Circle w has a center point of w and a radius of 11. point q is 11 units away from point w. where is point q

The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

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Answer:

The first graph represents y<2x-3

For this use some values for x e.g

X= 2 2(2)-3=y=1

So when x is 2 y is 1 so search for the graph that crosses the coordinate (2,1)

Which is graph A

The ratio is 2 : 3 and the value that completes the table is 15

From the question, we have the following parameters that can be used in our computation:

Table of values

The entries on the table of values are

Red and Green

Using one of the entries, we have

Red : Green = 2 : 3

To complete the table, we have

10 : Green = 2 : 3

Multiply by 5

10 : Green = 10 : 15

So, we have

Green = 15

Hence, the required entry on the table is 15

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Explanation:

Refer to the diagram below.

In order for triangle TOP to be isosceles, the missing side x must be either 5 or 7. This way we have exactly two sides that are the same length.

--------

If TP = 5, then the value of y could be either 5 or 11 to ensure that triangle TIP has exactly two sides the same length.

If TP = 7, then y = 7 or y = 11 for similar reasons.

--------

Therefore, the possible lengths for segment TO are 5, 7, and 11.

Answer:

7, 11

Step-by-step explanation:

its right- trust me-

We found that the GCD of the following pairs of integers is:6 for 60 and 90.10 for 220 and 1400.21 for 3273∙11 and 23∙5∙7.

Greatest Common Divisor is also known as GCD. It is defined as the highest number that divides two or more integers completely. Let's solve the given pairs of integers:1. To find the GCD of 60 and 90, first, we have to factorize both numbers into their prime factors.60 = 2² × 3 × 590 = 2 × 3² × 5Now we will select the common factors and multiply them. Here, 2 and 3 are common factors.

GCD(60,90) = 2 × 3 = 6Therefore, the GCD of 60 and 90 is 6.2. To find the GCD of 220 and 1400, first, we have to factorize both numbers into their prime factors.220 = 2² × 5 × 111400 = 2³ × 5² × 7Now we will select the common factors and multiply them. Here, 2 and 5 are common factors.

GCD(220,1400) = 2 × 5 = 10Therefore, the GCD of 220 and 1400 is 10.3. To find the GCD of 3273∙11 and 23∙5∙7, first, we have to factorize both numbers into their prime factors.3273∙11 = 3 × 7 × 13 × 1123∙5∙7 = 3 × 5 × 7 × 23Now we will select the common factors and multiply them.

Here, 3 and 7 are common factors. GCD(3273∙11, 23∙5∙7) = 3 × 7 = 21Therefore, the GCD of 3273∙11 and 23∙5∙7 is 21. Therefore, we found that the GCD of the following pairs of integers is:6 for 60 and 90.10 for 220 and 1400.21 for 3273∙11 and 23∙5∙7.

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well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so

\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)

Answer:

y = 28

Step-by-step explanation:

The dashes on line segments AC and BC indicate that the line segments are equal in length.

Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.

Interior angles of a triangle sum to 180°.  

Therefore:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 34° + 34° + 4y° = 180°

⇒ 68° + 4y° = 180°

⇒ 4y° = 112°

⇒ y = 112° ÷ 4°

⇒ y = 28

Answer:

39

Step-by-step explanation:

2×4²+7
2×16+7

32+7=39

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This relationship shows that the diameter of the central circle (2R) is twice the diameter of each outer circle (2r).

In this configuration, four outer circles are placed around a central circle, such that they are all tangent to the central circle and tangent to each other.
To determine the relationship between the diameter of the outer circles and the diameter of the inner circle, follow these steps:
1. Let the radius of the outer circles be r and the radius of the central circle be R.
2. In this arrangement, the distance between the centers of any two adjacent outer circles is equal to the sum of their radii, which is 2r.
3. Now, draw a straight line connecting the centers of these two adjacent outer circles.

This line will pass through the center of the central circle.
4. The length of this line is the sum of the radii of the outer circle, the central circle, and another outer circle, which is

r + R + r = 2r + R.
5. Observe that the line connecting the centers of the two adjacent outer circles, along with the radii connecting the center of the central circle to the points of tangency, forms a right-angled isosceles triangle.
6. Since it is an isosceles triangle, the length of the line connecting the centers of the two adjacent outer circles (2r + R) is also the length of the other side of the triangle, which is equal to the diameter of the outer circle (2r).
7. Therefore, the relationship between the diameter of the outer circles and the diameter of the inner circle is:

2r = 2r + R.
8. Simplify the equation to find the relationship: R = 2r.

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Answer: \(3\sqrt{10}\)

Step-by-step explanation:

By the geometric mean theorem,

\(\frac{y}{3}=\frac{27}{y}\\y^{2}=81\\y=9\)

So, by the Pythagorean theorem,

\(3^{2}+9^{2}=z^{2}\\90=z^{2}\\z=\boxed{3\sqrt{10}}\)

Let n be the number of years since the population started increasing, and let p(n) the the population after n years. We'll have that:

For n = 16, we'll have that:

This way, we can conclude that:

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

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D. The energy used is the same for both segments, the power while running is greater.

Walking and running both require energy, but the distance covered and the time taken are different. In this case, the person covers the same distance of 1 km in both segments.

Therefore, the energy used is the same for both. However, since running involves covering the same distance in less time, the power while running is greater. Power is the rate at which energy is used, and since running takes less time, the power output is higher.

D. The energy used is the same for both segments, the power while running is greater.

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We can prove CBF EDF using isometric transformations by using a translation, rotation, and reflection to turn one triangle into the other.

