Sigma n=1 to infinite ((-1)^n+1)/3n^5
use the alternating series estimation theorem to estimate the error in using the 3rd partial sum to approximate the sum of the series. (round your answer to 5 decimal places.)

At sunrise, shadows are longest and point towards the west as the sun rises in the east. Therefore, the correct order would be:

Longest shadows of the day, and they point to the west → shadows gradually become shorter → very short shadows or no shadows → shadows gradually become longer → longest shadows of the day, and they point to the east.

As the sun moves across the sky, shadows change in length and direction, reaching their shortest length at noon when the sun is directly overhead. After noon, the sun starts to move towards the west, and shadows gradually become longer until sunset when they are longest again, but this time pointing towards the east as the sun sets in the west.

Therefore, correct order of descriptions of shadows during the day, from sunrise to sunset, would be:

Read more about shadows  here:

https://brainly.com/question/922673

#SPJ1

See text below



How do shadows change during the day?

Drag and drop the descriptions of shadows to show the correct order, from sunrise to sunset.

longest shadows of the day, and they point to the west

longest shadows of the day, and they point to the east

shadows gradually become shorter

very short shadows or no shadows

shadows gradually become longer

The vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

To determine if the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly independent, we need to find the scalars a, b, and c that satisfy the equation:

a * [-5 4 5] + b * [2 -1 5] + c * [-17 16 45] = [0 0 0]

If the only solution is a = b = c = 0, the vectors are linearly independent. If there are other solutions where a, b, and c are not all zero, the vectors are linearly dependent.

Let's form a matrix with these vectors as columns:

|-5  2 -17|
| 4 -1  16|
| 5  5  45|

Now, we can row reduce this matrix to its reduced row echelon form (RREF):

| 1 -2  5|
| 0  1 -3|
| 0  0  0|

From the RREF, we can write the system of linear equations:

x - 2y + 5z = 0
y - 3z = 0

Solving this system, we get:

y = 3z
x = 2y - 5z = 6z - 5z = z

Since z can be any scalar, we have infinitely many solutions where not all of a, b, and c are zero. For example, when z = 1, we get x = 1 and y = 3. So, the scalars (1, 3, 1) make the equation true.

Thus, the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

To learn more about linearly dependent vectors visit : https://brainly.com/question/30840640

#SPJ11

The final expression for the given problem is (f(3+h) - f(3))/h = -h - 3.

To solve this problem, we first need to determine the value of f(3+h) and f(3):

Given \(F(x) = 4 + 3x - x^2\), we can find f(3+h) by substituting 3+h for x:

\(f(3+h) = 4 + 3(3+h) - (3+h)^2\\f(3+h) = 4 + 9 + 3h - (9 + 6h + h^2)\\f(3+h) = -h^2 - 3h + 4\)

Next, we can find f(3) by substituting 3 for x:

\(f(3) = 4 + 3(3) - (3)^2\\f(3) = 4 + 9 - 9\\f(3) = 4\)

Now we can substitute these values into the expression (f(3+h) - f(3))/h:

\((f(3+h) - f(3))/h = ((-h^2 - 3h + 4) - 4)/h\\(f(3+h) - f(3))/h = (-h^2 - 3h)/h\\(f(3+h) - f(3))/h = -h - 3\)

Therefore, the final expression for the given problem is:

(f(3+h) - f(3))/h = -h - 3

for such more question on expression

https://brainly.com/question/4344214

#SPJ11

Answer:

i) 4x

ii) Father's age = 3(x + 10)

Son's age = x + 10

iii) 4x + 10 = 3(x + 10)

iv) Present age of the son = x = 20

Present age of the father = 4x = 4(20)

= 80

Step-by-step explanation:

Present age of the son = x

Present age of the father = 4x

Age of the son in 10 years = x + 10

Age of the father in 10 years = 3(x + 10)

4x + 10 = 3(x + 10)

4x + 10 = 3x + 30

4x - 3x = 30 - 10

x = 20

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer:

x and y = 66.5

Step-by-step explanation:

180-47=133

133/2=66.5

\(\textit{Pythagorean Identities} \\\\ \sin^2(\theta)+\cos^2(\theta)=1\implies \cos^2(\theta )=1-\sin^2(\theta ) \\\\ 1+\cot^2(\theta)=\csc^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{1-\sin^2(\theta )}{1+\cot^2(\theta )}~~ = ~~\sin^2(\theta )\cos^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1-\sin^2(\theta )}{1+\cot^2(\theta )}\implies \cfrac{\cos^2(\theta )}{\csc^2(\theta )}\implies \cfrac{\cos^2(\theta )}{ ~~ \frac{1}{\sin^2(\theta )} ~~ }\implies \cos^2(\theta )\sin^2(\theta )\)

Answer:

y=4/7x+2/7

Step-by-step explanation:

For lines to be parallel, the slope must be the same. From the point-slope form that the equation of line g has taken, it can be easily identified that line g's slope is 4/7, so line h's slope must be as well.

