what does it mean when you need to be accurate to a certain number of decimal places lagrange remainder

The rate at which the height of the water is increasing when water is being pumped in at a rate of 2/3 m/s and the water is 9m deep is 0.667 m/s.

We can start by using the formula for the volume of a square pyramid to find the volume of water in the tank. Let V be the volume of water in the tank and h be the height of the water.

V = (s² [h])/3

We know that the base of the pyramid is 3m by 3m, so s = 3. Also, the height of the pyramid is 16m, so we have:

V = (3² [h])/3

V = 3h

Now, we can find the rate of change of the volume with respect to time:

dV/dt = 3 [dh/dt]

We know that water is being pumped in at a rate of 2/3 m/s, so dh/dt = 2/3. We want to find how fast the height increases when the water is 9m deep, so h = 9. Substituting these values, we get:

dV/dt = 3 [dh/dt]

dV/dt = 3 [2/3]

dV/dt = 2

Therefore, the rate at which the volume of water is increasing is 2 cubic meters per second. To find the rate at which the height of the water is increasing, we need to solve for dh/dt:

dV/dt = 3 [dh/dt]

2 = 3 * dh/dt

dh/dt = 2/3

So the height of the water is increasing at a rate of 2/3 m/s when the water is 9m deep. Rounded to 3 decimal places, the answer is 0.667 m/s.

Learn more about volume here: brainly.com/question/1578538

#SPJ4

Answer:

64 cookies : 1 cup of sugar : 8/3 or 2 2/3 cup of flour

Step-by-step explanation:

16 cookies : 1/4 cup of sugar : 2/3 cup of flour

Multiply each part by 4 to find how much flour and how many cookies would be used in the same recipe with 1 cup of sugar.

64 cookies : 1 cup of sugar : 8/3 or 2 2/3 cup of flour

The area of the triangle FGH is 13√10 unit²

Given,

The vertices;

F(2, -8), G(7, -7), H(6, -4)

We have to find the area of the triangle.

Area of triangle = 1/2bh²

Here,

Area of triangle FGH = 1/2 (GH) (FG)²

Now,

Length of FG = \(\sqrt{(7-2)^{2} =(-8--7)^{2} }\)  = \(\sqrt{5^{2}+1^{2} }\)  = \(\sqrt{25+1}\) = √26

Length of GH = \(\sqrt{(-7--4)^{2}+(7-6)^{2} }\) = \(\sqrt{-3^{2}-1^{2} }\) = \(\sqrt{9+1}\) = √10

Then,

Area of triangle FGH = 1/2 (GH) (FG)²

Area of triangle FGH = 1/2 × √10 × √26²

Area of triangle FGH = 1/2 × √10 × 26

Area of triangle FGH = 13√10

Therefore,

The area of the triangle FGH is 13√10 unit²

Learn more about triangle here;

https://brainly.com/question/12949215

#SPJ1

To determine the location of the maximum tensile bending stress with respect to the neutral axis, you need to find the point where the distance (y) is maximum.

To calculate the maximum tensile bending stress, you need to know the moment of inertia of the cross-sectional shape and the distance from the neutral axis to the point of interest.

The formula to calculate the maximum tensile bending stress (σ) is:

σ = (M * y) / I

where:

- M is the bending moment applied to the material

- y is the distance from the neutral axis to the point of interest

- I is the moment of inertia of the cross-sectional shape

Please provide the values for the bending moment (M), the moment of inertia (I), and the cross-sectional shape to calculate the maximum tensile bending stress and determine its location with respect to the neutral axis.

Know more about the tensile bending stress

https://brainly.com/question/13112339

#SPJ11

To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest

I = P * r * t.

I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,

Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.

To know more about simple interest visit:

https://brainly.com/question/20595462

#SPJ11

The rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

Given that,

In the same time it took to row 25 miles against the current, a rowing team was able to row 50 miles while travelling with it. 2 miles per hour was the current's speed.

We have to calculate the rowing team's speed in still water.

