FInd the equation of the line normal to the curve y=8tan(x^2) at x = 0.1825

The expression that gives the magnitude of the magnetic field in the region r1 < c (at F) is\(B(r_1) = \frac{mu_0 i(r_{21 }- b_2)}{(2 \pi r_1(a_2 - b_2))}\). This expression considers the distance from the wire, the geometry of the wire, and the current in the wire to calculate the magnetic field magnitude.

The expression that gives the magnitude of the magnetic field in the region r1 < c (at F) is \(B(r_1) = \frac{mu_0 i(r_{21 }- b_2)}{(2 \pi r_1(a_2 - b_2))}\).

This expression is derived from the Biot-Savart law, which relates the magnetic field generated by a current-carrying wire to the distance from the wire and the geometry of the wire.

In this case, the expression takes into account the variables r1 (distance from the wire), c (outer radius of the wire), a (inner radius of the wire), b (distance from the center of the wire to the point F), i (current in the wire), and mu0 (the permeability of free space).

The expression includes the difference between the squares of r1 and b2 in the numerator, and the product of 2 pi r1 and the difference between the squares of a2 and b2 in the denominator.

This formulation accounts for the geometry of the wire and the distance from the wire, providing the magnitude of the magnetic field at point F.

It's important to note that without additional information or context, it's difficult to determine the specific values of the variables in the expression.

Hence, the expression that gives the magnitude of the magnetic field in the region r1 < c (at F) is \(B(r_1) = \frac{mu_0 i(r_{21 }- b_2)}{(2 \pi r_1(a_2 - b_2))}\).

To know more about magnetic field refer here:

https://brainly.com/question/32559844#

#SPJ11

Bag one currently holds 25 kilograms of sugar, while bag two contains 75 kilograms of sugar.

Let's represent the initial amount of sugar in bag one as x and bag two as y. According to the given information, bag one has used 3 times as much sugar as bag two. This can be expressed as:

Bag one: x - 3y

Bag two: y

Furthermore, we are told that after using this amount of sugar, bag one has half as much sugar as bag two. Mathematically, we can express this as:

(x - 3y) = (1/2)y

Simplifying the equation, we get:

2(x - 3y) = y

2x - 6y = y

2x = 7y

Since we also know that the initial amount of sugar in each bag is 50 kilograms, we can set up another equation:

x + y = 100

We now have a system of two equations:

2x = 7y

x + y = 100

By solving these equations simultaneously, we find that x = 25 and y = 75. Thus, bag one currently holds 25 kilograms of sugar, while bag two contains 75 kilograms of sugar.

Learn more about: sugar

brainly.com/question/2801953

#SPJ11

   The number -√17, expressed as a value or number exponential is -17¹/².

  An exponential number is a mathematical expression and one of the many mathematical operations of reduction, it involves the successive multiplication of a number, it has the form:

aᵇ

Where:

  To convert a root into a exponential we must know the way in which these are related, and it is by means of the following property:

√a = a¹/²

  Now in our case we have -√17 which can be expressed as.

(-1)√17, where 17 = a, then

(-1)17¹/²

-17¹/²

Learn more about exponentials in:

https://brainly.com/question/11464095

#SPJ4

a) \(x^2\)is always non-negative, the solution to \(x^2 > 9\) is x < -3 or x > 3.

b) The quadratic function opens upwards, so the solution to \(x^2 - 5x + 4 < 0\) is 1 < x < 4.

c) The quadratic function opens upwards, so the solution to \(x^2 - 4x + 3 > 0\)  is x < 1 or x > 3.

(a) To solve\(x^2 > 9\), we first find the roots of \(x^2 - 9 = 0\) by factoring as

(x + 3)(x - 3) = 0.

This gives us two critical points, x = -3 and x = 3.

We can use these critical points to create intervals on the number line to

test the inequality.

(b) To solve\(x^2 - 5x < -4\), we first bring all the terms to one side to get

\(x^2 - 5x + 4 < 0.\)

We then find the roots of the quadratic equation \(x^2 - 5x + 4 = 0\)by

factoring as (x - 4)(x - 1) = 0.