To make sure that line h passes through point (3,2), you must use the point slope form.

y-y1=m(x-x1)

y1 represents the y value of the point you're trying to pass

m represents your slope

x1 represents the x value of the point you're trying to pass

leave y and x alone, as they're just variables in the equation.

Plug in the slope (4/7), and x1 and y1 values (3, 2).

y-2=4/7(x-3)

Distribute.

y-2=4/7x-12/7

Addition property of equality (add 2 to both sides to isolate y).

y=4/7x+2/7

There is your equation for line h.

Answer:

y = x + 2

Slope = rise / run

= 2 / 2 (or 1 bc 2 divided by 2 is 1)

The plotted point on the x axis is on 2

y = x + 2

Answer:

Step-by-step explanation:

area of triangle = 1/2 × b × h

here,

b = 37 m

h = 30 m

so area = 1/2 × b × h

= 1/2 × 37 × 30

= 555 m^2

hope this helps

plz mark as brainliest!!!!!!!

Answer:

you have it correct sir

Step-by-step explanation:

The maximum rate of change of f at P is 1.

To find the points on the surface xy - z^2 = 1 that are closest to the origin, we can use the method of Lagrange multipliers. Let's define the function g(x, y, z) = x^2 + y^2 + z^2, which is the square of the distance from the origin. Our constraint is the surface xy - z^2 = 1. The Lagrangian function is then:

L(x, y, z, λ) = e^(2xy)sin(z) + λ(xy - z^2 - 1)

Taking partial derivatives and setting them equal to zero, we get:

∂L/∂x = 2ye^(2xy)sin(z) + λy = 0

∂L/∂y = 2xe^(2xy)sin(z) + λx = 0

∂L/∂z = e^(2xy)cos(z) - 2λz = 0

∂L/∂λ = xy - z^2 - 1 = 0

Solving these equations, we get:

x = ±√(2/π), y = ±√(2/π), z = ±1/√π

Plugging these values into g(x, y, z), we get the closest point to the origin: (±√(2/π), ±√(2/π), ±1/√π)

To find the rate of change of the function f(x, y, z) = e^(2xy)sin(z) at the point P(0, 1, π/4) in the direction of the vector u = (1, 1, 0), we can use the directional derivative formula:

D_u f(P) = ∇f(P) · u

where ∇f is the gradient of f. Evaluating at P, we get:

∇f(P) = (2y e^(2xy)cos(z), 2x e^(2xy)cos(z), e^(2xy)sin(z))|_(0,1,π/4) = (√2/2, √2/2, 1/√2)

D_u f(P) = (√2/2, √2/2, 1/√2) · (1, 1, 0) = √2

Therefore, the rate of change of f in the direction of u at P is √2.

To find the direction in which f increases most rapidly at P, we need to find the unit vector in the direction of ∇f(P). This is given by:

u_max = ∇f(P)/||∇f(P)|| = (√2/2, √2/2, 1/√2) / ||(√2/2, √2/2, 1/√2)|| = (1/√3, 1/√3, 1/√3)

Therefore, the function f increases most rapidly at P in the direction of the vector u_max = (1/√3, 1/√3, 1/√3).

The maximum rate of change of f at P is ||∇f(P)||, which is:

||∇f(P)|| = ||(√2/2, √2/2, 1/√2)|| = 1

Therefore, the maximum rate of change of f at P is 1.

To Learn More About Maximum

https://brainly.com/question/82347

#SPJ11

To make the sum of 6x - 5 equal to zero, a polynomial of -6x + 5 should be added, which cancels out the x term and the constant term of the original expression. This addition ensures that both the x term and the constant term cancel each other, resulting in a sum of zero.

The polynomial that should be added to 6x - 5 so that the sum is zero, we need to determine the polynomial that cancels out the existing terms.

