y=x^2-3 graph the function

Note that  in this case,where the radius of convergence is 6, the interval of convergence is (-6, 6).

To find the power series representation, we can use the following steps

Let f(x) = 1 /6+  x.

Let g(x) = f( x  )- f(0).

Expand g(x) in a Taylor series centered at x = 0.

Add f(0) to the Taylor series for g(x).

The interval of convergence can be found using the ratio test. The ratio test says that the series converges if the limit of the absolute value of the ratio of successive terms is less than 1.

In this case, the limit of the absolute value of the ratio of successive terms is

lim_{n → ∞}  |(x+6)/(n + 1)|   = 1

Therefore, the interval of convergence is (-6, 6).

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Answer:

a = a

b = b

c = c

Step-by-step explanation:

Formula: \(a^2+b^2=c^2\)

C is always the largest number

a times a + b times b = c times c

Answer:

37.1°

Step-by-step explanation:

We can use trigonometrical ratios ( SOH CAH TOA) to find x.

Theta = 38° and y = 11cm.

From the diagram, y is the opposite of the triangle ( the side directly opposite the angle)

x is the hypotenuse.

Sine ratio is therefore suitable ( sin β = opposite/hypotenuse)

Thus,

sin 38 = 11/x

x sin38 = 11

x = 11/sin 38.

x ≈ 37.1° (1 d.p)

Hope this helps! :)

The length of an alpha helix with 31 amino acids is approximately 50.6 angstroms.

An alpha helix is a common secondary structure in proteins where the polypeptide chain forms a tightly coiled helical structure. The length of an alpha helix can be calculated using the formula:

Length = (3.6 * number of amino acids)^(1/2)

In this case, the number of amino acids is 31. Plugging this value into the formula, we get:

Length = (3.6 * 31)^(1/2)

      = (111.6)^(1/2)

      ≈ 10.56

However, this value is in units of turns, where one turn is equal to 3.6 amino acids. To convert it to length, we need to multiply by the pitch of the helix. The pitch is the vertical distance between one complete turn of the helix.

The average pitch of an alpha helix is approximately 5.4 angstroms per turn. Multiplying the number of turns by the pitch, we get:

Length = 10.56 * 5.4

      ≈ 57.02

Therefore, the length of an alpha helix with 31 amino acids is approximately 57.02 angstroms.

The length of an alpha helix with 31 amino acids is approximately 57.02 angstroms. This calculation takes into account the formula for calculating the length of an alpha helix and the average pitch of the helix. It is important to note that this is an approximation as the actual length can vary depending on factors such as the specific amino acid sequence and the presence of any structural constraints within the protein.

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Answer:

z = 600

Step-by-step explanation:

Method 1 - ratios

If 150 is 25% then z is 100%:

\(\begin{aligned} 150 : 25 & = z : 100\\\dfrac{150}{25} & = \dfrac{z}{100}\\150 \cdot 100 & = 25z\\15000 & = 25z\\z & = \dfrac{15000}{25}\\z & = 600 \end{aligned}\)

Method 2

Calculate the amount for 1%, then multiply by 100% to find z:

25% = 150

⇒ 1% = 150 ÷ 25 = 6

⇒ z = 100% = 6 x 100 = 600

Answer: Let's say Neima's earnings are x dollars.

Then, Eva's earnings would be x + 40 dollars.

And, Sarah's earnings would be 2x - 20 dollars.

The total combined earnings of the three would be:

x + (x + 40) + (2x - 20) = 500

Simplifying the above equation, we get:

4x + 20 = 500

4x = 480

x = 120

Therefore, Neima's earnings are $120, Eva's earnings are $160 ($120 + $40), and Sarah's earnings are $220 (2 x $120 - $20).

Step-by-step explanation:

The maximum clearance of the underpass ahead is 12 feet and 6 inches.

Based on the information provided, the sign indicates that there is an underpass ahead with a clearance of 12 feet and 6 inches. The sign further mentions that the train in question is also 12 feet and 6 inches long, and it highlights the presence of a narrow median, which is only 6-12 inches wide.

In this context, the sign serves as a warning to drivers approaching the underpass. The clearance measurement of 12 feet and 6 inches informs drivers of the maximum height of vehicles that can safely pass through the underpass without any risk of collision. Since the train length matches the clearance, it implies that vehicles longer than the underpass clearance may not be able to pass through safely if the train is present.

The mention of a narrow median emphasizes the limited space available between the opposing lanes of traffic. With a width of only 6-12 inches, the median may not provide sufficient room for larger vehicles to maneuver, particularly when encountering oncoming traffic or passing through the underpass while the train is present.

Overall, the sign conveys important information regarding the underpass clearance, the train length, and the narrow median, all of which should be considered by drivers to ensure safe passage through the upcoming area.

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The sign indicates the clearance height of an underpass, warns of a narrow median, and mentions the length of a train.

The sign in question is indicating that there is an underpass ahead with a clearance of 12 feet and 6 inches. This means that any vehicle taller than that would not be able to pass through without hitting the underpass ceiling. Additionally, the sign mentions that the train itself is also 12 feet and 6 inches long, so it is important for drivers to be cautious and aware of the height restrictions. The narrow median mentioned refers to the strip of land or barrier between lanes, which in this case is only 6-12 inches wide.

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Let's first find the area of the window:

Area of window = 4 * m * 4 * m = 16 * m^2

Now, let's find the area of the curtain:

Area of curtain = 3 * m * 2.5 * m = 7.5 * m^2

We're given that the area of the window is 2 square meters less than the area of the curtain, so we can set up the following equation:

16 * m^2 = 7.5 * m^2 - 2

Simplifying this equation, we get:

8.5 * m^2 = 2

m^2 = 2 / 8.5

m^2 = 0.2353

Taking the square root of both sides, we get:

m = 0.4851

Therefore, the possible areas of the window are:

16 * m^2 = 16 * (0.4851)^2 = 3.7 square meters (rounded to one decimal place).

The following formulas can be used to translate the Cartesian coordinate (2, 1) into polar coordinates: \(r = √(x^2 + y^2)(y / x)\)= arctan

We may determine the equivalent polar coordinates using the Cartesian coordinates (2, 1) as a starting point:

\(r = √(2^2 + 1^2) = √(4 + 1) = √5\)

We may use the arctan function to determine the value of :

equals arctan(1/2)

Calculating the answer, we discover:

θ ≈ 0.463

As a result, (r, ) (5, 0.463) are about the polar coordinates for the Cartesian point (2, 1).

You mentioned the Cartesian coordinate (-5,?) in relation to the second portion of your query. The y-coordinate appears to be lacking a value, though. Please provide me the full Cartesian coordinate so that I can help you further.

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Answer:

The answer is 1/6

Step-by-step explanation:

3/8 x 4/9 = top times top and bottom times bottom

12/72 = 1/6

Answer:

1/6

Step-by-step explanation:

3x4=12

8x9=72

12 divided by 6 equals 2

72 divided by 6 equals 12

2 divided by 2 equals 1

12 divided by 2 equals 6

Final simplififed answer is 1/6.

Hope this helps you out.

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

$60.20

Step-by-step explanation:

7.5 percent of 56 can be found by multiplying 56 times .075, which equals 4.2. Add that to 56 and you get the total cost, which is $60.20

Answer: The only reason would be the benefits of a mortgage plan. which includes, helping you to maintain your credit score, money available to you when need for curtain life decisions, and there are many tax benefits that come with a mortgage plan! Hope this helps! best of luck!

Answer:

2/8

Step-by-step explanation:

there is the 4 sections of a spinner and 2 sides on the coin when you lay it out that leaves 2 opportunities to spin a 3 or a 4 and flipping heads

The area of the region enclosed by the curve r = 9cos(3θ) is (27/2)π.

What is integration?

In mathematics, and notably in calculus, integration is a fundamental notion. It is a mathematical process that seeks to determine a function's integral. The accumulation or total of all infinitesimally small changes in a quantity is represented by the integral.

To find the area of the region enclosed by the curve r = 9cos(3θ), we can set up a double integral in polar coordinates.

In polar coordinates, the area element is given by dA = r dr dθ. To determine the limits of integration, we need to find the values of θ where the curve intersects itself and encloses a region.

The polar curve r = 9cos(3θ) completes one loop for every 2π/3 radians, so we can integrate over the range 0 ≤ θ ≤ 2π/3. The corresponding limits for r can be determined by setting r = 0 and solving for θ.

At r = 0, we have:

0 = 9cos(3θ)

cos(3θ) = 0

The equation cos(3θ) = 0 has solutions at θ = π/6, π/2, 5π/6. These values divide the interval [0, 2π/3] into three subintervals.

Now we can set up the double integral:

Area = ∬R dA

Using polar coordinates, we have:

dA = r dr dθ

The limits of integration are:

0 ≤ r ≤ 9cos(3θ)

0 ≤ θ ≤ 2π/3

Thus, the double integral becomes:

Area = ∫[0 to 2π/3] ∫[0 to 9cos(3θ)] r dr dθ

Now we can evaluate this double integral:

Area = ∫[0 to 2π/3] (1/2)r² ∣[0 to 9cos(3θ)] dθ

Area = (1/2) ∫[0 to 2π/3] (81cos²(3θ)) dθ

Using the trigonometric identity cos²(3θ) = (1 + cos(6θ))/2, we can simplify further:

Area = (1/2) ∫[0 to 2π/3] (81/2)(1 + cos(6θ)) dθ

Area = (81/4) ∫[0 to 2π/3] (1 + cos(6θ)) dθ

Now we can integrate term by term:

Area = (81/4) [(θ + (1/6)sin(6θ)) ∣[0 to 2π/3]]

Area = (81/4) [(2π/3 + (1/6)sin(4π) - (1/6)sin(0))]

Simplifying further:

Area = (81/4) [(2π/3 + 0 - 0)]

Area = (81/4) (2π/3)

Area = (27/2)π

Therefore, the area of the region enclosed by the curve r = 9cos(3θ) is (27/2)π.

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The probability that the bolt will be inserted in 19 minutes or less is 0.8413.

It should be noted that the probability will be illustrated as:

P(X < x) = P[z < (x - u/sd)]

where

x = number

u = mean

SD = standard deviation

Therefore given the numbers, this will be:

P(x < 19) = P(z < (19 - 15)/4)

= P(z < 4/4) = P(z < 1)

= 0.8413

Therefore, the probability that the bolt will be inserted in 19 minutes or less is 0.8413.

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The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately Normally distributed. For a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less?

If ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3), then the perimeter of triangle ABC will be [√58/(√2 - 1)]

As per the question statement, ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3).

We are required to calculate the perimeter of triangle ABC.

To solve this question, first we need to calculate the distances between AB, BC ad AC, which are the three sides of our concerned triangle ABC, and then add them up to obtain our desired answer. And to calculate the lengths of AB, BC ad AC, we will need to use the distance formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by

√[(x₂ - x₁)² + (y₂ - y₁)²]

Considering points A(4, 1) and B(-3, -2), we can say that [(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-3, -2)]. Therefore, distance AB = √[{(-3) - 4}² + {(-2) - 1}²]

Or, AB = √[{-(3 + 4)}² + {-(2 + 1)}²]

Or, AB = √[(-7)² + (-3)²]

Or, AB = √[(49 + 9)]

Or, AB = √58

Similarly considering points A(4, 1) and C(-1, 3), we can say that

[(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance AB = √[{(-1) - 4}² + (3 - 1)²]

Or, AC = √[{-(1 + 4)}² + (3 - 1)}²]

Or, AC = √[(-5)² + (2)²]

Or, AC = √[(25 + 4)]

Or, AC = √29

Finally considering points B(-3, -2) and C(-1, 3), we can say that

[(x₁, y₁) = (-3, -2)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance BC = √[{(-1) - (-3)}² + {3 - (-2)}²]

Or, BC = √[{-(1) + 3}² + (3 + 2)²]

Or, BC = √[(3 - 1)² + (5)²]

Or, BC = √[(4 + 25)]

Or, BC = √29

Therefore, the perimeter of Triangle ABC  = (AB + BC + AC)

Or, perimeter of Triangle ABC  = (√58 + √29 + √29)

Or, perimeter of Triangle ABC  = [√(29 * 2) + √29 + √29]

Or, perimeter of Triangle ABC  = [(√29*√2) + √29 + √29]

Or, perimeter of Triangle ABC  = √29(√2 + 1 + 1)

Or, perimeter of Triangle ABC  = √29(√2 + 2)

Or, perimeter of Triangle ABC  = (√29*√2)(1 + √2)

Or, perimeter of Triangle ABC  = (√58)(1 + √2)

Or, perimeter of Triangle ABC  = \(\frac{\sqrt{58} (1+\sqrt{2})(1-\sqrt{2}) }{(1-\sqrt{2})} =\frac{\sqrt{58} [(1)^{2}-(\sqrt{2})^2 }{(1-\sqrt{2})}}\)

Or, perimeter of Triangle ABC  = \(\frac{\sqrt{58} [(1-2) }{(1-\sqrt{2})}}=\frac{-\sqrt{58}}{(1-\sqrt{2})}}=\frac{\sqrt{58}}{(\sqrt{2}-1)}}\)

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Answer:

Dimensions = 4cm, 11cm and 21cm

  OR

Dimensions = 4cm, -21cm and -11cm

Step-by-step explanation:

Solving the quadratic equation by using the factorization method;

x² + 12x - 220 = 0

Factors = 22 and -10

x² + 22x - 10x - 220 = 0

x(x + 22) - 10(x + 220) = 0

(x - 10)(x + 22) = 0

Therefore, x = 10 or x = -22

Given the following data;

Length of one side = (x + 1)cm

When x = 10

Length of one side = (10 + 1)cm

Length of one side = 11cm.

When x = -22

Length of one side = (-22 + 1)cm

Length of one side = -21cm

Length of the other side = (x + 11)cm

When x = 10

Length of the other side = (10 + 11)cm

Length of the other side = 21cm

When x = -22

Length of the other side = (-22 + 11)cm

Length of the other side = -11cm

Check;

Volume of a cuboid = L*L*L

Volume of a cuboid = 4 * 11 * 21

Volume of a cuboid = 924cm³

In that equation, you have to add the 5 over to the 3. You do this because you want the variable (x) by itself, meaning on one side. That’s why after you add the 5, you will have to divide by 2 to get x by itself. Hope this helps.

Step-by-step explanation:

17². + 144²=x²

289 + 20736=x²

x²=21025

x =√21025

x=145

145 miles apart

50 miles apart

hope this helps

To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

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First, we need a few things.

The first term = 26

The common difference = 22 - 26 = -4

26 - 4(n - 1) is our equation.

Let's plug 50 into n to find a50

a50 = 26 - 4(50 - 1)

a50 = 26 - 4(49)

a50 = 26 - 196

a50 = -170

The answer to the question is 46

Answer:

8

Step-by-step explanation:

5 2/5 + 2 3/5

Put the whole numbers and the fractions separately to add it easier.

(5 + 2 ) + ( 2/5 + 3/5 )

Add them

7 + 1

Final answer is:

8

I hope it helps! Have a great day!

Lilac~

The sum of the two given mixed numbers is given by:

(5 + 2/5) + (2 + 3/5) = 8

To add two mixed numbers we just combine the whole parts and the rational parts. In this case, we will have:

(5 + 2/5) + (2 + 3/5).

Combining the correspondent parts, we have:

(5 + 2/5) + (2 + 3/5) = (5 + 2) + (2/5 + 3/5) = 7 + 5/5 = 8

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Step-by-step explanation:

The area of a parallelogram is height * base

See diagram

area = 6 sin 60   *  8 =  ~  41.57 units^2

The area of the parallelogram LMNO is equal to 18 square units.

Since Parallelograms are quadrilaterals formed by two pairs of parallel sides, the area of a parallelogram (A), in square units, is the following formula:

A = b · h

Where, b - Length of the base and h - Length of the height.

Now, to determine the area of the parallelogram. First, the lengths for the base and the height of the parallelogram:

b = 6, h = 3

A = 6 · 3

A = 18

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Answer:

Step-by-step explanation:

the word ‘HONOLULU’ has 8 letters

In this word ,the letters O , L and U are repeated each two times.

the number of permutations of the two letters O , o is 2!

the number of permutations of the two letters L , L is 2!

the number of permutations of the two letters U , U is 2!

the number of permutations (distinguishable or not) of the letters in HONOLULU is 8!

then

the number of distinguishable permutations of the letters in HONOLULU :

\(=\frac{8!}{2!\times 2!\times 2!}\)

\(=5040\)