COMMON IDENTITIES IN VECTOR ANALYSIS
How do i prove that .......... if F, G, and H are scalar fields?

The required quotient is given as [tex]7x^3-x^2-8x-24[/tex]  and the remainder term is 119

In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}[/tex] .

It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.

Here,

When performing synthetic division of polynomials, the terms in the product that remain as fractions are referred to as the division's remainder, whereas the polynomial is referred to as the division's quotient.
[tex]= \frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}\\=7x^3-x^2-8x-24+\frac{119}{x+1}[/tex]

Thus, the required quotient is given as [tex]7x^3-x^2-8x-24[/tex]  and the remainder term is 119

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The patient should receive 909 mL of the TPN solution per day.

To determine the amount of the TPN solution the patient should receive per day, we need to use the following formula:

amount of TPN solution = (grams of protein needed / percentage of amino acids in TPN solution) × 100

In this case, we are given that the TPN solution contains 8.25% amino acids and that the patient needs 75 grams of protein per day. Substituting these values into the formula, we get:

amount of TPN solution = (75 / 8.25) × 100

amount of TPN solution = 9.09 × 100

amount of TPN solution = 909 mL

Therefore, the patient should receive 909 mL of the TPN solution per day.

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The player that has a ratio that means they have a better batting average is B. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30

From the information Illustrated, the ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most.

For the season so far, Jana has hit the ball 12 times out of 15 attempts. This will be:

= 12/15

= 0.8

Tasha has hit the ball 9 times out of 10 attempts. This will be:

= 9/10

= 0.9

The player that has a ratio that means they have a better batting average is Tasha.

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Using ratios and proportions, he can make 15 batch of muffins from 2 bags of cornmeal

Ratio is used for comparing two quantities of the same kind. The ratio formula for two numbers, a and b is expressed as a : b or a/b. When two or more ratios are equal, they are said to be in proportion. The concept of ratio and proportion is based on fractions.

Proportion refers to the equality of two ratios. Two equivalent ratios are always in proportion. Proportions are denoted by the symbol (: :) and they help us to solve for unknown quantities. In other words, proportion is an equation or statement that is used to depict that the two ratios or fractions are equivalent.

In this problem, we know that he has 2 bags of cornmeal

1 bag of cornmeal = 25 serving

2 bags = x

x = 2 * 25 = 50 servings

When making muffins, he needs 2.5 cups in a batch

But 3/4 cup = 1 serving

x cups = 50 serving

x = 50 * 3/4

x = 37.5 cups

1 batch = 2.5 cups

x batch = 37.5 cups

x = 37.5 / 2.5

x = 15 batch

He can make a 15 batches

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Answer:

  no

Step-by-step explanation:

Tom wants to know if a 70 cm chest will fit in the space left by a 67 in bed in a room 86 in wide.

The space available is 86 in -67 in = 19 in.

An approximate conversion between cm and inches is that 10 cm corresponds to about 4 in. Then 70 cm will correspond to 7×4 = 28 inches, much too wide for a 19-inch space.

The chest will not fit next to the bed.

first we go 45+25=70 so now 80-70=$10.00

Did you mess up one of the answer because I did it two ways and got 10.00?

Answer:

Counter Clockwise Torque = 360 Nm

Clockwise Torque = 240 Nm

Step-by-step explanation:

Answer: 16/45 of the spool

Step-by-step explanation:

2/5 of 8/9

2/5 * 8/9 = 16/45 (multiply numerators, and multiply denominators)

Cannot be further simplified.

Answer:

18/45

Step-by-step explanation:

Multiply both denominators to get a common denominator, in this case, it would be 45.

(8/9)*5=40/45

(2/5)*9=18/45

y=1/3x+4 is perpendicular to y=-3x-4,

y=2/5x-7 is perpendicular to y=-5/2x+7,

y=-5/2x+8 is perpendicular to y=2/5x+6,

y=-2x+6 is perpendicular to y=1/2x+3 and  

y=7/5x-9 is perpendicular to y=-5/7x-11.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We know that the product of slopes of perpendicular lines is -1.

mM=-1

m is slope of one line and M is the slope of perpendicular line.

M=-1/m

y=1/3x+4

The perpendicular line is y=-3x-4

y=2/5x-7

The perpendicular line is y=-5/2x+7

y=-5/2x+8

The perpendicular line is y=2/5x+6

y=-2x+6

The perpendicular line is y=1/2x+3

y=7/5x-9

The perpendicular line is y=-5/7x-11.

Hence, the lines with corresponding perpendicular lines are

y=1/3x+4---> y=-3x-4

y=2/5x-7-----> y=-5/2x+7

y=-5/2x+8----->y=2/5x+6

y=-2x+6---->y=1/2x+3

y=7/5x-9-----> y=-5/7x-11.

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The amount of each payment is $699.

What is payment?

Payment refers to the exchange of something of value as a condition of a contract. While one party pays money and receives something else of value, the other party gets paid in return for delivering a good or service. Physical currency was once the most common form of payment, but nowadays most forms of payment use technology.

Given: Buy 2 personal watercrafts for $3,495 each.

So, the price for 2 watercrafts is, 2 x $3495 = $6990

They make 10 equal payments for the watercrafts.

So each payment is of $6990/10 = $699.

Hence, the amount of each payment is $699.

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Answer:

  A, C

Step-by-step explanation:

You want to know which answer choices are angles that are coterminal with 3π/2.

Angles are coterminal when their terminal rays lie in the same position. In general, any angle will be coterminal with angles that are an integer multiple of 2π added to the original.

That is, an angle is coterminal with all angles that have the same value modulo 2π.