Since the given expression is 6x - 5, we want to add a polynomial of the form -6x + 5 to it.

By adding this polynomial, the x term from the original expression will cancel out with the -6x term we are adding, and the constant term -5 will cancel out with the +5 term we are adding.

When we add 6x - 5 to -6x + 5, the x terms cancel each other out, resulting in 0x or simply 0. Similarly, the constant terms cancel each other out, resulting in 0.

Therefore, the sum of 6x - 5 and -6x + 5 is indeed zero.

In conclusion, to make the sum of 6x - 5 and the added polynomial equal to zero, we should add -6x + 5 to it.

To know more about polynomial refer here:

https://brainly.com/question/30322199#

#SPJ11

Based on the provided information, Bonnie has 180 sheets of paper in her stack.

If 300 sheets of paper weigh 1 kg, then 600 sheets of paper will weigh 2 kg. This is because the weight of the paper is directly proportional to the number of sheets. Therefore, if the weight is doubled, the number of sheets will also be doubled.

To find the number of sheets of paper that Bonnie has, we can use the following equation:

Number of sheets = (Weight of Bonnie's stack of paper) * (300 sheets / 1 kg)

Plugging in the given values, we get:

Number of sheets = (600 g) * (300 sheets / 1 kg)

Number of sheets = (600 g) * (300 sheets / 1000 g)

Number of sheets = 180,000 / 1000

Number of sheets = 180

Therefore, Bonnie has 180 sheets of paper in her stack.

Learn more about Weight:

https://brainly.com/question/25973294

#SPJ11

Step-by-step explanation:

Since Total workers = Permanent + Temporary workers,

w = 44 + t.

Hence when t = 5, w = 44 + 5 = 49.

The raisins that Anaya needs more will be 5/6 cups.

It should be noted that from the information, recipe for 4 cups of trail mix calls for 2/3 cups of raisins. Anaya has 1 1/2 cups of raisins.

The amount that's needed for 14 cups will be:

= 14/4 × 2/3

= 2 1/3

It's not enough

The amount needed will be:

= 2 1/3 - 1 1/2

= 2 2/6 - 1 3/6

= 5/6

Learn more fraction on:

brainly.com/question/1622425

#SPJ1

Answer:

(3n)- 6 or the other way around 6-(3n)

Step-by-step explanation:

The probability of a patient scoring above 192 on the endurance test is approximately 40.90%. A patient at the 80th percentile receives a score of approximately 208.2.

a. To find the probability that a patient will score above 192, we need to use the Z-score formula. The Z-score measures the number of standard deviations a data point is from the mean. In this case, the formula is Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

First, calculate the Z-score: Z = (192 - 185) / 30 = 7/30 ≈ 0.23.

Next, we need to find the probability of scoring above this Z-score. Using a Z-table or a calculator, we find that the probability is approximately 0.4090, or 40.90%.

b. To find the score that corresponds to the 80th percentile, we need to find the Z-score that has an area of 0.80 to the left. Using the Z-table or a calculator, we find that the Z-score is approximately 0.84.

Now, we can use the Z-score formula to find the corresponding score: X = Z * σ + μ. Plugging in the values, we get X = 0.84 * 30 + 185 = 208.2.

Therefore, a patient at the 80th percentile receives a score of approximately 208.2.

a. To find the probability of a patient scoring above 192 on the endurance test, we first calculate the Z-score. This allows us to standardize the score by measuring how many standard deviations it is from the mean. We then use a Z-table or calculator to find the probability corresponding to this Z-score, which is approximately 0.4090 or 40.90%.

b. To find the score at the 80th percentile, we first need to find the Z-score that corresponds to an area of 0.80 to the left. Using a Z-table or calculator, we find this Z-score to be approximately 0.84. We then use the Z-score formula to find the corresponding score, which is approximately 208.2.

Learn more about the probability: https://brainly.com/question/31828911

#SPJ11

Answer:

38.58

Step-by-step explanation:

Answer: its 41 dude

To find dz/dt using the chain rule, we need to calculate the derivatives of z with respect to x and y separately, and then multiply them by the derivatives of x and y with respect to t.