We know that,

Let rowing rate in still water = r

And current rate = c = 2 mph

Rowing with the current means the overall speed is r + c = r + 2

Rowing against the current means the overall speed is r - c = r - 2

Distance = Rate × Time

50 = (r+2) × t  ----->equation(1)  

25 = (r-2) × t  ----->equation(2)

By solving

Divide equation(1) by equation(2)

50/25 = (r+2) × t / (r-2) × t

2=r+2/r-2

2(r-2)=r+2

2r-4=r+2

2r-r=2+4

r=6mph

Substitute in equation(1)

50 = (r+2) × t

50=(6+2)×t

50=8t

t=50/8

t=6.25 hrs

t= 6 hours 15 minutes

Therefore, the rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

To learn more about miles visit: https://brainly.com/question/23245414

#SPJ4

Answer:

The best point estimate of the population proportion p is 0.0251.

The 99​% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

In clinical​ trials, among 4547 patients treated with the​ drug, 114 developed the adverse reaction of nausea.

This means that \(n = 4547, \pi = \frac{114}{4547} = 0.0251\)

The best point estimate of the population proportion p is 0.0251.

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a pvalue of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0251 - 2.575\sqrt{\frac{0.0251*0.9749}{4547}} = 0.0191\)

The upper limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0251 + 2.575\sqrt{\frac{0.0251*0.9749}{4547}} = 0.0311\)

The 99​% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).

The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

\(Ax + By + C = 0\)

Equation of Straight Line or Slope:

\(y = mx+b\)

Point-slope form:

\(y-y_{1} = m(x-x_1)\)

Slope when 2 points are given:

\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)

Quadratic Equation:

\(Ax^2 + Bx +C = 0\)

When lines are parallel:

Slope of both lines are equal. \(m_1 = m_2\)

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).

Work Formula:

Total Work Done = Number of Days \(\times\) Efficiency

where Efficiency is inversely proportional to Time Taken.

To know more about Algebra, visit: https://brainly.com/question/24875240

#SPJ4

Answer:

Step-by-step explanation:

The length and the width of the rectangle basee on the perimeter will be 2 and 4cm.

How to calculate the value?

From the given rectangle,

Length of the rectangle = 5 cm

Width of the rectangle = 10 cm

Ratio of length : width = 1 : 2

Perimeter of the rectangle = 2(l + b)= 150 cm

l + b = 75 -----(1)

Since, l : b = 1 : 2

b = 2l ------(2)

From equations (1) and (2)

l + 2l = 75

3l = 75

l = 75/3

l = 25 m

Width 'b' = 2(25) = 50 m

Now we have to draw a rectangle with a scale = 25 : 2

Therefore, the scale factor =

l = 2 cm

Similarly,

w = 4 cm

Now we can draw a rectangle with length = 2 cm and width = 4 cm.

Answer:

3 : 4, D

Step-by-step explanation:

Since the ratio is 9 : 12, simply put it in fraction form and simplify.

The value of x and y from the simultaneous equation; 3x + 2y = 19, 4x - y = 29 is 7 and -1 respectively.

3x + 2y = 19 (1)

4x - y = 29 (2)

Multiply (2) by 2

8x - 2y = 58 (3)

Add (1) and (3)

3x + 2y = 19 (1)

8x - 2y = 58 (3)

11x = 77

x = 77/11

x = 7

4x - y = 29 (2)

4(7) - y = 29

28 - y = 29

subtract 28 from both sides

-y = 29 - 28

-y = 1

y = -1

Therefore, the solution to the equation is (x, y) = (7, -1)

Read more on simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

The exact y-coordinate of the center of mass of the system is 9/10.

To find the y-coordinate of the center of mass of the system, we can use the formula:

y_cm = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)

where m1, m2, m3, and m4 are the masses and y1, y2, y3, and y4 are the corresponding y-coordinates of the points P1, P2, P3, and P4.

Substituting the given values, we get:

y_cm = (31 + 25 + 14 + 4(-2)) / (3 + 2 + 1 + 4)

y_cm = (3 + 10 + 4 - 8) / 10

y_cm = 9/10

Therefore, the exact y-coordinate of the center of mass of the system is 9/10.

For more questions like Coordinate click the link below:

https://brainly.com/question/16634867

#SPJ11

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

Learn more about alternate interior angles at

https://brainly.com/question/20344743

#SPJ1

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

Learn more about Fourier transform

brainly.com/question/29063535

#SPJ11

Answer:

\({ \tt{x + 83 = 180}}\)

[ Property of angles on a straight line ]

\({ \tt{x = 180 - 83}} \\ \\ { \boxed{ \tt{x = 97 \degree}}}\)

\({ \tt{(4y - 27) = x}} \\ \)

[ Property of alternate angles ]

\({ \tt{4y - 27 = 97}} \\ { \tt{4y = 124}} \\ { \tt{ \frac{4y}{4} = \frac{124}{4} }} \\ \\ { \boxed{ \tt{y = 31 \degree}}}\)

the domain of the function p(x) = √(17/(x + 5)) is all real numbers except x = -5.

In interval notation, the domain is (-∞, -5) U (-5, ∞).

To find the domain of the function p(x) = √(17/(x + 5)), we need to consider the values of x that make the expression inside the square root valid.

In this case, the expression inside the square root is 17/(x + 5). For the square root to be defined, the denominator (x + 5) cannot be zero because division by zero is undefined.

Therefore, we need to find the values of x that make the denominator zero and exclude them from the domain.

Setting the denominator (x + 5) equal to zero and solving for x:

x + 5 = 0

x = -5

So, x = -5 makes the denominator zero, which means it is not in the domain of the function.

To know more about function visit:

brainly.com/question/31062578

#SPJ11

Answer:

4.5 = x

Step-by-step explanation:

Given:

22.5 = 5x

(we need to find out what x is)

22.5 / 5 = 4.5

meaning that the duck traveled at 4.5 kilometers per hour.

Check:
4.5 x 5 = 22.5

Answer:

77 minutes or 1 hour, 17 minutes

Step-by-step explanation:

7000 feet in 20 minutes is 700 feet in 2 minutes or

350 feet per minute

to find the number of minutes to go 26950 feet we can divide that by 350

26950 ÷ 350 = 77 minutes or 1 hour, 17 minutes

A. 24.12 days

B. 18.1%

C. 29868 years

Using the formula for exponential decay:

N(t) = N0 * (1/2)^(t/T)

We can rearrange this equation to solve for t:

t = T * log(0.125) / log(0.5)

simplifying, we get:

t = 8.04 * log(0.125) / log(0.5) ≈ 24.12 days

Therefore, it takes about 24.12 days for only 12.5% of the sample to remain.

Using the same formula for exponential decay

N(11) = N0 * (1/2)^(11/12.3)

Dividing N(11) by N0 and multiplying by 100 gives us the percentage remaining:

N(11)/N0 * 100 = (1/2)^(11/12.3) * 100 ≈ 18.1%

Therefore, about 18.1% of the tritium sample will remain after 11 years.

The rate of decay of C-14 is given by:

A(t) = A0 * (1/2)^(t/T)

t = T * log(A(t)/A0) / log(0.5)

Plugging in the values for A(t), A0, and T, we get:

t = 5730 * log(15.1/15.3) / log(0.5) ≈ 29868 years

Therefore, the age of the paper that the map is written on is about 29868 years.

Learn more about radioactive decay

brainly.com/question/1770619

#SPJ11

The probability that no two adjacent people would stand is option C: 49/256, as there are 256 distinct counting rotations.

First, we assume that one person stands up. There are 8 possible ways to select which person does. We can, next, assume that no two adjacent people stand up. There are 4 ways to choose which of the remaining 7 people will stand up (since no two adjacent people can stand up).

Then, we can assume that no two adjacent people stand up again. There are 3 ways to choose which of the remaining 6 people will stand up (since no two adjacent people can stand up).

We continue this process until there is only one person left who can stand up.

The number of arrangements according to the number of people standing.

Therefore, the number of arrangements that no two adjacent people will stand.

n(S) = 1 + 8 + 20 + 16 + 2 + 2 = 49

The total number of possible outcomes is:

2⁸ = 256

So, the probability that no two adjacent people will stand would be:

= 49/256.

To know more about probability, refer:

https://brainly.com/question/6649771

#SPJ4

Complete question is:

Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?

