1). (is y = 0 a critical point? does it solve the algebraic equation you get?).dy = ry In(K/y
y = k asymptotically stable critical point because f'(k) < 0 and f'(0) > 0. So y = 0 is an an asymptotically unstable critical point.
The Gompetz equation is dy/dt = ry In(K/y).
In order to find critical points equate dy/dt equal to zero
dy/dt = 0
ry In(k/y) = 0
Here, k and r are constants
y In(k/y) = 0
y = 0
In (k/y) = 0
Eliminating In
k/y = e^0
k/y = 1
Multiply by y on both side, we get
k = y
y = 0 and y = k
The critical points are 0 and k
Since zero is a critical point
dy/dt = f(y)
dy/dt = ry In(k/y)
Differentiation on both side
f'(y) = ry In(k/y) - ry × y/k × k/[tex]y^2[/tex]
f'(y) = r In(k/y) - r
f'(k) = r In(k/k) - r
f'(x) = -r < 0
So that, y = k asymptotically stable critical point because f'(k) < 0
f'(0) > 0
That means y=0 is asymptotically unstable critical point.
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pls help I can't figure out the problem and I need help it worth a lot of points in my grade
Answer:
Perimeter 18.42
Area 20.13
Step-by-step explanation:
Perimeter:
This is the distance around the figure.
The distance around the triangle is 9.
The distance around the 1/2 circle
c= 2[tex]\pi[/tex]r
c [2(3.14)(3)]/2
c = 9.42
9.42 + 9 = 18.42
Area:
triangle
a = 1/2(bh)
a - 1/2 (3)(4)
a = 6
circle
a = 1/2([tex]\pi r^{2}[/tex])
a = 1/2(3.14)(9)
a = 14.13
6 + 14.13 = 20.13