consider the plane curve defined by the Paramatric equations X= 7 + t sin (t) X=49+ t cos (t) Calculate the Arc length of the curve over the domain ort R 211

Answer: 113

Step by Step explanation:  

12/2=6

inches.π⋅6^2≈113

The area of the circle with diameter 12 units is 113.04 square units.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The given circle has a diameter of 12.

We have to find the area of the circle.

The formula for Area of circle=πr²

Radius of circle = Diameter/2

=12/2

Radius=6

Now let us put r value in Area of circle formula

A=3.14×6²

=3.14×36

=113.04 square units.

Hence, the area of the circle with diameter 12 units is 113.04 square units.

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a, a² + 1 and a + 6 are all in arithmetic progression, in which there is a fixed difference d between consecutive terms. This mean we have

a² + 1 = a + d

a + 6 = a² + 1 + d

Eliminate d and solve for a :

(a² + 1) - (a + 6) = (a + d) - (a² + 1 + d)

a² - a - 5 = -a² + a - 1

2a² - 2a - 4 = 0

a² - a - 2 = 0

(a - 2) (a + 1) = 0

a - 2 = 0   or   a + 1 = 0

a = 2   or   a = -1

The inequality that can be used to represent the number of doll Johnny can buy is x ≤ 10.61

Johnny is budgeting for his trip to the toy store.  He does not want to spend more than $80 on Christmas presents.

He wants to buy a toy car that costs $32.25 and some dolls that cost $4.50 each. The number of dolls he can buy can be represented with the inequality as follows:

let

x = number of dolls

Therefore,

4.50x + 32.25 ≤ 80

subtract 32.25 from both sides of the inequality

4.50x + 32.25 ≤ 80

4.50x + 32.25 - 32.25 ≤ 80 - 32.25

4.50x ≤ 47.75

divide both sides by 4.50

4.50x/ 4.50 ≤ 47.75 / 4.50

x ≤ 10.6111111111

x ≤ 10.61

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Answer:

Distance = Rate x Time

Is that what you are trying to figure out?

Answer:

R=D/T

Step-by-step explanation:

since D equals R times T, R would equal D divided by T

Answer:

25x²-60x+36

Step-by-step explanation:

(5x-6)²

Expand the brackets.

(5x-6)(5x-6)

5x(5x-6)-6(5x-6)

Multiply.

25x²-30x-30x+36

Add or subtract the like terms.

25x²-60x+36

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. A few examples of perfect squares trinomials are,

a² + b² + 2ab = (a + b)²

a² + b² - 2ab = (a - b)²

The expansion of the given binomial expression, (5x - 6)² can be done as,

(5x - 6)²

= (5x)² + 6² - 2(5x)(6)

= 25x² + 36 - 60x

Hence, The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

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Answer:

It’s either SAS or AA.

Answer:

68 percent

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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This is an exercise in applying the power rule, which says

\(f(x) = x^n \implies f'(x) = nx^{n-1}\)

Starting with

\(7g^8 + 2g^7 + 4g^6 + 3g^5 + g^2 + 5g + 276.3\)

we have

• first derivative

\(56g^7 + 14g^6 + 24g^5 + 15g^4 + 2g + 5\)

• second derivative

\(392g^6 + 84g^5 + 120g^4 + 60g^3 + 2\)

• third derivative

\(2352g^5 + 420g^4 + 480g^3 + 180g^2\)

• fourth derivative

\(11760g^4 + 1680g^3 + 1440g^2 + 360g\)

• fifth derivative

\(\boxed{47040g^3 + 5040g^2 + 2880g + 360}\)

Answer:

0.2hrs/dollars

Step-by-step explanation:

Given parameters:

Cost of bike = $31

Time duration  = 6hrs

Unknown:

Hours customers get per dollar = ?

Solution:

The number of hours customer gets per dollar is;

      Number of hrs/dollar = \(\frac{time duration }{cost}\)

    Number of hrs/dollar  = \(\frac{6hrs}{31}\)  

    Number of hrs/dollar = 0.2hrs/dollars

Answer:

The HCF of \(a=2^1 \cdot 3^4 \cdot 5^1\) and \(b = 2^3 \cdot 3^2 \cdot 5^2\) is \(90\).

Step-by-step explanation:

To calculate the HCF of two numbers given their prime factorization, we take the lowest exponent of every prime when comparing the two numbers.

So the HCF of \(a=2^1 \cdot 3^4 \cdot 5^1\) and \(b = 2^3 \cdot 3^2 \cdot 5^2\) is \(2^1 \cdot 3^2 \cdot 5^1 = 90\).

Answer:

40.9ft

Step-by-step explanation:

The perimeter is when you add all the sides together.

8 + 10 + 10 + 4 + 8.9 = 40.9ft

The number in which the value of 3 is 3-1/100 is 345. The correct option is a.

The given number is 43,781.

The value of the 3 in 43,781 is 3,000.

The value of 3-1/100 is 2.99.

We are supposed to find out in which number 2.99 is the value of the 3 in 43,781.

Given options are:

a. 345

b. 237,895

c. 5,732

We'll calculate the values of 3-1/100 in each option.

a. The value of 3-1/100 in 345 is 2.99.

So, the correct option is a.

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This study design can be viewed as an observational comparative study.

In an observational comparative study, the researcher compares groups or conditions that already exist and observes any differences or relationships between them. In this case, the researcher is comparing two sites in a rocky intertidal zone, one with the presence of sea-stars and the other without sea-stars.

The researcher is interested in examining the impact of sea-star predation on the interactions between mussels and barnacles, the dominant and inferior competitors, respectively. By comparing the numbers of the competing species between the two sites, the researcher can analyze the potential influence of sea-star predation on the competitive exclusion of barnacles by mussels.

This study design allows for the examination of natural differences and associations without direct manipulation by the researcher.

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Answer:

A. y+4=f(x)

Step-by-step explanation:

if you were to make this a y= equation then you would have to move the 4 to the other side by subtracting 4 from both sides therefore making the value of f(x) - 4

you should try it out in a graphic calculator like Desmos, it's an online graphic calculator

Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

We know that odd consecutive numbers means the difference between the numbers will be 2

So, let the first odd number be x

Second number will be = x + 2

Third number will be = x + 2 + 2 = x + 4

Now, we are given that, the sum of these odd integers is 153

So, we get the equation as:

x + x + 2 + x + 4 = 153

3 x + 6 = 153

3 x = 153 - 6

3 x = 147

x = 147 / 3

x = 49

Largest integer = x + 4 = 49 + 4 = 53

Therefore, we get that, the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

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Answer:

The function form is:

f(x) = 2x - 8

Answer:

Step-by-step explanation:

nothing makes it true

The area of a circle is 158.3 sq. m.

Consider we need to find the area of the given circle.

The radius of a circle is 7.1 m.

The area of a circle is the place occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the circumference of a circle is called the area of the circle.

The area of the circle is:

\(A = \pi r^{2}\) , where r is the circle's radius.

Putting r = 7.1 , π = 3.14, we get

\(A = 3.14 *(7.1)^{2}\)

A = 158.2874

A ≈ 158.3

So, the area of a circle is 158.3 sq. m.

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

After one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

To calculate the amount of money you will have in the savings account after one year with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

Let's solve it step by step:

Given:

P = $3,000 (principal amount)

r = 6% = 0.06 (annual interest rate as a decimal)

n = 1 (compounded annually)

t = 1 (one year)

Using the formula:

A = 3000 * (1 + 0.06/1)^(1*1)

A = 3000 * (1 + 0.06)^1

A = 3000 * (1.06)^1

A ≈ $3180

So, after one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

It seems there was a discrepancy in the answer provided. Based on the given information, the correct calculation yields $3,180, not $5,372.54.

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Answer:

y = -6

Step-by-step explanation:

y = mx +  b

-6 = -5(0) + b

b = -6

Answer:

The volume of a sphere of radius r is:

S = (4/3)*pi*r^3

The volume of a cylinder of radius r and height h is:

C = pi*r^2*h

For this problem the height of the cylinders will be equal to the diameter of the spheres, which is equal to two times the radius.

First, let's use the radius: r = 2.

The volume of the sphere will be:

S = (4/3)*3.14*(2)^3 = 33.49

The volume of the cylinder, where h = 2*2 = 4, is:

C = 3.14*(2^2)*4 = 50.24

Now, let's choose the radius r = 3.

The volume of the sphere will be:

S = (4/3)*3.14*3^3 = 113.04

The volume of a cylinder with this radius and h = 3*2 = 6, is:

C = 3.14*(3^2)*6 = 169.56

Answer:

Sample space = { 1, 2, 3, 4, 5, 6}

Explanation:

The sample space is the set with all the possible outcomes of the experiment. So if we roll a 6 sided die, we have the possible outcomes:

{ 1, 2, 3, 4, 5, 6}

Because we have 6 possible results. one for every side of the die

Therefore, the sample space is { 1, 2, 3, 4, 5, 6}

Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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Answer:

A scientist adds drops of liquid to a test tube. The test tube has marks every ml.

Each drop contains 0.14 mL. Between which two marks on the test tube will the

liquid be after the sixth drop is added?

a. 1/5 and 2/5, between 0.2 and 0.4 mL's

b.2/5 and 3/5, between 0.4 and 0.6 ml's

c.3/5 and 4/5, between 0.6 and 0.8 mL's

d. 4/5 and 5/5, between 0.8 and 1 ml