(a) 47/256

(b) 3/16

(c) 49/256

(d) 25//128

(e) 51/256

It seems there are some errors in the provided equations. Let's go through them one by one and correct them:

Equation 1: y' + 2y = 15

The correct form of this equation is:

y' + 2y = 15

Equation 2: y = 515 + ce^(2x)

It seems there is an extra "=" sign. The correct form is:

y = 515e^(2x) + ce^(2x)

Equation 3: y = 21 + ce^(-2x)

Similarly, there is an extra "=" sign. The correct form is:

y = 21e^(-2x) + ce^(-2x)

Equation 4: y = 215 + e^(2) + ce^(-2)

It seems there is an incorrect placement of "+" sign. The correct form is:

y = 215 + e^(2x) + ce^(-2x) Equation 5: y = 15 + ce^(2x)

There is an extra "=" sign. The correct form is:

y = 15e^(2x) + ce^(2x)

If you would like to solve any particular equation, please let me know.

Learn more about equations here

https://brainly.com/question/14686792

#SPJ11

The startup costs of the company are -$13,000 (negative indicates a cost, rather than profit).

The profit equation given is P(z) = -2z^2 + 920z - 13000, where z represents the number of thousands of items sold.

The startup costs of the company refer to the initial expenses incurred before any items are sold. This is equivalent to the profit the company would make if it sells 0 thousand items.

To find the profit when the company sells 0 thousand items, we need to substitute z = 0 in the profit equation:

P(0) = -2(0)^2 + 920(0) - 13000

= 0 - 0 - 13000

= -13000

Therefore, the startup costs of the company are -$13,000

Learn more about startup cost here

brainly.com/question/15290847

#SPJ4

I have solved the question in general, as the given question is incomplete

The complete question is:

A company's profit when it sells x thousand items is predicted to be P(z) = -2z^2 + 920z-13000. a) What is the company's startup costs?

The correlation coefficient {r} = 0.01 represents the worst correlation.

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data

Given are the correlation values as given in the image.

The correlation coefficient {r} = 0.01 represents the worst correlation. It is shows that the data is scattered to a very large extent and the dependency between the two variables is not mathematically structured according to some rule.

Therefore, the correlation coefficient {r} = 0.01 represents the worst correlation.

To solve more questions on correlation, visit the link below -

brainly.com/question/12431044

#SPJ1

Answer:

450 bacteria

Step-by-step explanation:

90 percent of 100 is 90 90x5 is 450

To find the inverse of a matrix, we need to determine if it is invertible, or non-singular. A matrix is invertible if and only if its determinant is non-zero.

Let's calculate the determinant of the given matrix:

[0  -5  9  6]

To calculate the determinant, we can use the formula for a 4x4 matrix:

det(A) = aei - afh - bdi + bfg + cdh - ceg

Substituting the values from the given matrix:

det(A) = 0(-5)0 - 0(9)6 - (-5)(0)6 + (-5)(9)0 + 9(0)6 - 9(-5)0

= 0 + 0 - 0 + 0 + 0 + 0

= 0

The determinant of the matrix is zero, which means it is not invertible. Therefore, the inverse of the matrix does not exist.

Learn more about Determinants here:

https://brainly.in/question/3663047

#SPJ11

The online shopping site would sell 756000 items in 30 minutes

Given

The online site would sell 420 items in a second

To find number of items it would sell in 30 minutes first of all convert minutes into seconds and continue to solve the problem.

To convert minutes into seconds just multiply minutes with 60.

because one minute is equal to 60 seconds.

Therefore 30 minutes = 30 x 60 seconds

30 minutes = 1800 seconds

Say the number of items sold by sire in 30 minutes be x.

now according to the condition in equation

420 x 1800 = x

x= 756000

Hence the site will sell 756000 items in 30 minutes.

To learn more about Time visit

https://brainly.com/question/15056141?referrer=searchResults

#SPJ1

Answer:

I think i need the asnwer too

Step-by-step explanation:

The function that models the averageTannual cost of owning a small dog for x years is f(x) = (180 + 400x) / x

The total cost of owning a small dog for x years can be expressed as the sum of the one-time cost and the continuing costs for x years, which is:

Total Cost = One-time Cost + Continuing Costs for x years

Total Cost = $180 + $400x

In this case, to find the average annual cost, we divide the total cost by the number of years:

Average Annual Cost = Total Cost / x

Average Annual Cost = ($180 + $400x) / x

Therefore, the function that models the average annual cost of owning a small dog for x years is: f(x) = ($180 + $400x) / x

Learn more about functions on

https://brainly.com/question/22340031

#SPJ1