Colin & Brian share a lottery win of £2100 in the ratio 4 : 1.
Colin then shares his part between himself, his wife & their son in the ratio 2 : 5 : 3.
How much more does his wife get over their son?​

Answers

Answer 1

Answer:

2

Step-by-step explanation:

I think but am not sure sorry I can not help


Related Questions

GIVING BRAINLIEST!!! PLS HELP!!! :((

GIVING BRAINLIEST!!! PLS HELP!!! :((

Answers

Answer:

2nd answer

Step-by-step explanation

Answer:

people are survivors and also a good person that can help with dysphoria of a child then a person that has a relationship to the parent and also wants you are not links with the person that is not a good friend or not a child and not everyone have to do that with a friend who are you stu you are a incel.co girl gamer who are not the only one of the things I do understand what I don't like it then you would know what he'll be like you and what you want me and then you are going

The tallet tree in the world i in redwood California a of April 2019 if you’re tanding on the trail 220 feet from the bottom of the tree you have to look up it i 60° angle to ee the top how tall i the tree

Answers

The height of the tree is approximately 380.04 feet.

Trigonometry involves the study of angles and their relationship to the sides of a right triangle

The tallest tree in the world is a redwood in California and if you're standing 220 feet from the bottom of the tree, you have to look up at a 60-degree angle to see the top. To find the height of the tree, we need to use a concept in mathematics called trigonometry.

The height of the tree can be found using the formula:

Height of tree = Distance from bottom of tree * tan (angle of elevation)

In this case, the distance from the bottom of the tree is 220 feet and the angle of elevation is 60 degrees. Plugging in these values into the formula, we get:

Height of tree = 220 * tan (60)

The value of tan (60) can be found using a calculator or a trigonometry table. The result is approximately 1.732. So the height of the tree can be calculated as:

Height of tree = 220 * 1.732 = 380.04 feet

So in summary, the height of the tree can be found by using the concept of trigonometry and the formula for the height of a tree based on the distance from the bottom of the tree and the angle of elevation to the top of the tree.

Complete Question:

2. The tallest tree in the world is a redwood in California (as of April 2019) If you're standing on the trail 220 feet from the bottom of the tree, you have to look up at a 60 degree angle to see the top. How tall is the tree? Draw the pic so that you know what you are solving for.

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Find the accumulated present value of an investment over a
20-year period if there is a continuous money flow of $3700 per
year and the current interest rate is 5%, compounded
continuously.

Answers

The accumulated present value is approximately $10090.18.

To find the accumulated present value of an investment with a continuous money flow of $3700 per year over a 20-year period, compounded continuously at an interest rate of 5%, we can use the continuous compound interest formula:

A = P * e⁽ʳᵗ⁾,

where:

A is the accumulated present value,

P is the continuous money flow per year,

e is the base of the natural logarithm (approximately 2.71828),

r is the interest rate,

t is the time period in years.

Given:

P = $3700,

r = 5% = 0.05,

t = 20 years,

Plugging in the values into the formula, we have:

A = $3700 * e⁽⁰°⁰⁵ * ²⁰⁾.

Calculating the exponential term:

e⁽⁰°⁰⁵ * ²⁰⁾ ≈ 2.71828¹ ≈ 2.71828.

Multiplying by the continuous money flow per year:

A ≈ $3700 * 2.71828 ≈ $10090.18.

Therefore, the accumulated present value of the investment over the 20-year period, with a continuous money flow of $3700 per year and a 5% continuous interest rate, is approximately $10090.18.

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Find the missing side. Round to the nearest tenth A) 21.3C) 9.2B) 9.5D) 11.5

Find the missing side. Round to the nearest tenth A) 21.3C) 9.2B) 9.5D) 11.5

Answers

We need to find the side that uses the adjacent and hypotenuse ratio. Using SOHCAHTOA:

Cosine is the ratio between adjacent and hypotenuse. Since x is adjacent to 49 and 14 is the hypotenuse, we can solve for x.