Given:

z =  \(cosh^{2} (xy)\)

x = (1/2)t

y = \(e^{t}\)

Let's start by finding the partial derivatives of z with respect to x and y:

∂z/∂x = \(2cosh(xy) * sinh(xy) * y\)  (using the chain rule)

∂z/∂y = \(2cosh(xy) *sinh(xy)*x\)    (using the chain rule)

Next, let's find the derivatives of x and y with respect to t:

dx/dt = 1/2

dy/dt = \(e^{t}\)

Finally, we can use the chain rule to find dz/dt:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

      = \(2cosh(xy) *sinh(xy)*y*(1/2) + 2cosh(xy)*sinh(xy)*x*e^{t}\)

Now, substitute the given expressions for x and y:

\(dz/dt = 2cosh((1/2)t*e^{t} * sinh((1/2)t*e^{t} *(1/2)* + 2cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t} *((1/2)t)\)

Simplifying further, we have:

\(dz/dt = cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t})* e^{t} + cosh((1/2)t* e^{t}*sinh((1/2)t*e^{t}* ((1/2)t)\)

This is the expression for dz/dt using the chain rule with the given values of x and y.

To know more about chain rule refer here:

https://brainly.com/question/31585086?#

#SPJ11

The result of adding these two numbers together such as -3.4 + 4.2 is 0.8.

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number, and every real number to a number line point.

On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.

In this case, -3.4 will be on the left side and you'll move to the right and add 4.2. The value is 0.8.

Learn more about number line on:

https://brainly.com/question/24644930

#SPJ1

A deck of 52 cards is shuffled thoroughly, and n cards are turned up. The probability that one face card turns up is (1/4) × (n/52).

The probability of one face card turning up when n cards are turned up from a shuffled deck of 52 cards is determined by the following formula:
Probability of 1 face card = (number of face cards/number of total cards) × (n/52)

Therefore, the probability of one face card turning up when n cards are turned up is (12/52) × (n/52), or (1/4) × (n/52).

For example, if 10 cards are turned up, the probability of one face card turning up would be (1/4) × (10/52) = 0.2, or 20%.

In general, the more cards are turned up, the higher the probability that one face card turns up. This is because there is a higher chance of drawing at least one face card from the larger sample.

Therefore, The probability that one face card turns up in a shuffled deck is (1/4) × (n/52).

To know more about probability refer here:

https://brainly.com/question/30034780

#SPJ11

6.5 = n This step uses the division property of equality to divide the total number of pounds of raisins and peanuts (8) by the difference in the amounts of raisins and peanuts (1.5)

The link between two or more variables can be shown mathematically in a straight line using linear equations. A linear equation has the following fundamental form: y = mx + b, where m is the slope of the line, x is the independent variable, and b is the y-intercept (the point where the line intersects the y-axis). Since the slope of a linear equation is constant, the values of the variables have no effect on it. This allows for a predictable and consistent relationship between the variables. In many disciplines, including algebra, geometry, physics, and economics, linear equations are employed.

How to solve?

Given: Ms. Jones needs 8 pounds of raisins and peanuts

Step 1: 8 - n = 1.5

This step uses the subtraction property of equality to subtract the unknown number of pounds of peanuts (n) from the total number of pounds of raisins and peanuts (8) in order to determine how much more peanuts there are compared to raisins.

Step 2: 8 - 1.5 = n

This step uses the subtraction property of equality to subtract the difference in the amounts of raisins and peanuts (1.5) from the total number of pounds of raisins and peanuts (8) in order to determine the number of pounds of peanuts.

Step 3: 6.5 = n

This step uses the division property of equality to divide the total number of pounds of raisins and peanuts (8) by the difference in the amounts of raisins and peanuts (1.5) in order to determine the number of pounds of peanuts.

To learn more about Linear Equation, visit:

https://brainly.com/question/19157308

#SPJ4

Answer:

y = 7x -9

Step-by-step explanation:

This is a linear equation.

The change in y over the change in x is 9.  The y-intercept will be (0, -9).

If you follow the pattern as x is -1 and you go up 1 to zero, the the y goes up 7 from -16 to get -9

Answer:

y = 7x - 9

Step-by-step explanation:

y = 7x - 9

Let checks

-16 = 7(-1) - 9

-16 = -16

-23 = 7(-2) - 9

-23 = -23

So, y = 7x - 9 is the correct answer.

Answer:

x * 5

Step-by-step explanation:

prosucts refer to multiplication

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

C on ed 2020

Answer:

7

Step-by-step explanation:

have a good day !!!!!!!!!