This gives us two critical points, x = 1 and x = 4. We can use these critical

points to create intervals on the number line to test the inequality.

(c) To solve \(x^2 - 4x > -3\), we first bring all the terms to one side to get

\(x^2 - 4x + 3 > 0\).

We then find the roots of the quadratic equation \(x^2 - 4x + 3 = 0\) by

factoring as (x - 3)(x - 1) = 0.

This gives us two critical points, x = 1 and x = 3.

We can use these critical points to create intervals on the number line to

test the inequality.

such more question on quadratic function

https://brainly.com/question/17482667

#SPJ11

Answer:

$8

Step-by-step explanation:

20% is 1/5, so you can basically divide $40 by 5, which is $8.

Answer:

they are wrong the first one is the B one and the next one is D have a good day.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

LM = KI/2

LM = 16/2

LM = 8

The first column is found by plugging in the x values to get corresponding y values. For instance, if x = -5, then y is...

y = x^2+3x-18

y = (-5)^2+3(-5)-18

y = 25-15-18

y = 10-18

y = -8

So that explains how they got -8 in the second column, next to x = -5.

--------------

The column of first differences is found by subtracting the adjacent terms in the y column. The distance from y = -8 to y = -14 is 6 units, so we'll write 6 in the first row of the "first differences" column. The rest of the values of this column are filled out in a similar fashion. This means that you'll need to completely fill out the y column before you can move onto the "first differences" column.

--------------

The second differences is found by subtracting the adjacent first differences. You should find the results of this column are all the same value. This is true of any quadratic function.

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

To know more about nonzero vector refer here:

https://brainly.com/question/32673773#

#SPJ11

Stratified random sampling is a reliable and effective method for studying farmers' needs,

What is Stratified random sampling?

Stratified random sampling is a sampling technique used in statistical analysis, where the population is first divided into subgroups or strata based on some relevant characteristics, and then random samples are selected from each stratum.

Stratified random sampling would be effective for studying farmers' needs for several reasons:

It would ensure a sample of the population that accurately represents the population by dividing the population into subgroups based on specific characteristics such as crop type, farm size, or geographic location.

This would reduce the risk of bias in the study's findings and ensure that the results can be generalized to the larger population of farmers.

Stratified random sampling would reduce selection bias by selecting participants randomly from each subgroup, rather than selecting them based on convenience or availability.

It would allow farmers who grow in very specific conditions to voice their needs and have them heard.

Stratified random sampling can be more efficient and cost-effective for the researchers.

Overall, stratified random sampling is a reliable and effective method for studying farmers' needs, providing valuable insights into the diverse needs of the population.

To know more about Stratified random sampling visit:

brainly.com/question/20692763

#SPJ1

Answer:

hence the midpoint of AB is 1/2,1

Step-by-step explanation:

A(-2,5)

B(3,-3)

now midpoint of AB is given by

\(mid \: point \: of \: ab = (\frac{ - 2 + 3}{2} ) \: ( \frac{5 - 3}{2} ) \\ = ( \frac{ 1}{2} ) \: (1)\)

Probability that the sample mean hardness for a random sample of 44 pins is at least 51 = 0.1%

Rockwell hardness of pins of a certain type are known to have a

Mean value = μ = 50

Standard deviation = 1.8

n= 44

X = 51

Using Central Limit Theorem:

Z = (X- μ)/s

s =  \(1.8/\sqrt{n}\)

s = \(1.8/\sqrt{44}\)

s = 0.271

Z = (51-50)/0.271

Z = 1/0.271

Z = 3.69

Z = 3.7 has a p-value of 0.9999

so, 1-0.9999 = 0.0001

Probability that the sample mean hardness for a random sample of 44 pins is at least 51 = 0.1%

Learn more about mean:

https://brainly.com/question/13451489

#SPJ4

Bonnie earns $1750 a month and claims 2 exemptions. Exemptions are a type of tax deduction that reduces the amount of income that is subject to tax.

