find the taylor polynomial t3x for the function f cen- e^-x sinx

A. The total charge in the device at t = 1 s is 28(1 + e⁻²¹) × 10⁻³ mC.

B. The power consumed by the device at t = 1 s is 27 sin(44) × 28(1 + e⁻²¹) mW.

To calculate the total charge in the device at t = 1 s, we need to integrate the current over time.

Given:

v(0) = 27 sin(44) V

i(0) = 28(1 + e⁻²¹) mA

We'll convert the current to amperes for consistency:

i(0) = 28(1 + e⁻²¹) × 10^(-3) A

We integrate the current from t = 0 to t = 1 s to find the total charge:

q(t) = ∫[0 to t] i(t') dt'

Since q(0) = 0, we can write:

q(t = 1) = ∫[0 to 1] i(t') dt'

Let's perform the integration:

q(t = 1) = ∫[0 to 1] 28(1 + e⁻²¹) × 10⁻³ dt'

= 28(1 + e⁻²¹) × 10⁻³ ∫[0 to 1] dt'

= 28(1 + e⁻²¹) × 10⁻³ [t'] [0 to 1]

= 28(1 + e⁻²¹) × 10⁻³ (1 - 0)

= 28(1 + e⁻²¹) × 10⁻³ mC

Therefore, the total charge in the device at t = 1 s is 28(1 + e⁻²¹) × 10⁻³ mC.

B. To calculate the power consumed by the device at t = 1 s, use the formula:

P(t) = v(t) × i(t)

Given v(0) = 27 sin(44) V and i(0) = 28(1 + e⁻²¹) mA, we need to evaluate v(t) and i(t) at t = 1 s:

v(t = 1) = 27 sin(44)

i(t = 1) = 28(1 + e⁻²¹)

Now we can calculate the power:

P(t = 1) = v(t = 1) × i(t = 1)

= 27 sin(44) × 28(1 + e⁻²¹)

Therefore, the power consumed by the device at t = 1 s is 27 sin(44) × 28(1 + e⁻²¹) mW.

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The complete question goes thus:

The voltage v1) across a device and the current i(t) through it are (0) = 27 sin(44) V and (0) = 28(1 + e-21) mA.

Calculate the total charge in the device at t = 1 s, assuming q(0) = 0. The total charge in the device at t = 1 s is ___ mC.

Calculate the power consumed by the device at t = 1 s. The power consumed by the device at t = 1 s is ___ mW.

Answer:

V = 7234.56 km^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

V = 4/3 (3.14) (12)^3

V = 7234.56 km^3

Answer:

7234, 56 km³

Step-by-step explanation:

π×R³×4/3=3.14×1728×4/3=7234, 56 km³

Francisco teaches group lessons to all of the violin and viola students at the Scott School of Music. All of his classes have the same number of students.

What is the greatest number of students he can have in each class We can determine the greatest number of students that Francisco can teach in each class by finding the greatest common factor (GCF) of the total number of violin and viola students at the school.

Suppose there are a total of m violin students and n viola students. Then the total number of students at the school is m + n. Let's find the GCF of m and n in order to determine the greatest number of students Francisco can teach in each class.

GCF of m and n will give us the number of students that can be divided equally among all the classes. Following the steps to find GCF :

Step 1 :List down all factors of m and n

Step 2 :Identify the common factors of both m and n

Step 3 :Find the largest common factor m and n. We find the factors of m and n below: Suppose m = 36 and n = 72.Therefore, the greatest common factor of m and n is 36.So, the greatest number of students that Francisco can teach in each class is 36.

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The value of the account in 2019 is $1398.

The formula that can be used to determine the growth rate is:

g = (FV / PV)^1/n - 1

Where:

(1060 / 750)^1/5 - 1 = 7.164%

The formula for calculating future value:

FV = P (1 + r)^n

$750 x ( 1.07164)^9 = 1398

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Answer:

LOL

Step-by-step explanation:

Answer:

AC ≈ 4.7 ft.

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

\(\cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}\)

SOLUTION :-

Side adjacent to ∠A = AC = x

Hypotenuse = AB = 5 ft

⇒ \(\cos 20 = \frac{x}{5}\)

⇒ \(0.9396.... = \frac{x}{5}\)

⇒ \(x = (0.9396...) \times 5 = 4.6984....\) ≈ 4.7 ft

The length of the base is Height/15

From the question, we have the following parameters that can be used in our computation:

Area = 1/30 square feet

The area of a triangle is calculated as

Area = 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

1/2 * Base * Height = 1/30

So, we have

Base * Height = 1/15

Evaluate

Base = Height/15

Hence, the base is Height/15

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Answer:

A=2x^2+5x

Step-by-step explanation:

length of frame = 2x+5

width of frame = x

A=lw

A=(2x+5)x

A=2x^2+5x

Linear regression is a statistical tool used in predictive analytics to identify the relationship between a dependent variable and one or more independent variables.

Linear regression is a statistical technique used in predictive analytics to identify the relationship between a dependent variable and one or more independent variables. It is used to predict future outcomes by analyzing data from the past. It works by fitting a linear equation to the data, which is then used to estimate the value of the dependent variable for any given combination of values of the independent variables. The linear equation is constructed by finding the line of best fit through the data points. Linear regression can be used to identify trends and patterns in the data, and to make predictions about future outcomes. It is a powerful tool for predicting the future, and can be used to make informed decisions about how to best use resources.

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we should reject H0 if the standardized test statistic is greater than 1.645

Given a sample size of n = 48 and a level of significance of α = 0.1, we can use the z-test to test the claim μ ≤ 25.6.

Since the level of significance is α = 0.1, we need to find the critical value corresponding to a 90% confidence level (1 - α).

The critical value for a 90% confidence level is 1.645.

what is statistic?

A statistic is a numerical value or measure that summarizes a specific characteristic or property of a sample or population. It is commonly used in statistics and research to provide information about a data set or to make inferences about a larger population based on the observed sample.

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(a) correctly describes the relationship between a parameter and a statistic.

The correct description is:

a) A statistic is calculated from sample data and is generally used to estimate a parameter.

In statistics, a parameter refers to a characteristic or measure that describes a population, while a statistic is a characteristic or measure calculated from sample data. Statistics are often used to estimate or infer the corresponding parameters of the population. Therefore, option (a) correctly describes the relationship between a parameter and a statistic.

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To determine the time required to produce 9.59 mol of H2 in the electrolysis of water, we need to calculate the total charge (Q) required using Faraday's law of electrolysis. The equation relating charge (Q), current (I), time (t), and Faraday's constant (F) is:

Q = I * t

The charge (Q) can be determined by multiplying the current (I) by the time (t). Rearranging the equation to solve for time:

t = Q / I

We also need to consider the relationship between the charge (Q) and the moles of hydrogen gas (H2) produced during electrolysis. From the balanced chemical equation of water electrolysis:

2 H2O → 2 H2 + O2

We can see that 2 moles of H2 are produced for every 2 moles of water, or 1 mole of H2 for every mole of water.

Given that 9.59 mol of H2 will be produced, we know that the same number of moles of water (9.59 mol) will be electrolyzed. This implies that 9.59 mol of water will require 9.59 moles of electrons.

One mole of electrons corresponds to a charge of 1 Faraday (F), which is approximately equal to 96,485 C.

Using the given current of 126.0 mA (0.126 A) and Faraday's constant:

Q = (9.59 mol H2) * (2 mol e^- / 1 mol H2) * (96,485 C / 1 mol e^-)

Q ≈ 1,846,153 C

Now we can calculate the time required using the equation:

t = Q / I

t = (1,846,153 C) / (0.126 A)

t ≈ 14,639,622 seconds

Therefore, it will take approximately 14,639,622 seconds to produce 9.59 mol of H2 in the electrolysis of water with a current of 126.0 mA.

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Answer:

The answer is A. 18.84

Step-by-step explanation:

Hope this helps =)

Answer:

Step-by-step explanation:

y=10

Answer:

28125

Step-by-step explanation:

300÷20=15

15×1875=28125

Answer:

2 weeks

Step-by-step explanation:

54.00 + 0.15 = 54.15

140/54.15 = about 2.5

Since she can only spend $140, she has to round down, so the answer is 2 weeks.

Answer:C-34

Step-by-step explanation:

Answer:

12 less than a number means to subtract 12 from that number. So, 12 less than 20 is 8 , because is 20−12 , 12 less than 12 is 0 , because it's 12−12 , and so on. But since you don't know which number you need to subtract from, it's a variable, and you can call it as you like, usually x .

Answer:

  P'(3, -12)

Step-by-step explanation:

Assuming we're dilating the figure by a factor of 3 using the origin as the center of dilation, the coordinates of P' will be 3 times those of P:

  P' = 3P

  P' = 3(1, -4)

  P' = (3, -12)

Answer:

18 in

Step-by-step explanation:

len = y

width= y - 6

the area of rectangle is len x width

(Y) x (Y-6) = 216

Y^2 - 6Y = 216, Y^2 - 6y -216 = 0

y = (36 /2) or (-24 /2)

len couldn't be negative so 18

Compared with the graph of the parent function, an equation which shows only a vertical compression by a scale factor of 1/3 and a shift downward of 4 units is: A. y = 1/3∛x - 4.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (1/3x, 1/3y)

Where:

In this scenario, the only equation that is vertically compressed by a scale factor of 1/3 and translated (shifted) downward by 4 units is given by:

y = 1/3∛x - 4.

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Answer:

The first part is A

and second part is D

Step-by-step explanation:

100% on edge 2023

Answer:

18.75 I believe is the answer

The wind speed for the flight is 2 miles per hour.

Let's assume the wind speed is represented by "w" miles per hour.

When the drone flies with the wind, its effective speed is the sum of its own speed and the wind speed, so it travels at 5 + w miles per hour. Therefore, the time it takes to fly 35 miles with the wind is given by:

time = distance / speed

time = 35 / (5 + w)

Similarly, when the drone flies against the wind, its effective speed is the difference between its own speed and the wind speed, so it travels at 5 - w miles per hour. The time it takes to fly 15 miles against the wind is given by:

time = distance / speed

time = 15 / (5 - w)

Since the flight time is the same for both scenarios, we can set the two expressions for time equal to each other:

35 / (5 + w) = 15 / (5 - w)

Now, we can solve this equation to find the value of "w," the wind speed.

Cross-multiplying:

35(5 - w) = 15(5 + w)

175 - 35w = 75 + 15w

Combining like terms:

50w = 100

Dividing both sides by 50:

w = 2

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Answer:

B: \(y=-\frac{1}{3}x+7\)

Step-by-step explanation:

Straight lines are set out in the format of \(y = mx+c\), where \(m\) is the gradient, and \(c\) is the y-intercept.

The gradient between parallel lines remains the same, and this means the gradient of the new line will also be \(-\frac{1}{3}\).

This rules out options C and D.

Going back to the format, so far, we have filled in \(y=-\frac{1}{3}x+c\). We are still looking for the y-intercept.

We can find that using the coordinate you've been given, \((6,5)\).

This coordinate tells us that when \(x=6\), \(y=5\). Therefore we can substitute those in the places of \(x\) and \(y\) in the original equation.

This leaves us with \(5 = -\frac{1}{3}(6)+c\).

We can now rearrange for \(c\).

\(5 = -2 + c\\c=7\)

Now we have all the values we need, we can form the final equation.

\(y=-\frac{1}{3}x+7\)

This indicates the answer is option B. Hope this helps.

Answer:

Midpoint is\((-25.15,10.2)\)

Step-by-step explanation:

A line segment refers to line that has two endpoints.

Let \((a,b),(c,d)\) be the endpoints of a line segment.

Midpoint of the line segment is given by \((\frac{a+c}{2} ,\frac{b+d}{2})\)

Take the given points as follows:

\((a,b)=(-24.6,38.1)\\(c,d)=(-25.7,-17.7)\)

Midpoint of a line segment \(=(\frac{-24.6-25.7}{2},\frac{28.1-17.7}{2})\)

\(=(\frac{-50.3}{2} ,\frac{20.4}{2} )\\=(-25.15,10.2)\)

Answer:

5x-8

Step-by-step explanation:

Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185