For the given angle and each of the answer choices, the attachment calculates the coefficient of π modulo 2. The ones that match the given angle are ...

 A. 11π/2 mod 2π = 3π/2

  C. -7π/-2 mod 2π = 3π/2

__

Additional comment

Both -π/-2 and π/2 match the angle π/2, which is not the same as 3π/2.

Of course, the minus signs in numerator and denominator cancel, so -7π/-2 is the same as 7π/2.

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Elena can make 20/3 cups of purple paint

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.

Since Elena has 2/3 cup of white paint. then;

1 1/2 cups of red paint (1 1/2=1.5)

1/2 cup of white paint (1/2=0.5)

Then the ratio is 3:1.5:0.5

Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)

Let x the number of cups of purple paint

5/ 0.5 = x / (2/5)

x = 20/3 cups of purple paint

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Answer:  5.36 × [tex]10^{-8}[/tex]

Step-by-step explanation:

5.36 × [tex]10^{-8}[/tex]

The value of the cosine of the angle of (a - b) will be 0.80.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

It is a function that repeats itself in a particular time interval.

Suppose that sin(a) = 4/6 and cos(b) = 1/5.

Then the value of 'a' is given as,

sin(a) = 4/6

sin(a) = 2/3

a = 41.81°

Then the value of 'b' is given as,

cos(b) = 1/5

b = 78.46°

Then the value of the cosine of the angle of (a - b) will be given as,

⇒ cos(41.81° - 78.46°)

⇒ cos(-36.65°)

⇒ cos 36.65°

⇒ 0.80

The value of the cosine of the angle of (a - b) will be 0.80.

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Yes, it wasn't fair because some kids got more pizza.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A coach took his team out for pizza after their last game.

There were 14 players, so they had to sit in smaller groups at different tables.

Six players sat at one table and got 4 small pizzas to share equally.

Each of them got = 4/6 = 0.67

The other 8 players sat at a different table and got 6 small pizzas to share equally.

Each of them got = 6/8 = 0.75

0.75 > 0.67

Therefore, some kids got more pizza.

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Answer:

The value of n is [tex]10^{-3}[/tex]

What is log function?

The logarithm (log) function is a mathematical function used to determine the logarithm of a number. The logarithm of a number is the exponent to which a particular base must be raised in order to produce that number. For example, the logarithm of 8 with base 2 is equal to 3 because 2 to the third power is 8. In mathematics, the logarithm of a number can be expressed as logbX, where b is the base and X is the number.

Step-by-step explanation:

We can write -

0.006 = 6 x 10^-3

10ⁿ =  6 x 10^-3

[tex]10^{n+3}[/tex]  = 6

log([tex]10^{n+3}[/tex]) = log(6)

(n + 3) log 10 = log (6)

n +3 = log(6)/log(10)

n + 3 = 0.78

n = -3 + 0.78

n = -3 (approx.)

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Answer:11 cones

Step-by-step explanation: She can by 11 since $3x 11 =$33

Yes, Ted’s conclusion is reasonable.

Setting the two equations equal and solving for t will solve for the time when the two pools are at the same depth.

Option A is the correct answer.

An equation is a mathematical statement made up of two expressions connected by an equal sign.

We have,

d = 5 - (1/4)t ____(1)

d = 7 - (1/3)t ____(2)

Now,

The time at which the depth d is the same.

Make (1) and (2) equal.

5 - (1/4)t = 7 - (1/3)t

(1/3)t - (1/4)t = 7 - 5

(4t - 3t)/12 = 2

t = 2 x 12

t = 24

Thus,

Yes, Ted’s conclusion is reasonable.

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Answer: 0=8n

Step-by-step explanation: Add 2n+6n = 8n, so 0=8n

Answer:

0

Step-by-step explanation:

0=2n+6n

add 2n + 6n =8n

0=8n

divide both sides by 8 and you get 0
I'm not sure though unless it's 0=8n

Answer:

False

Step-by-step explanation:

Assuming monthly payments

  12 payments per year   X   10 years = 120 payments

Answer: first one

Step-by-step explanation: when u divide the equation to (x+2) and (x-1)

1. The z-scores are given as follows:

Due to the lower z-score, Joe had a better time.

2. The actual score is of 40.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the mean and the standard deviation for his distribution, and also that 15 seconds = 0.25 minutes, the z-score for Joe is obtained as follows:

Z = (19.75 - 22.5)/4

Z = -0.6875.

For Sara, the z-score is calculated as follows:

Z = (28.33 - 31.25)/6

Z = -0.49.

Joe had a better time, as his lower z-score means that a lower percentage of runners spent less time than him, that is, a lower percentage of runners ran faster than him.

For item 2, the actual score is calculated as follows:

-2 = (X - 50)/5

X - 50 = -10

X = 40.

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The number that is thought in the form of expression will be 2x - 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Let the number be 'x'. Then the expression is given as,

⇒ (x - 4) × 2

Simplify the expression, then we have

⇒ (x - 4) × 2

⇒ 2x - 4

The number that is thought in the form of expression will be 2x - 4.

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Answer:

Step-by-step explanation:

[tex]\sqrt{2x+1} = -4 -1[/tex]

[tex]\sqrt{2x-1} = -5[/tex]

the number under a square root is always 0 or a positive number, so it can’t be equal to a negative number

Answer:x = -9, y = -3

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

We can find slope by using change in y over change in x, as shown:

3-(-1) = 4, and 2-4=-2, and 4/-2 = -2, so our answer is -2.

Answer and Step-by-step explanation: I used demos and got (6,0) as my answer.

Answer:

1x2=2 3x3x1=3

Step-by-step explanation: