He was, without a doubt, the most prolific writer of mathematics of all time. Euler is credited as being the first mathematician to define function in the way we currently think of functions. In his book, Introductio in analysin infinitoriumin, he stated, “A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”

Based on what we know a function to be today, what did Euler mean by an analytic expression?

an expression formed with many variables and no numbers
an expression formed with many numbers and no variables
an expression formed from operations such as addition, multiplication, powers, and roots
an expression formed using only multiplication of a variable and a number

The arc length can be found using the formula, ∅ × r, which is: (5π)/3.

Arc length = ∅ × r, where ∅ is the central angle in radians, and r is the radius of the circle.

Given the following:

Length of the arc = 60° × π/180 × 5 = (60 × π × 5)/180

Length of the arc = (300π)/180 = (5π)/3

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Answer:

2nd answer is correct.

Step-by-step explanation:

z² = 0.36

z² = [tex]\frac{36}{100}[/tex]

z² = [tex]\frac{6 * 6}{ 10 *10}[/tex]

z = ± √ ( [tex]\frac{6 * 6}{ 10 *10}[/tex] )

z  = ± [tex]\frac{6}{10}[/tex]

z = ± 0.6

Therefore,

z = + or - 0.6

Step-by-step explanation:

[tex] \sin( \alpha - \beta ) = \sin( \alpha ) \cos( \beta ) - \cos( \alpha ) \sin( \beta ) [/tex]

Using the Pythagorean theorem,

[tex] \cos( \alpha ) = \frac{4}{5} [/tex]

[tex] \sin( \beta ) = \frac{8}{10} [/tex]

[tex] \sin( \alpha - \beta ) = ( \frac{3}{5} )( \frac{3}{5} ) - ( \frac{4}{5} )( \frac{4}{5} )[/tex]

[tex] \frac{9}{25} - \frac{16}{25} = \frac{ - 7}{25} [/tex]

Answer + Step-by-step explanation:

the inequality by finding the boundary line, then shading the appropriate area.

y > − 5/2x − 5

(anything in shaded region)

The answer would be A; Three choices for size, two choices for the crust, and two choices for topping.

The true statement are those statements that satisfy the given condition.

A tree diagram. The sizes are large, medium, and small.

The crusts are thin or thick. The toppings are tomato or meatball.

Sizes;

Small, Medium, and Large,

so they have 3 choices for size.

Crust;

Thin or thick for each size,

so they have 2 choices for the crust.

Topping;

Tomato or meatball for each one,

So, they have 2 choices for toppings.

The answer would be A; Three choices for size, two choices for the crust, and two choices for topping.

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Answer:

A

Step-by-step explanation:

did the test

The number line that represents the solution set for the inequality is the number line on option B.

Option B is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Let's simplify the inequality.

2x - 6 ≥ 6(x - 2) + 8

2x - 6 ≥ 6x - 12 + 8

2x - 6x ≥ 6x - 4

-4x ≥ 6x - 4

-4x - 6x ≥ - 4

-10x ≥ -4

x ≥ 4/10

x ≥ 2/5

x ≥ 0.4

Now,

This number line will start from 0.4 till infinity on the right side of the number line.

Thus,

The number line on option B is the correct answer.

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Answer:

t = -25

Step-by-step explanation:

-4/5=20/t

you are asked to find the value of t.

so let's make t the subject of the equation by Cross multiplication.

-4t= 100

dividing through by -4

t = -100/4

t= -25

Functions are written in terms of variables. The value of the function when x  is -8 is 124

Functions are written in terms of variables. Given the function below;

g(x) = 2x^2 - 4

If the value of x is -8, substiute

g(-8) = 2(-8)^2 -4

g(-8) = 2(64) - 4

g(-8) = 124

Hence the value of the function when x  is -8 is 124

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Answer:

830000.

Step-by-step explanation:

Given number is 825125

The number at the thousands place is 5 which is equal or above 5. So, round up the value.

rounded value of 825125 is 830000.

Therefore, 825125 rounded to the nearest Ten Thousands is 830000.

Answer:

830,000

Step-by-step explanation:

bbbvxxbbbdhdhdvdvshdbsbskzi99999999

Evaluando una ecuación exponencial, veremos que luego de 5 años el capital se convierte en $12,884.08

Esta situación se podra modelar con la ecuación exponencial:

f(n) = $8,000*(1 + 10%/100%)ⁿ

Donde n es el número de años.

Podemos simplificar la ecuación para obtener:

f(n) = $8,000*(1.1)ⁿ

Ahora queremos ver el valor que toma esto cuando n = 5, asi obtenemos:

f(n) = $8,000*(1.1)⁵ = $12,884.08

Así que luego de 5 años, el capital se convierte en $12,884.08.

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The hull speed of the Santa Monica in terms of the length, ln of the Nina Pinta is given as a√b where a = 1.34 and b = ln - 10

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

v = 1.34√l

where l is the hull length in feet and v is the hull speed in knots.

Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta and ln is the length of Nina. Hence:

v = 1.34√(ln - 10) = a√b

The hull speed of the Santa Monica in terms of the length, ln of the Nina Pinta is given as a√b where a = 1.34 and b = ln - 10

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Answer:

What are the restrictions on ln? the answer is 10

Step-by-step explanation:

did it on edge

The sinusoidal function described is f(x) = 4*cos(x/2) + 2.

First, the amplitude is equal to half of the difference between the maximum and the minimum, so the amplitude is:

A = (6 - (-2))/2 = 4

The midline is equal to the minimum plus the amplitude:

M = -2 + 4 = 2.

now, we know that the y-intercept (when the function is evaluated in x = 0) is 6, so from that we conclude that we have a cosine function:

f(x) = 4*cos(kx) + 2

Notice that when evaluated in zero, we get:

f(0) = 4*cos(0) + 2 = 6.

Finally, we need to find the value of k.

Notice that the period of this function is 4π, while the period of the general cosine function is 2π, then we must have:

k*4π = 2π

Solving for k, we get:

h = (2π)/(4π) = 1/2.

Then the sinusoidal function described is f(x) = 4*cos(x/2) + 2.

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The equation that best models the data is (a) y = 186 - 6.2x

The data is not provided; so I would give a general guide on how to model a linear equation.

Assume the points on the line are:

(0,186) and (1,179.8)

Start by calculating the slope of the line using:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

This gives

[tex]m = \frac{179.8 - 186}{1 - 0}[/tex]

Evaluate

m = -6.2

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives

y = -6.2(x - 0) + 186

Evaluate

y = -6.2x + 186

Rewrite as:

y = 186 - 6.2x

Hence, the equation that best models the data is (a) y = 186 - 6.2x

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Answer:

d) $8,100

Step-by-step explanation:

Given information:

If the money triples (multiplies by 3) every 10 years,
then in 40 years time it will triple 4 times, as 40 ÷ 10 = 4

⇒ Account balance after 40 years = $100 × 3 × 3 × 3 × 3

                                                         = $100 × 3⁴

                                                         = $8,100

Proof

In 10 years time the balance of the account will be:

$100 x 3 = $300

In another 10 years time, the balance of the account will be:

$300 x 3 = $900

In another 10 years time, the balance of the account will be:

$900 x 3 = $2700

In another 10 years time, the balance of the account will be:

$2700 x 3 = $8100

(i) In decimals: 0.65

(ii) In percentage: 65%

The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.

Answer:

0.65 or 65%

Step-by-step explanation:

Answer:

y = - 10x + 40

Step-by-step explanation:

Two points

[tex](0,40), (4, 0)[/tex]

Slope

[tex]m=\frac{0-40}{4-0} =-\frac{40}{4} =-10[/tex]

Equation:

[tex]y-40=-10(x-0)[/tex]

[tex]y-40=-10x[/tex]

[tex]y=-10x+40[/tex]

Hope this helps

Answer:

its an isosceles triangle which means that the sides a and c are the same

so C is the correct answer!!

Step-by-step explanation:

The average baggage-related revenue per passenger is $16.30 per passenger.

Expected value formula: x×p(x)

First step

No passenger=0×.54

No passenger=0

Second step

One checked luggage for first bag=.30×$25

One  checked luggage for first bag=$7.50

Third step

Two piece  for the first and second bag=.16×($25+$30)

Two piece  for the first and second bag=.16×$55

Two piece  for the first and second bag=$8.80

Last step

Expected value=$7.50+$8.80

Expected value=$16.30

Therefore the average baggage-related revenue per passenger is $16.30 per passenger.

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The equation that represents the statement is 2^2 + 1 = 21 and it is false

The statement is given as:

Two to the second power + 1 equals 21

Equals mean =

So, we have:

Two to the second power + 1 = 21

Two to the second power means 2^2

So, we have

2^2 + 1 = 21

Evaluate the exponent

4 + 1 = 21

Evaluate the sum

5 = 21

The above equation is false, because 5 does not equal 21

Hence, the equation that represents the statement is 2^2 + 1 = 21 and it is false

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Answer:

Step-by-step explanation:

Two to the second power +1 equals 21 what is the Equation

2 to the 2nd power is conventionally written as 2², with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 2^2.

so

2² + 1 = 21

4 + 1 = 21

5 = 21

the equation is false

Answer: 5/13

Step-by-step explanation:

[tex]f(2)=\frac{3(2)^{2}-7}{4(2)^{2}-3}=\boxed{\frac{5}{13}}[/tex]

Answer:

x+y = 15

2x - y = 6

using elimination method

3x = 21

x = 7

therefore

7+y = 15

y = 15 - 7

y = 8

Answer:

The length of the diagonal of Stacy’s ceiling is 30√2 or 42.43

Step-by-step explanation:

a² + b² = c²

30² + 30² = c²

900 + 900 = c²

√1,800 = √c²

30√2 = c

The graph of vector v with an initial point at R (–19, 6) and terminal point at S (–35, 13). Option C; v = -16i + 7j represents the linear form of RS.

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

c

Given;

The graph of vector v with an initial point at R (–19, 6) and terminal point at S (–35, 13).

v = (-35 +19)i + (13 - 6)j

v = (-16)i + (7)j

v = -16i + 7j

Thus, Option C; v = -16i + 7j represents the linear form of RS.

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Answer:

v = -16i + 7j

Step-by-step explanation:

I took the test :)

The 46th term of the arithmetic progression is 288.

An arithmetic progression is a series of numbers called a sequence and the difference from one interval to another is constant.

From the given information:

156, 153, 150, ...

The 46th term will be:

[tex]\mathbf{a_{46} = a+ (n - 1) d}[/tex]

[tex]\mathbf{a_{46} = 153+ (46 - 1) 3}[/tex]

[tex]\mathbf{a_{46} = 153 + (45) 3}[/tex]

[tex]\mathbf{a_{46} =288}[/tex]

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The number is that was multiplied by 6 is 2.

The equation that can be derived from the question is :

7 + (6a) = 19

Where a is the unknown number that 6 was multiplied with

Given the above equation, in order to determine the value of a, take the following steps:

Combine similar terms: 6a = 19 - 7

Subtract similar terms: 6a = 12

Divide both sides by 6: a = 12 / 6

a = 2

Here is the complete question:

Seven increased by the product of six and the number is 19. What is the number?

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[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]

if (20 + 549+ 48574 - 46567476 x 987665) is the calculations of a number of apples, its total value is mathematically given as

X=−4.59930662*10^13

Generally, the equation for the statement is mathematically given as

20 + 549+ 48574 - 46567476 x 987665 +1

Let's equate it to x, Therefore

X= 20 + 549+ 48574 - 46567476 x 987665 +1

Using BODMAS

X= 20 + 549+ 48574 - 4.59930662*10^13 +1

X=49143-4.59930662×10^13

X=−4.59930662×10^13

In conclusion, the number of apples

X=−4.59930662*10^13

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Based on the statistics, an average American spends $299.7 on lotteries each year

The population is given as:

Population = 325 million

23% are under the age of 18.

This means that this category is not eligible to play lotteries.

The eligible population is:

Eligible = (1 - 23%) * 325 million

Evaluate

Eligible = 250.25 million

The total amount is given as:

Total = $75 billion

So, the amount spent by each is:

Amount = Total/Eligible

This gives

Amount = $75 billion/250.25 million

Evaluate

Amount = $299.7

Hence, an average American spends $299.7 on lotteries each year

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