\(\cos (49\degree)=\frac{x}{14}\)

First, multiply both sides by 14.

\(\begin{gathered} 14\times\cos (49)=\frac{x}{14}\times14 \\ 14\cos (49)=x \end{gathered}\)

Next, we need to simplify the left side of our equation. We will do this using a calculator.

\(14\cos (49)=9.18\approx9.2\)

This leads to choice C, 9.2, being the correct answer.

NEED HELPPPP PLSSSSS !!!

NEED HELPPPP PLSSSSS !!!

Answers

Answer: The answer is choice b .

Step-by-step explanation: HOPE IT HELPS .

If the growth rate is 47% what is the growth factor?

Answers

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\\ r=rate\to 47\%\to \frac{47}{100}\dotfill &0.47\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A = P(1 + 0.47)^{t} \implies A =P(1.47)^t\hspace{5em}\stackrel{ Growth~Factor }{\text{\LARGE 1.47}}\)

Help I do t no and I have a big test today

Help I do t no and I have a big test today

Answers

Answer:

the area of the trapezoid is 78cm^3

Step-by-step explanation:

78cm^3 (trapezoid).....

HELP.... ME PLEASEE ASAP!!!! PLEASEE.....

HELP.... ME PLEASEE ASAP!!!! PLEASEE.....

Answers

32+(2x-12)=90

32+2x-12=90

2x+20=90

2x=70

x=35

Answer:

A x=35

Step-by-step explanation:

(2x-12)+32=90

2x-12=90-32

2x-12=58

2x=12+58

2x=70

x=70/2=35

Please help I don’t get it ?

Please help I dont get it ?

Answers

Answer:

Step-by-step explanation:

Pattern: Decrement the x and y axis size by 2 each time.

To draw the next three, simply remove two from the vertical axis and horizontal axis. Do this three times.

The sequence numerically may look something like this:

X { 13, 11, 9, 7, 5, 3, 1 }

Y { 13, 11, 9, 7, 5, 3, 1 }

Sonequa has two containers one in the shape of a cylinder and the other in the shape of a cone the two containers of equal radii and equal Heights she investigated the relationship between the volume of the cone and the cylinder by transferring water between the two containers which of the following claims is most likely to be supported using the result of sonequa investigation

Answers

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

Of the smoothie sold yesterday at Isaac's smoothie shop 1/4 we're banana and another 2/3 were strawberry What fraction of smoothies were either banana strawberry?

Answers

Answer:

11/12

Step-by-step explanation:

Fraction of smoothie that is Banana = 1/4

Fraction of smoothie that is strawberry = 2/3

The fraction of smoothies that were either banana or strawberry

= 1/4 + 2/3

Least Common Denominator= 12

= (3 × 1 + 2 × 4)/12

= 3 + 8/12

= 11/12

The fraction of smoothies were either banana or strawberry is 11/12

Alan is putting 11 books in a row on his bookshelf. He will put one of the books, The Iliad, in the first spot. He will put another of the books, The Odyssey, in the last spot. In how many ways can he put the books on the shelf

Answers

Alan can put the 11 books on the shelf, with The Iliad in the first spot and The Odyssey in the last spot, in 9! (362,880) ways

To determine the number of ways Alan can put the 11 books on his bookshelf with The Iliad in the first spot and The Odyssey in the last spot, we can follow these steps:

1. There are 11 spots on the bookshelf, but since The Iliad is in the first spot and The Odyssey is in the last spot, we are left with 9 spots for the remaining 9 books.
2. To arrange the 9 books, we can use the concept of permutations, which refers to the number of ways the books can be ordered.
3. The number of permutations for 9 books is calculated as 9! (9 factorial), which means 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Therefore, Alan can put the 11 books on the shelf, with The Iliad in the first spot and The Odyssey in the last spot, in 9! (362,880) ways.

