The first term in a sequence is 5. Each new term in the sequence is obtained by adding 4 to the previous term. Determine an equivalent position-to-term formula. Your answer should be an expression in terms of .

To compare this number we need a calculator to find the square root of 55.

Using a calculator, you'll find that the root of 55 is equal to an irrational number 7.41619848... Remember that irrational number an infinite decimal numbers without decimal patters as rational numbers have.

So, basically, if we compare these

The surface area is \(π(9/4) * (3/2)^(2/3)\)   square units.

To find the surface area of the surface obtained by rotating the curve y = \((8x)^(1/3),\) for 0 ≤ x ≤ 27/8, about the y-axis, we can use the formula for surface area of revolution:

S = 2π∫[a, b] y \(√(1 + (dy/dx)^2) dx\)

First, let's find dy/dx by differentiating y with respect to x:

\(dy/dx = d/dx [(8x)^(1/3)] = (1/3)(8x)^(-2/3) * 8 = (8/3)(8x)^(-2/3)\)

Next, let's find the bounds of integration. We are rotating the curve for 0 ≤ x ≤ 27/8, so our bounds are a = 0 and b = 27/8.

Substituting y and dy/dx into the surface area formula, we have:

S = \(2π∫[0, 27/8] (8x)^(1/3) √[1 + ((8/3)(8x)^(-2/3))^2] dx\)

To simplify the integral, let's make a substitution: u = \((8x)^(1/3)\) Then, du = \((1/3)(8x)^(-2/3) * 8 dx.\)

After substituting and simplifying, the integral becomes:

\(S = 2π∫[u(a), u(b)] u √(1 + (3/8)^2) du\)

 =\(2π(9/8) ∫[u(a), u(b)] u du\)

 = \(2π(9/8) * [u^2/2]\)evaluated from u =\((8a)^(1/3) to u = (8b)^(1/3)\)

Substituting a = 0 and b = 27/8, we have:

\(S = 2π(9/8) * [(8(27/8)^(1/3))^2/2 - (8(0)^(1/3))^2/2]\)

\(= 2π(9/8) * [(8(27/8)^(1/3))^2/2 - 0]\)

 \(= π(9/4) * [(27/8)^(2/3)]\)

Now, let's simplify further:

\(S = π(9/4) * [(27/8)^(2/3)]\)

 =\(π(9/4) * [(3/2)^(2/3)] [since 27/8 = (3/2)^3]\)

 \(= π(9/4) * (3/2)^(2/3)\)

Therefore, the surface area is \(π(9/4)\) * \((3/2)^(2/3)\) square units.

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Answer: .

Step-by-step explanation:

The other person answered it well :D

Answer:

To make x the subject of the equation means to solve the equation for x (get x by itself on one side). We do the order of operations in reverse, because we are using inverse operations. First, add the 2 to both sides (to keep the equation “balanced” we must do the same thing to both sides). y+2=3x. Then divide both sides of the equation by 3 (or multiply both sides by 1/3.

Step-by-step explanation:

Answer:

\(x = \frac{y + 2}{3} \)

Step-by-step explanation:

\(y = 3x - 2 \\ y + 2 = 3x \\ \frac{y + 2}{3} = \frac{3x}{3} \\ \\ x = \frac{y + 2}{3} \)

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sin(45) =opp/18

opp=18sin(45)

h = 9 root 2

The focal length of the glass lens in Figure 1 assuming the refractive index of the glass lens material is 1.5. is approximately 187 cm.

To find the focal length of the glass lens in Figure 1, we need to use the lensmaker's formula, which relates the focal length of a lens to the radii of curvature of its two surfaces.

The lensmaker's formula is given by:

1/f = (n - 1) * ((1/R₁) - (1/R₂))

where: f is the focal length of the lens,

n is the refractive index of the lens material,

R₁ is the radius of curvature of the first surface,

R₂ is the radius of curvature of the second surface.

In this case, let's assume the refractive index of the glass lens material is 1.5.

Given: R₁ = 29 cm

R₂ = 42 cm

n = 1.5

Using the lensmaker's formula:

1/f = (1.5 - 1) * ((1/29) - (1/42))

Simplifying the equation:

1/f = 0.5 * (0.0345 - 0.0238)

1/f = 0.5 * 0.0107

1/f = 0.00535

Taking the reciprocal of both sides:

f = 1 / 0.00535

f ≈ 187 cm

Therefore, the focal length of the glass lens in Figure 1 is approximately 187 cm.

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The complete question is:

Find the focal length of the glass lens in the figure (Figure 1). Take R1 = 29 cm and R2 = 42 cm Express your answer to two significant figures and include the appropriate units.

To find the slopes of the secant lines, we need to calculate the average rate of change of the function over different intervals.

Given: f(x) = 23 cos(x) and x = 2

Let's fill in the table with the intervals and corresponding secant line slopes:

Interval | Slope of Secant Line

(x, π/2) | (f(π/2) - f(x)) / (π/2 - x)

We will calculate the secant line slopes for each interval using the givenfunction.

Interval | Slope of Secant Line

(x, π/2) | (f(π/2) - f(x)) / (π/2 - x)

(1, π/2) | (f(π/2) - f(1)) / (π/2 - 1)

(1.5, π/2) | (f(π/2) - f(1.5)) / (π/2 - 1.5)

(1.8, π/2) | (f(π/2) - f(1.8)) / (π/2 - 1.8)

(1.9, π/2) | (f(π/2) - f(1.9)) / (π/2 - 1.9)

(1.99, π/2) | (f(π/2) - f(1.99)) / (π/2 - 1.99)

(1.999, π/2) | (f(π/2) - f(1.999)) / (π/2 - 1.999)

(2, π/2) | (f(π/2) - f(2)) / (π/2 - 2)

Let's evaluate these values:

Interval | Slope of Secant Line

(1, π/2) | (f(π/2) - f(1)) / (π/2 - 1)

(1.5, π/2) | (f(π/2) - f(1.5)) / (π/2 - 1.5)

(1.8, π/2) | (f(π/2) - f(1.8)) / (π/2 - 1.8)

(1.9, π/2) | (f(π/2) - f(1.9)) / (π/2 - 1.9)

(1.99, π/2) | (f(π/2) - f(1.99)) / (π/2 - 1.99)

(1.999, π/2) | (f(π/2) - f(1.999)) / (π/2 - 1.999)

(2, π/2) | (f(π/2) - f(2)) / (π/2 - 2)

Now, let's substitute the function values and calculate the slopes:

Interval | Slope of Secant Line

(1, π/2) | (23 cos(π/2) - 23 cos(1)) / (π/2 - 1)

(1.5, π/2) | (23 cos(π/2) - 23 cos(1.5)) / (π/2 - 1.5)

(1.8, π/2) | (23 cos(π/2) - 23 cos(1.8)) / (π/2 - 1.8)

(1.9, π/2) | (23 cos(π/2) - 23 cos(1.9)) / (π/2 - 1.9)

(1.99, π/2) | (23 cos(π/2) - 23 cos(1.99)) / (π/2 - 1.99)

(1.999, π/2) | (23 cos(π/2) - 23 cos(1.999)) / (π/2 - 1.999)

(2, π/2) | (23 cos(π/2) - 23 cos(2)) / (π/2 - 2)

Evaluating these expressions, we get:

Interval | Slope of Secant Line

(1, π/2) | 20.2621

(1.5, π/2) | 20.4202

(1.8, π/2) | 20.4471

(1.9, π/2) | 20.4522

(1.99, π/2) | 20.4528

(1.999, π/2) | 20.4529

(2, π/2) | 20.4529

By observing the values in the table, we can make a conjecture about the slope of the tangent line at x = 2. The slopes of the secant lines seem to be approaching the value 20.4529 as the interval gets closer to x = 2. Therefore, we can conjecture that the slope of the tangent line at x = 2 is approximately 20.4529.

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Answer: 220 miles

Step-by-step explanation: If she travels 55 miles per hour, for four hours, then you need to do 55 times 4. The answer is 220.

Main answer:Long multiplication is a method of multiplying two difficult-to-multiply numbers.

supporting answer:

what is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

body of the answer:

let us understand long multiplication by taking an example

     6.Add the two partial products

final answer: by following above steps we can perform long multiplication

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Long multiplication is a method of multiplying two difficult-to-multiply numbers.

What is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

Let us understand long multiplication by taking an example

1. Write the two numbers one beneath the other in the order of their digits. On top, write the larger number, and on the left, a multiplication sign.

2. Multiply the top number's one digit by the bottom number's one digit.

3. Put a 0 below the one's digit,

4. Multiply the top number's ones digit by the bottom number's tens digit.

5. Multiply the top number's tens digit by the bottom number's tens digit.

6. Add the two partial products

By following the above steps we can perform long multiplication

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Answer:

-27 °C

Step-by-step explanation:

-15 -12 = -27

-12 * 4= 48 and -12+4= -8

Answer:

13300.1333333333 is the answer

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Answer:

8/3 aka D

Step-by-step explanation:

Answer:

D is the answer

Step-by-step explanation:

3/10*8/3=4/5

Answer:

36

Step-by-step explanation:

you have to times the base by height. so basically, the formual is A(area)=bh (base x height). in this case it is 9x4.

Answer:

The answer is 36.

Step-by-step explanation:

Imagine chopping the parallelogram into half.

You will have a height of 4 cm and a length of 9.

Now multiply.

9x4=36

Here is the two-way frequency table

            Girls         Boys          Total

Walk      22            16                 38

Ride       29            9                  38

Total      51           25                  76

A two-way frequency table is a table that is used to observe the frequency of a dataset.

Total number of girls = total number of people surveyed - total number of boys

76 - 25 = 51

Total number of boys that walk = total number of boys - number of boys that ride the bus

25 - 9 = 16

Total number of people who ride the bus = total number of girls who ride the bus + total number of boys who ride the bus

29 + 9 = 38

Total number of people who walk = total number of girls who walk + total number of boys who walk

22 + 16 = 38

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Answer:

Wdym?

Step-by-step explanation:

Im confused

The t value needed to develop the 95% confidence interval for the population mean sat score is 1.998.

We are given the sample of 64 sat scores, which is n=64.

Average score is given as 1200.

Sample Standard deviation of sat scores is 200.

We have to find the t value to develop 95% confidence interval.

We will use t test, as population standard deviation is not known.

To find t value, first we will calculate the degrees of freedom,

Degrees of freedom, df=n-1

df=64-1

df=63

From the t table for  df=63 and 95% confidence Level, we have the t value as 1.998.

Therefore, the t value needed to develop the 95% confidence interval for the population mean sat score is 1.998.

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Answer:

(x-6)^2+(y-4)^2=10

Step-by-step explanation:

use the equation of a circle ( x- x coordinate of center)^2+(y-y coordinate of the center)^2=radius squared.

to solve for the radius, make a right triangle from the center to the point on the circle. 1^2+3^2=r^2. So r^2 is 10

Answer:

Step-by-step explanation:

By process of elimination we see that only D or E could be correct. Now to find the angle o, we must subtract

360- 150 - 150 = 60

Now we divide that between angle o and m and... we get 30!

The answer is... angle j is 150 and angle o is 30

The expression that might be utilised to determine Samantha's monthly salary, m, is 462.30m.

This expression represents the product of the amount Samantha earns per month ($462.30) and the number of months she works (m). When you multiply these two values, you get the total amount she earns working any number of months. For example, if she works for 3 months, the expression would be:

462.30 x 3 = 1386.90

So, Samantha would earn $1386.90 for working 3 months. Similarly, if she works for 6 months, the expression would be:

462.30 x 6 = 2773.80

So, Samantha would earn $2773.80 for working 6 months.

In general, the expression 462.30m represents a linear relationship between the amount Samantha earns and the number of months she works. As the number of months increases, the amount she earns also increases proportionally. This is because her earnings are directly proportional to the amount of time she works.

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the main answer is that the mean value of the activity time is 21.67. This is calculated using the formula (optimistic + 4 * most likely + pessimistic) / 6.

To find the mean value of the activity time, we can use the three estimates provided: optimistic, most likely, and pessimistic time.

1. The optimistic time is the shortest possible time for completing the activity, which is 11 units.
2. The most likely time is the time that is most likely to be taken to complete the activity, which is 21 units.
3. The pessimistic time is the longest possible time for completing the activity, which is 35 units.

To calculate the mean value, we can use the following formula:
Mean value = (optimistic + 4 * most likely + pessimistic) / 6

Substituting the given values, we get:
Mean value = (11 + 4 * 21 + 35) / 6

Calculating the numerator first:
11 + 4 * 21 + 35 = 11 + 84 + 35 = 130

Now, we can calculate the mean value:
Mean value = 130 / 6

Dividing 130 by 6, we get:
Mean value = 21.67 (rounded to two decimal places)

Therefore, the mean value of the activity time is 21.67.

the main answer is that the mean value of the activity time is 21.67. This is calculated using the formula (optimistic + 4 * most likely + pessimistic) / 6.

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The required perpendicular segment to DE is EF.

In simple geometry, two geometric objects are perpendicular if the intersection at the place of intersection known as a foot results in right angles. The perpendicular symbol can be used to graphically depict the condition of perpendicularity.

In the given diagram we can see that segment DE and EF.

So, we can say that,

Segment DE is perpendicular to segment EF.

Thus, required perpendicular segment to DE is EF.

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Complete question:

Answer:

you should say that Richard thought Charles was going to make 1111.  

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

hiii

Answer: Greater than 10.

Step-by-step explanation:

I'm going to explain this in standard slope intercept form (y=mx+b) because it is easiest for this situation. I will also include converting it to point slope form. I will also show how to do straight into point slope form if you find that more helpful.

First thing is to identify difference in x and y in both points. From point 1 to point to, the x changes -4 and the y changes +4. We can rapresent this in rise over run fraction

\( \frac{4}{ - 4} = - 1\)

So the slope is -1 because the slope is the simplified rise over run fraction.

Our next step is to find the y-intercept. This is easy because the first point is the y-intercept, so -3 is our y-intercept.

Now we know the equation.

\(y = - x - 3\)

All we have to do now is convert it into point-slope form. So here is point slope form: y + y1 = m(x + x1). Y1 is the y-intercept and m is the slope.

\(y - 3 = - 1(x + x1)\)

So x1 is the x intercept, so to find this you find the x value when y is 0. You can do this by using the standard form I've done because it is easiest.

\(0 = - x - 3 \\ x = - 3\)

So when y is 0, then x is -3. Here is the complete point slope form of the line.

\(y - 3 = - 1(x - 3)\)

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

To put the line directly into point slope for you need to find the slope, y-intercept, and x-intercept and place the values in accordingly. If you aren't given the y-intercept and x-intercept straight away it can be difficult for some putting it directly in point slope form. That is why I recommend putting it into standard form then point-slope form.

Answer:

y=-1x-3

Step-by-step explanation:

First, you have to find the slope using the formula I attached. Using this formula, you will subtract the second y from the first y, which is 1-(-3) for this problem. That equals 4, so that will be the numerator of the slope. Next, you have to subtract the second x from the first x, which is -4-0 for this problem. That equals -4, so that will be the denominator for this slope. the fraction now is \(\frac{4}{-4}\), which is -1. The slope is -1. The current equation looks like this: y=-1x+b. Now we can solve for b, or the y-intercept. To do this, you have to use the x and y of one of the coordinates, it doesn't matter which one, the answer will be the same. Use the first one, for example. The x is 0 and the y is -3, so the our equation to find b is -3=-1(0)+b, which is -3=0+b, which is -3=b, or b=-3. So now we know what b is. Now we have to two components we need to write the equation, the slope (-1) and the y-intercept (-3). Now we can write the equation. y=-1x+(-3), or y=-1x-3.