In order to prove CBF EDF using isometric (rigid) transformations, we need to use a sequence of transformations to turn one triangle into the other.  First, we need to use a translation to move triangle CBF onto EDC. This will ensure that points C and D are in the same position. Second, we need to rotate triangle CBF so that the angle formed by line segments CF and DF is equal to the angle formed by line segments ED and EC. This will ensure that angles B and E are congruent. Finally, we need to use a reflection to flip triangle CBF across the line segment ED, so that the side lengths and angles of triangle CBF match those of triangle EDC. This will ensure that the side lengths of triangle CBF are equal to the side lengths of triangle EDC. By completing these steps, we have successfully proven CBF EDF using isometric transformations.

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Step-by-step explanation:

the slope of a line is the ratio "y coordinate change / x coordinate change" when going from one point to another.

so, when we are going from e.g. (0, 1) to (1, 3)

x changes by +1 (from 0 to 1)

y changes by +2 (from 1 to 3)

and the slope is then +2/+1 = 2

and although I cannot see that result in the answer options, 2 is the right answer. I hope it is just under the given screenshot.

The length of the missing side is 39 units

The parallelogram is a simple 2D-shaped quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides and opposite angles are equal.

Here we have,

The length of the sides of a parallelogram is 2x+10, 5x- 20 and 4x-1

As we know parallel lines of a Parallelogram are equal

Take any two sides as equal and find the missing side

Let the sides with lengths be equal 2x+10, 5x- 20

=> 2x+10 = 5x- 20      

=> 5x - 2x = 20+ 10

=> 3x = 30

=> x = 10  

Therefore, the lengths of the 3 sides are  

2x+10 = 2(10) + 10 = 30

5x- 20 = 5(10) - 20 = 30

4x-1 = 4(10) - 1 = 40 - 1 = 39    

The length of the missing side is 39 units

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Answer:

60 units^2

Step-by-step explanation:

In order to find the area of a triangle, you do baseXheight/2. However, we don't have the height. So, we use the pythagorean theorem to solve for the missing side.

8^2+x^2=17^2

64+x^2=289

x^2=225

x=15

So, now we can solve for the area.

15*8=120

And divide by 2 we get 60

Answer:

the number of boxes that would take fill

the storage completely is 60 boxes.

Step-by-step explanation:

given:

A storage unit has the dimensions 6 ft. x 7 1/2 ft. x 4 1/2 ft.

find:

What number of

1 1/2 ft. x 1 1/2 ft. x 1 1/2 ft. cardboard boxes would it take to completely

fill this storage unit?

Volume of a storage unit = 6 x 7.5 x 4.5

Volume of a storage unit = 202.5  ft³

Volume of a cardboard box = 1.5 x 1.5 x 1.5

Volume of a cardboard box = 3.38 ft³

to get the number of cardboard boxes to fill in the storage unit,

Number of boxes =     202.5 ft³    

                                     3.38 ft³

Number of boxes = 60

therefore,

the number of boxes that would take fill the storage completely is 60 boxes.

Step-by-step explanation:

the photo should explain

Answer:

y=0.16666666666x-2

Step-by-step explanation:

Answer:

.003411

Step-by-step explanation:

Is the OBJ box supposed to mean something?

Answer:

x = 5

Step-by-step explanation:

The interior angles of a triangle always have to add up to 180 degrees.

This means you can form an equation with the three angles you have:

(10x - 4) + (8x + 3) + 91 = 180

Then, solve:

\(10x-4+8x+3+91=180\)

combine like terms

\(18x+90=180\)

subtract 90 from both sides

\(18x = 90\)

divide both sides by 18

\(x = 5\)

Answer:

sxdcfghnujgyhuj

Step-by-step explanation:

Answer: B

Step-by-step explanation: you just plug in the numbers for x and y

We need to convert kilograms to pounds.

1 kilogram is equal to 2.20462 pounds.

Therefore, we can use the rule of three to find the value of 74 kilograms in pounds:

1 kilogram ------------- 2.20462 pounds

74 kilogram ----------- x

Where x = (74 kilogram * 2.20462 pounds)/ 1 kilogram = 163.14188

Rounded to the nearest hundred x = 163.14

Answer:

c

Step-by-step explanation:

To eliminate the x terms and solve for y in the fewest steps, the constants which the equations should be multiplied by before adding the equations together is:

This refers to the mathematical statement which shows the equality of two algebraic expressions.

With this in mind, we can see that if you want an equation eliminated in the fewest steps , then the first equation should be multiplied by 7 and the second equation by -6.

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The length of the shadow of the pole when the tip is moving at x ft/sec is h = √(xL) ft/sec.

Let the length of the pole be L ft. Let h be the length of the pole's shadow when the tip is moving at x ft/sec. From the problem, we know that the rate of change of the length of the shadow of the pole is x ft/sec. Thus, dh/dt = x We can form similar triangles using the pole, its shadow, and the sun as shown below: According to the geometry of the similar triangles above, we have:(L + h) / L = (L + h - x) / h This can be simplified to:1 + h/L = (h - x) / h Multiplying both sides by h, we have:h + h²/L = h - x Adding -h to both sides, we get:h²/L = -x Multiplying both sides by -L, we get:h² = xL.

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Answer:

435 ft

Step-by-step explanation:

area of triangle:

A = (b x h) : 2

A = (15 x 4) : 2

A = 60 : 2

A = 30 ft

area of rectangle:

A = b x h

A = 25 x 15

A = 375 ft

area of the yard = area of the triangle + area of the triangle + area of the rectangle (Here, both triangles have the same area.)

area of the yard: 30 + 30 + 375 = 435 ft.

So, the area of the yard is 435 ft.

I hope this was helpful. :)

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