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i need help answering this question

i need help answering this question

Answers

Answer:

a = 80

b = 3/4

the general equation is;

y = 80•(3/4)^x

Step-by-step explanation:

Here, we want to get the values of a and b

We are going to use the two points given

(0,80) and (1,60)

So we have this as;

for the first point;

80 = a•b^0

anything raised to power of 0 is 1

Thus;

80 = a * 1

a = 80

for the second point;

60 = 80 * b^1

60 = 80b

b = 60/80

b = 3/4

So we have the general equation as;

y = 80•(3/4)^x

Jacks father drives to work in 30 minutes while driivng at his usual speed. When traffic is bad, he drives 30 miles per hour slower and the trip takes one hour longer. How far is Jack's father's work from home

Answers

Answer:

The distance of Jack's father's work from home is 22.5 miles.

Step-by-step explanation:

Given;

time it takes Jacks father at usual speed, t = 30 minutes = 0.5 hour

Jacks father speed when traffic is bad, = 30 mph slower

let the usual speed = v

let the distance of Jack's father's work from home = y

When traffic is normal;

\(v = \frac{y}{0.5 } ---- equation \ (1)\)

When traffic is bad;

\(v - 30 \ mph = \frac{y}{1 \ + \ 0.5} \\\\v -30 = \frac{y}{1.5} \\\\v= 30 +\frac{y}{1.5} ----equation \ (2)\)

Solve equation (1) and (2) together;

\(\frac{y}{0.5} = 30 \ + \ \frac{y}{1.5} \\\\y = 0.5(30 \ + \ \frac{y}{1.5})\\\\y = 15 + \frac{y}{3} \\\\y - \frac{y}{3} = 15\\\\\frac{3y-y}{3} =15\\\\\frac{2y}{3} =15\\\\2y = 3(15)\\\\2y = 45\\\\y = \frac{45}{2} \\\\y = 22.5 \ miles\)

Therefore, the distance of Jack's father's work from home is 22.5 miles.

The required distance of Jack's father's work from home is y = 22.5miles.

Given that,

Jacks father drives to work in 30 minutes while driving at his usual speed.

When traffic is bad, he drives 30 miles per hour slower and the trip takes one hour longer.

We have to determine,

How far is Jack's father's work from home.

According to the question,

Let, the usual speed = v

And the distance of Jack's father's work from home = y

Jacks father at usual speed taking time, t = 30 minutes = 0.5 hour,

Jacks father speed when traffic is bad, = 30 mph slower.

The formula for speed is defined as = distance ÷ time.

Therefore,

Jacks father drives to work in 30 minutes while driving at his usual speed.

\(Speed = \dfrac{distance}{time}\\\\v = \dfrac{y}{0.5}\)

Then,

When traffic is bad, he drives 30 miles per hour slower and the trip takes one hour longer.

\(Speed = \dfrac{distance}{time}\\\\v - 30mph = \dfrac{y}{1+0.5}\\\\v = \dfrac{y}{1+0.5} + 30\)

Substitute the value of v from equation 1 to equation 2,

\(v = \dfrac{y}{1+0.5} + 30\\\\\dfrac{y}{0.5} = \dfrac{y}{1.5} + 30\\\\\dfrac{y}{0.5} = \dfrac{y +30(1.5)}{1.5}\\\\y (1.5) = 0.5(y +45)\\\\1.5y = 0.5y + 22.5 \\\\1.5y - 0.5y = 22.5\\\\1y = 22.5\\\\y = 22.5 \ miles\)

Hence, The required distance of Jack's father's work from home is y = 22.5miles.

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3. Mel has a bag of 8 marbles: 2 red, 3 yellow, and 3 green. She draws a marble from the bag,
writes down the color, replaces it, and draws again. She repeats this process for 40 trials and
records drawing a yellow marble 12 times. How does the experimental probability of selecting
a yellow marble compare to the theoretical probability? Explain.

Answers

We can see that the experimental probability is smaller than the theoretical one.

How do the probabilities compare?

The theoretical probability is equal to the quotient between the number of yellow marbles and the total number, so here we have:

T = 3/8 = 0.375

The experimental probability is equal to the quotient between the number of times that Mel got a yellow marble and the total number of trials, so here we have:

E = 12/40 = 0.3

So the experimental probability is smaller than the theoretical one.

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according to the cynic what will happen when the meek inherit the earth

Answers

The Cynic believes that when the Meek inherit the Earth, there will be a shift towards an easier and less complicated life.

What did the Cynic believe ?

In general, the Cynics believed in living a simple and ascetic life, free from materialism and societal norms.

It can be assumed that the Cynics may believed that the inheritance of the Earth by the meek would lead to a shift in values and beliefs towards simplicity, frugality, and self-sufficiency, rather than wealth, power, and status. This is a stark opposite to the world as it currently is as this world has wealth and power as the most power defining factors of status.

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geometry triangle help pls

geometry triangle help pls

Answers

Answer:

equilateral trianglethe last optionpls mark brainlest

help me now asap please

help me now asap please
help me now asap please

Answers

Answer:

C

Step-by-step explanation:

Let's first convert both Brooke's time and Lamont's time into the same unit so that we can more easily compare them. To make it simpler, we'll convert both times into minutes.

Brooke: 1 hr 45 min

We know that there are 60 minutes in 1 hour, so we essentially have:

60 min and 45 min  ⇒  60 + 45 = 105 min

Lamont: 115 min

This is already in minutes, so we don't have to do anything to it.

We now have 105 minutes for Brooke and 115 minutes for Lamont. Let's compare:

- Since we know Brooke took 105 minutes, we can eliminate A and B.

- Clearly, 105 < 115, which means Brooke took less time that Lamont to finish the race

- If Brooke took less time, that means she's faster.

Thus, the answer is C.

~ an aesthetics lover

Answer:

Time taken by Brooke = 1h 45min

= 60min + 45min

= 105min

Time taken by Lamont = 115min

Brooke finished in 105min, so she was faster.

Option 3 is correct.

We are unable to use a method like gradient descent for classifying error in classification because

Answers

Gradient descent cannot be used directly for classifying error in classification because the error rate is not a smooth function of the model parameters and gradients cannot be computed.

Gradient descent is an optimization algorithm that is commonly used in machine learning to minimize a cost function. The cost function is a measure of how well the model performs on the training data, and the goal of the optimization algorithm is to find the model parameters that minimize this cost function.

In classification tasks, the cost function is typically a measure of the error rate or misclassification rate of the model. However , the error rate is not a smooth function of the model parameters, and it is not possible to compute gradients with respect to the model parameters. This makes it difficult to use gradient descent directly for optimizing the parameters of a classification model.

Instead, specialized optimization algorithms such as stochastic gradient descent (SGD) and its variants are used to train classification models. These algorithms are designed to work with non-smooth, non-convex cost functions and are able to handle the discrete nature of the output labels in classification tasks. Additionally, other metrics such as accuracy, precision, recall, and F1 score can be used as evaluation metrics instead of the error rate.

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let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia. can we conclude, at the 0.01 level of significance, that the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country? perform a two-tailed test. then answer the questions below.

Answers

According to the two tailed test, the difference between the first and second country is 40.

Two tailed test:

Two tailed test also means the two-sample t-test is used to determine if two population means are equal.

Given,

Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia.

Here we need to find the the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country.

While we looking into the given question,

For the first country,

Number of samples = 1800

Number of women with iron-deficiency anemia = 392

And for the second country,

Number of samples = 1700

Number of women with iron-deficiency anemia = 352

So, there difference between them is calculated as,

=> 392 - 352

=> 40

And as per the two tailed test both countries doesn't have the same proportion and the sample values is also differs this situation.

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Find the area of the rectangle to the right. 9 inches for width and 5y inches for the length

Answers

Answer:

The area is 45 inches

Step-by-step explanation:

L×W=A

FOR EACH SITUATION IDENTIFY IT AS AN EXPONENTIAL GROWTH OR EXPONENTIAL DECAY. town's population was 3800 in 2005 and growing at a rate of 2% every year.​

Answers

The function of the town's population is an exponential growth

How to classify the function as growth or decay

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

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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By visual Inspection, determine the best-fitting regression model for the
scatterplot.
A. No pattern
B. Linear
C. Quadratic
D. Exponential

By visual Inspection, determine the best-fitting regression model for thescatterplot.A. No patternB.

Answers

I think it’s letter B

Answer: Linear

Step-by-step explanation:

Please print, write neatly answers on the pages provided Show all work 5.1 Expand Binomials, pages 234-341 2 marks each 1. Expand and simplify. a) (x+6)(x-2) b) (x-3)(x+3) c) (3x + 4)(2x - 1) d) (2x + 1)² 2. Write an expression, in simplified form, for the area of the figure. 5 marks 5x+4 X+6 2x + 1 x + 3

Answers

Expanded and simplified form of equation are (x+6)(x-2) = x² + 4x - 12, (x-3)(x+3)= x² - 9,  (3x + 4)(2x - 1)= 6x² + 5x - 4, (2x + 1)²= 4x² + 4x + 1 and the simplified expression for the area of the figure is 10x⁴ + 103x³ + 301x² + 270x + 72.

a) (x+6)(x-2)

= x(x) + x(-2) + 6(x) + 6(-2)

= x² - 2x + 6x - 12

= x² + 4x - 12

b) (x-3)(x+3)

= x(x) + x(3) - 3(x) - 3(3)

= x² + 3x - 3x - 9

= x² - 9

c) (3x + 4)(2x - 1)

= (3x)(2x) + (3x)(-1) + (4)(2x) + (4)(-1)

= 6x² - 3x + 8x - 4

= 6x² + 5x - 4

d) (2x + 1)²

= (2x + 1)(2x + 1)

= (2x)(2x) + (2x)(1) + (1)(2x) + (1)(1)

= 4x² + 2x + 2x + 1

= 4x² + 4x + 1

The expression for the area of the figure is (5x + 4)(x + 6)(2x + 1)(x + 3).

To simplify this expression, we can perform multiplication by expanding and combining like terms:

(5x + 4)(x + 6)(2x + 1)(x + 3)

= (5x + 4)(2x + 1)(x + 6)(x + 3)

= (10x² + 5x + 8x + 4)(x + 6)(x + 3)

= (10x² + 13x + 4)(x + 6)(x + 3)

= (10x² + 13x + 4)(x² + 9x + 18)

Expanding further:

= 10x²(x² + 9x + 18) + 13x(x² + 9x + 18) + 4(x² + 9x + 18)

= 10x⁴ + 90x³ + 180x² + 13x³ + 117x² + 234x + 4x² + 36x + 72

= 10x⁴ + 103x³ + 301x² + 270x + 72

Therefore, the simplified expression for the area of the figure is 10x⁴ + 103x³ + 301x² + 270x + 72.

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On the left, model 4 + (-6). On the right, model 4 - 6.

I need to know where the dots would be placed on this number line

On the left, model 4 + (-6). On the right, model 4 - 6.I need to know where the dots would be placed

Answers

Answer:

On the left because their both positive and the other one is not and also the left one is on the left y axil

write the word sentence as a equation. Then solve the equation 13 subtracted from a number w is 15

Answers

w-13=15 add 13 on both sides to isolate variable and you get w=13+15, w=28

What is 24*25 equal to?

Answers

Answer:

600

Step-by-step explanation:

24*25 means 24 and 25 are multiplied.

24 x 25 = 600

In the following questions, the bold letters X, Y, Z are variables. They can stand for any sentence of TFL. (3 points each) 4.1 Suppose that X is contingent and Y is a tautology. What kind of sentence must ¬XV y be? Explain your answer. 4.2 Suppose that X and Y are logically equivalent, and suppose that X and Z are inconsistent. Does it follow that Y must entail ¬Z? Explain your answer. 4.3 Suppose that X and X → > Z are both tautologies. Does it follow that Z is also a tautology? Explain your answer.

Answers

4.1 If X is contingent (neither a tautology nor a contradiction) and Y is a tautology (always true), ¬X V Y is a tautology.

4.2 No, it does not necessarily follow that Y must entail ¬Z. Y does not necessarily entail ¬Z.

4.3 The tautologies of X and X → Z do not provide sufficient information to conclude that Z itself is a tautology.

4.1 If X is contingent (neither a tautology nor a contradiction) and Y is a tautology (always true), the sentence ¬X V Y must be a tautology. This is because the disjunction (∨) operator evaluates to true if at least one of its operands is true. In this case, since Y is a tautology and always true, the entire sentence ¬X V Y will also be true regardless of the truth value of X. Therefore, ¬X V Y is a tautology.

4.2 No, it does not necessarily follow that Y must entail ¬Z. Logical equivalence between X and Y means that they have the same truth values for all possible interpretations. Inconsistency between X and Z means that they cannot both be true at the same time. However, logical equivalence and inconsistency do not imply entailment.

Y being logically equivalent to X means that they have the same truth values, but it does not determine the truth value of ¬Z. There could be cases where Y is true, but Z is also true, making the negation of Z (¬Z) false. Therefore, Y does not necessarily entail ¬Z.

4.3 No, it does not necessarily follow that Z is also a tautology. The fact that X and X → Z are both tautologies means that they are always true regardless of the interpretation. However, this does not guarantee that Z itself is always true.

Consider a case where X is true and X → Z is true, which means Z is also true. In this case, Z is a tautology. However, it is also possible for X to be true and X → Z to be true while Z is false for some other interpretations. In such cases, Z would not be a tautology.

Therefore, the tautologies of X and X → Z do not provide sufficient information to conclude that Z itself is a tautology.

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A wire is bent into a circular coil of radius r=4.8 cm with 21 turns clockwise, then continues and is bent into a square coil (length 2r ) with 39 turns counterclockwise. A current of 11.8 mA is running through the coil, and a 0.350 T magnetic field is applied to the plane of the coil. (a) What is the magnitude of the magnetic dipole moment of the coil? A ⋅m
2
(b) What is the magnitude of the torque acting on the coil? N=m

Answers

The magnitude of the magnetic dipole moment of the coil is approximately 0.079 A·m². The magnitude of the torque acting on the coil is approximately 0.068 N·m.

(a) To find the magnitude of the magnetic dipole moment (M) of the coil, we can use the formula M = NIA, where N is the number of turns, I is the current flowing through the coil, and A is the area of the coil. For the circular coil, the area is given by A = πr², where r is the radius. Substituting the values N = 21, I = 11.8 mA = 0.0118 A, and r = 4.8 cm = 0.048 m, we can calculate the magnetic dipole moment as M = NIA = 21 * 0.0118 * π * (0.048)² ≈ 0.079 A·m².

(b) The torque acting on the coil can be calculated using the formula τ = M x B, where M is the magnetic dipole moment and B is the magnetic field strength. The magnitude of the torque is given by |τ| = M * B, where |τ| is the absolute value of the torque. Substituting the values M ≈ 0.079 A·m² and B = 0.350 T, we can calculate the magnitude of the torque as |τ| = M * B ≈ 0.079 A·m² * 0.350 T ≈ 0.068 N·m.

Therefore, the magnitude of the magnetic dipole moment of the coil is approximately 0.079 A·m², and the magnitude of the torque acting on the coil is approximately 0.068 N·m.

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The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?
6
20
27
30

Answers

\(\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{llll} \textit{"y" varies}\\ \textit{directly with "x"}\\ \textit{inversely with "z"} \end{array}\qquad y=\cfrac{kx}{z}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ z=4\\ y=15 \end{cases} \\\\\\ 15=\cfrac{k(10)}{4}\implies \cfrac{4}{10}\cdot 15=k\implies 6=k\hspace{8em}\boxed{y=\cfrac{6x}{z}} \\\\\\ \textit{when x = 20 and z = 6, what's "y"?}\qquad y=\cfrac{6(20)}{6}\implies y=20\)

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