The more exemptions an individual claims on their W-4 form, the less tax will be withheld from their paycheck. Therefore, claiming 2 exemptions means that Bonnie will have less tax withheld from her paycheck than if she claimed 0 or 1 exemption. The exact amount of tax withheld depends on factors such as her tax bracket, filing status, and other deductions or credits she may be eligible for. Claiming exemptions does not affect how much tax an individual owes for the year; it only affects how much tax is withheld from their paycheck throughout the year.

If too little tax is withheld, the individual may owe money when they file their tax return. If too much tax is withheld, they will receive a refund. Bonnie's specific tax situation will depend on a variety of factors, so it is not possible to determine her exact tax liability without additional information.

To learn more about Deduction :

https://brainly.com/question/4708897

#SPJ11

37 is at the 50th percentile in the given set of values.

To find the percentile of 37 in the given set of values, we need to count the number of values in the set that are less than or equal to 37, and then divide by the total number of values in the set.

The given set has 16 values, and there are 8 values that are less than or equal to 37.

So, the percentile of 37 is:

Percentile = (number of values below score / total number of values) × 100

Percentile = (8 / 16) × 100

Percentile = 50

Therefore, 37 is at the 50th percentile in the given set of values.

Learn more about the percentile here:

https://brainly.com/question/1594020

#SPJ1

The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

To learn more about :  dimensions

https://brainly.com/question/28107004

#SPJ8

The new cost equation after an increase in the interest rate by $3 would be:  TC = 250 + 75q + 3

The fixed cost of production is $250.

To calculate the average variable cost (AVC), we need to divide the total variable cost (TVC) by the quantity of output (q) at a given level of production.

In this case, the total cost (TC) equation is given as TC = 250 + 75q, where q is the total quantity of output.

To find the TVC at 50 units of goods, we substitute q = 50 into the TC equation:

TC = 250 + 75(50)

TC = 250 + 3750

TC = 4000

Since the fixed cost is $250, the TVC would be:

TVC = TC - Fixed Cost

TVC = 4000 - 250

TVC = 3750

Now we can calculate the AVC:

AVC = TVC / q

AVC = 3750 / 50

AVC = 75

Therefore, the average variable cost is $75.

The marginal cost (MC) is the additional cost incurred by producing one additional unit of output. In this case, it is given as 5 (assuming it's $5 per unit).

The average fixed cost (AFC) is the fixed cost per unit of output. Since AFC is the fixed cost divided by the quantity of output (q), we can calculate it as:

AFC = Fixed Cost / q

AFC = 250 / 50

AFC = 5

Therefore, the average fixed cost is $5.

Hence, the correct choice is option B: TC = 250 + 75q + 3.

Learn more about interest rate

https://brainly.com/question/29451175

#SPJ11

Answer:

174.5m

Step-by-step explanation:

So we have to break the shapes down to triangle, rectangle and the small rectangle

Area of rectangle=WxL

Area of triangle= (BxH)÷2

triangle=

(23x11)÷2

=253÷2

=126.5m

rectangle=

9x19

=28m

square#2(the small one)=

5x4

=20m

All:

20+28+126.5

=174.5m

Answer:

(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯     is true

Step-by-step explanation:

The positions of the letters in naming the triangles in the statement of congruent tells you which sides are congruent.

△ABC≅△EFG

Sides AB and EF are congruent

△ABC≅△EFG

Sides BC and FG are congruent

△ABC≅△EFG

Sides AC and EG are congruent

Look at the choices:

(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯     is true

Answer:

The answer is m=-2 or m=7.

Step-by-step explanation:

The steps to solve this equation are below:

Factor: to get (m+2)(m−7)=0.

m+2=0 or m−7=0

m=−2 or m=7. So, your answer is m=-2 or m=7.

Answer:

m = 7

m = -2

Step-by-step explanation:

ax^2 + bx + c

1m^2 - 5m - 14

a = 1

b = -5

c = -14

-b ± √b^2 - 4ac/2a

-(-5) ± √(-5)^2 - 4(1)(-14)/2(1)

5 ± √25 + 56/2

5 ± √81/2

5 ± 9/2

5 + 9/2

14/2 = 7

5 - 9/2

-4/2 = -2

The selection chances and the required probability for 9 women and 6 men is given by ,

Different groups of applicants selection = 3003

Selection of trainee entirely of women = 126

Probability of selection of entirely women from 15 people = 4.19%

Total number of women = 9

Total number of men = 6

Total = 9 + 6

        = 15

The total number of groups of applicants that can be selected for the positions can be calculated using the combination formula,

nCr = n! / r!(n-r)!

where n is the total number of applicants (15),

And r is the number of positions to be filled (5).

Number of different groups of applicants that can be selected for the positions is,

15C5

= (15! )/(15-5)!5!

=(15! )/(10)!5!

= 3003

Number of different groups of trainees that consist entirely of women can be calculated by selecting 5 women from the 9 available,

9C5

= (9! )/(9-5)!5!

=(9! )/(4)!5!

= 126

Probability of selecting a group of five trainees ,

Consist entirely of women can be calculated by dividing the number of different groups of all-women trainees (126) by the total number of different groups of trainees (3003),

Required probability

= 126/3003

≈ 0.0419

Probability that the trainee class will consist entirely of women is approximately 0.0419, or 4.19% (rounded to four decimal places).

Therefore, for a group of 15 people,

Selection of different groups of people = 3003

Selection of trainee represents entirely women =126

probability of selecting entirely women = 4.19%

learn more about probability here

brainly.com/question/31061073

#SPJ4

Answer:

A

Step-by-step explanation:

From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.

A function is an argument, concept, or regulation that demonstrates an association between two variables. Functions may be located throughout mathematics and are necessary for the expansion of significant linkages.

If the number of values of the variable 'y' is more than one for a given value of 'x', then it is not a function.

The table is given below.

   x         y

 - 5        20

   0        20

   5        20

  10        20

From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ9

The complete question is attached below.

Answer: y=$4.50+$3.20x

Step-by-step explanation: You already have to pay $4.50 plus $3.20 every mile driven (x) equals your final cost (y)

Answer:2

Step-by-step explanation:

First combine like terms

2x+3x=5x

5x+3=X+11

Then move the variable to one side by subtracting x from both sides

X-x cancel watcher out

5x-x=4x

Now you have

4x+3=11

Subtract 3 from both sides

4x=8 then divide by 4

X=2

Answer:

75.36 in3

Step-by-step explanation:

Mark me brainliest?

Answer:

5/2

Step-by-step explanation:

(2n+4)+6=-9+4(2n+1)

2n+4+6=-9+8n+4

2n+10=-9+8n+4

2n-8n=-9+4-10

-6n=-5-10

-6n=-15

6n=15

n=15/6

simplify

n=5/2

The link represented by function g multiplies the dependent variable by 9 for every increase of 2 units in the independent variable. The equation that represents g is \(g(x)= 2 \times3^x\),and the function has a value of 2 at 0

Let x be the independent variable, and let g(x) be the dependent variable.

According to the problem, for every 2 units the independent variable increases, the dependent variable is multiplied by 9. This suggests an exponential relationship of the form:

 \(g(x)= a \times b^x\)

where a is the initial value of the dependent variable (when x=0), and b is the growth factor (how much the dependent variable changes for every unit increase in x).

We are given that g(0) = 2, so we can plug in these values and solve for a:

 \(g(0)= a \times b^0\)

a = 2

So now we have:

\(g(x)= 2 \times b^x\)

We still need to find the growth factor b. We are told that the dependent variable is multiplied by 9 for every 2 units the independent variable increases. In other words:

\(g(x+2) = 9 \times g(x)\)

Using our equation for g(x), we can substitute in and simplify:

  \(2 \times b(x+2) = 9 \times 2\times b^x\)

Simplifying, we get:

\(b^2\) = 9

Taking the square root of both sides (we take the positive square root since b must be positive in order for g to be an increasing function), we get:

b = 3

So the final equation for g(x) is:

\(g(x) = 2 \times 3^x\)

For more such questions on variable

https://brainly.com/question/25223322

#SPJ4

It's linear and equation of the function is :

f ( x ) = 2x - 1

Answer:

Can you explain what the press deal and recieve cards means?

Step-by-step explanation: