please find the angle 1​

The given series, Σ(4n^3 + 5) from n = 1 to infinity, can be analyzed to determine its convergence or divergence.

To determine the convergence or divergence of the series, we need to examine the behavior of its terms as n approaches infinity. In this case, the terms of the series are given by 4n^3 + 5.

As n increases, the dominant term in the series is the term with the highest power of n, which is 4n^3. The constant term 5 becomes negligible in comparison.

Since the term 4n^3 grows without bound as n approaches infinity, the series diverges. This means that the sum of the series does not approach a finite value but instead becomes infinitely large as more terms are added.

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a) The balloon's height can be determined using the laws of sines and cosines. By measuring the angles of elevation at two points, along with the distance between them, the height of the balloon is found.

b) The angle between the two slanted sections of the shed's roof can be calculated using the laws of sines and cosines. The dimensions of the roof sections are given, and by applying the appropriate formulas, the angle θ can be determined.

a) Let's denote the height of the balloon above the ground as "h" and the distance from point A to the balloon as "x". We can set up two right triangles to solve for "h".

In the first triangle, we have the angle of elevation at point A, which is 32 degrees. The side opposite this angle is "h" and the adjacent side is "x". Using the sine function, we have:

sin(32°) = h / x

Rearranging the equation, we get:

h = x * sin(32°)

In the second triangle, Henry walks 120 feet closer to point B, so the distance from point A to the balloon becomes "x - 120". The angle of elevation at this new position is 54 degrees. The side opposite this angle is still "h", and the adjacent side is now "x - 120". Using the sine function again, we have:

sin(54°) = h / (x - 120)

Rearranging the equation, we get:

h = (x - 120) * sin(54°)

Since the height of the balloon "h" is the same in both equations, we can set the two expressions equal to each other:

x * sin(32°) = (x - 120) * sin(54°)

Now we can solve for "x":

x * sin(32°) = x * sin(54°) - 120 * sin(54°)

x * sin(32°) - x * sin(54°) = -120 * sin(54°)

x * (sin(32°) - sin(54°)) = -120 * sin(54°)

x = (-120 * sin(54°)) / (sin(32°) - sin(54°))

Once we find the value of "x", we can substitute it back into either of the equations to find the height "h" of the balloon above the ground.

b) Let's denote the height of the shed's walls as "h". We can set up a right triangle to solve for the angle between the two slanted sections of the roof.

In the triangle, the height of the shed's walls "h" is the opposite side of the angle θ, and the difference in lengths between the two slanted sections (12 ft - 5 ft = 7 ft) is the adjacent side. We can use the tangent function to find the angle:

tan(θ) = h / 7

To find θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(h / 7)

To find the value of θ, we need to know the value of "h." If the height of the shed's walls is not given, we cannot determine the exact value of θ.

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The radius of 8th sphere is 3/2.

The 8th sphere's center and the hexagon's two opposing ends should form an isosceles triangle. Then put up another triangles between the point of tangency of the 7th and 8th spheres, and the point of tangency between the 7th sphere and 2 of the original spheres on different sides of the hexagon. Each triangle's side length should be expressed in terms of r (the sphere's 8 radius) and h. (the height of the first triangle). The values of h and r may then be determined by setting up two equations for the two triangles using the Pythagorean Theorem.

(1+r)² = \(2^{2}\) + \(h^{2}\)

(3√2)² =3² + (h+r)²

r= 3/2

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Answer:

-54

Step-by-step explanation:

\(8(-9) - 6(-3)\\\)

Multiply 8 by -9 and 6 by -3

\(-72 - (-18)\)

Subtract\(Value = -54\)

Hope this helps

plz mark brainliest

Therefore, the acute angle between the lines is approximately 39 degrees (rounded to the nearest degree).

To find the acute angle between the two lines, we can determine the slopes of the lines and then use the formula:

θ = arctan(|(m1 - m2) / (1 + m1 * m2)|)

Given the equations of the lines:

5x - y = 2

2x + y = 7

We can rewrite the equations in slope-intercept form (y = mx + b) to find the slopes (m1 and m2):

5x - y = 2

-y = -5x + 2

y = 5x - 2

From equation 1), the slope is m1 = 5.

2x + y = 7

y = -2x + 7

From equation 2), the slope is m2 = -2.

Substituting the values into the formula, we have:

θ = arctan(|(5 - (-2)) / (1 + (5 * -2))|)

θ = arctan(|(5 + 2) / (1 - 10)|)

θ = arctan(|7 / (-9)|)

Using a calculator, we find that arctan(7 / (-9)) ≈ -38.66 degrees.

Since we are looking for the acute angle between the lines, we take the positive value of the angle, which is approximately 38.66 degrees.

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Answer:

x = 19 1/3

Step-by-step explanation:

6/14 = 7/(x-3)

Using cross products

6 * (x-3) = 7*14

6x -18 = 98

Add 18 to each side

6x-18+18 =98+18

6x = 116

Divide each side by 6

6x/6 = 116/6

x =58/3

x = 19  1/3

Answer= 58/3

Step by Step

Step 1: Cross-multiply.

6*(x−3)=(7)*(14)

6x−18=98

Step 2: Add 18 to both sides.

6x−18+18=98+18

6x=116

Step 3: Divide both sides by 6.

6x /6 = 116 /6

x= 58 /3

The given equations of the lines containing segments XY and WZ show that the segments are parallel to each other.

To determine how segments XY and WZ are related, we need to analyze the given equations of the lines containing the segments.

The equation x - 3y = -12 can be rewritten as x = 3y - 12.

Similarly, the equation x - 3y = -6 can be rewritten as x = 3y - 6.

By comparing the equations, we can observe that both lines have the same slope, which is 3. This indicates that the lines are parallel.

Since segments XY and WZ lie on parallel lines, they are also parallel to each other. In a quadrilateral, parallel segments have certain properties:

Corresponding angles are congruent: The corresponding angles formed by the intersection of parallel lines are equal. In this case, the angles formed by segments XY and WZ are congruent.

Opposite sides are parallel: Since segments XY and WZ are both parallel to the same line, they are also parallel to each other.

Opposite sides are congruent: If the opposite sides of a quadrilateral are parallel, then they are congruent. Therefore, segments XY and WZ have equal lengths.

The given equations of the lines containing segments XY and WZ show that the segments are parallel to each other. As a result, the corresponding angles formed by the segments are congruent, the opposite sides are parallel, and the segments have equal lengths.

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Answer:

Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.

Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.

Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.

Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.

ion:

The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.

The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

An expression of two terms having a degree n can be represented as,

(a - b)ⁿ = \(^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n\).

Given, (y - 3)⁴ = \(^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4\).

(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.

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Answer:

6 + y

Step-by-step explanation:

By BODMAS rule,

1st : Multiply

Then add,

2 + 2 x 2 + y

2 + (2 x 2) + y

= 2 + 4 + y

= 6 + y

a. \(123.1(1.069)^3 \approx 150.4\)

b. \(123.1(1.069)^{20} \approx 467.5\)

The major axis lies along the z-axis, while the minor axis lies along the x-axis.

Given quadric surface is ( 3x)² − y + (2z)² = 0.

The equation of a quadric surface can be given by Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0, where A, B, C, D, E, F, G, H, I, J ∈ ℝ and (x, y, z) ∈ ℝ³.

(a) Type of quadric surface defined by the above equation is an elliptic paraboloid.

(b) The trace obtained by intersecting the surface with the xy-plane can be obtained by replacing z with 0. So, the equation is 9x² - y = 0, which can be written as y = 9x².

The trace is a parabola which opens upwards and intersects the y-axis at the origin.

(c) The trace obtained by intersecting the surface with the plane y = 1 can be obtained by replacing y with 1.

So, the equation is 9x² + 4z² = 1.The trace is an ellipse in the xz-plane, centered at the origin.

The major axis lies along the z-axis, while the minor axis lies along the x-axis.

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Answer:

I think 84 but you may need to check just to be sure :)

a)

Answer:

5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10, 2, 3, 5, 8

Explanation:

Diginacci Sequence

5+8=13, 8+1=9, 1+3+1+2=7, 1+2+7=10, 7+1+0=8, 1+0+8=9, 8+9=17, 9+1+7=17

Answer:

15.7

Step-by-step explanation:

5 * 3.14 = 15.7

Answer:

Below

Step-by-step explanation:

CIRCUMFERENCE of a CIRCLE is given by  :  pi * d

  Circumference = pi * 5 in = 15.7 inches   (Don't forget UNITS !!)

Answer:

r=2

Step-by-step explanation:

To find the slope, we take the difference in the y values over the difference in the x values

m = ( y2-y1)/(x2-x1)

2 = ( 9-3)/ (5-r)

2 = (6)/(5-r)

Multiply each side by (5-r)

2 ( 5-r) = 6

Divide each side by 2

5-r = 6/2

5-r = 3

Subtract 5 from each side

5-r-5 = 3-5

-r = -2

r = 2

Answer:

r = 2

Step-by-step explanation:

To solve this problem, we have to use the following formula for slope:

\(\boxed{m= \frac{y_2 - y_1}{x_2 - x_1}}\),

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of two points.

We are given the coordinates \((r, 3)\) and \((5, 9)\), and told that \(m = 2\). To find the value of r, we have to substitute the given values into the formula and then solve for r :

\(2 = \frac{9 - 3}{5-r}\)

⇒ \(2 = \frac{6}{5-r}\)

⇒ \(2\times (5-r) = \frac{6}{5-r} \times (5 - r)\)         [Multiplying both sides by (5 - r)

⇒ \(2(5-r) = 6\)

⇒ \(\frac{2}{2}(5-r) = \frac{6}{2}\)                                [Dividing both sides by 2]

⇒ \(5- r = 3\)

⇒ \(5 - r - 5 = 3 - 5\)                         [Subtracting 5 from both sides]

⇒ \(-r = -2\)

⇒ \(\frac{-r}{-1}= \frac{-2}{-1}\)                                       [Dividing both sides by -1]

⇒ \(r = \bf 2\)

Answer:

4x-6+5x+1

9x-5

Step-by-step explanation:

Answer:

9x-5

Step-by-step explanation:

like terms are added together, in this case, x

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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The simplified equation with combined like terms is 7x - 6 = 8, and the value of x is 7.

To simplify the equation 7x - 6 - 5x = 8 and combine like terms, we can start by combining the x terms on the left side of the equation:

7x - 5x - 6 = 8

Simplifying further, we have:

2x - 6 = 8

To isolate the term with x, we can add 6 to both sides of the equation:

2x - 6 + 6 = 8 + 6

Simplifying:

2x = 14

Finally, to solve for x, we divide both sides of the equation by 2:

2x/2 = 14/2

Simplifying:

x = 7

Therefore, the simplified equation with combined like terms is:

7x - 6 = 8, and the value of x is 7.

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Answer:

1. 34/9

2. 1/3

Step-by-step explanation:

Rise/run

1. (30-(-4))/(7-(-2))=34/9

2. (15-5)/(12-(-3))=10/15=1/3

Answer:

The answer is DE

Step-by-step explanation:

I learned about it in school.

The radius of a circle with center O is DO. Therefore, option B is the correct answer.

Given that, a circle, with center O, represents a radius of the circle.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

Here, DO and OC is the radius of a circle with center O.

The radius of a circle with center O is DO. Therefore, option B is the correct answer.

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Answer:

If x and y are supplementary then x + y = 180

If angle y = 33 then angle x = = 180 -33

angle x = 147 degrees

Step-by-step explanation:

Answer:

E. b + u = 21

Step-by-step explanation:

b = (bicycles)

u = (unicycles)

The Question gives you the answer.

" the number of bicycles plus the number of unicycles is 21"

*put as an equation*

b + u = 21

<3 Enjoy,

    Dea

The volume of the prism is  determined as 23.4 in³.

The volume of the prism is calculated by applying the following formula as follows;

Mathematically, the formula for volume of a prism is;

V = ¹/₂ x b x h x l

where;

The height of the prism is calculated as;

h = √ (3² - 1.5²)

h = 2.6 in

The volume of the prism is calculated as;

V = ¹/₂ x 3 x 2.6 x 6

V = 23.4 in³

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Answer:

\(y=-3x+6\)

Step-by-step explanation:

First, let’s determine the slope of the original equation.

We have \(x-3y=3\)

Subtract x from both sides and then divide both sides by -3. So:

\(-3y=-x+3\\y=\frac{1}{3}x-1\)

Therefore, the slope of our original line is 1/3.

Remember that perpendicular lines have slopes that are negative reciprocals of each other.

Therefore, the slope of our new perpendicular line is the negative reciprocal of 1/3.

Thus, the slope of our new line will be -3. We flip the fraction and add a negative.

So, the slope of our new line is -3. We also know that it passes through the point (5, -9).

Now, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

So, substitute -3 for m and (5, -9) for (x₁, y₁). This yields:

\(y-(-9)=-3(x-5)\)

We want our line in slope-intercept form. So, distribute the right:

\(y+9=-3x+15\)

Subtract 9 from both sides. Therefore, our equation is:

\(y=-3x+6\)

Answer:

5

Step-by-step explanation:

Answer:

Table A: 5 / 4

Table B: 3 / 4

Step-by-step explanation:

Table A y / x

place 5 as y and 4 as x

5 / 4 this cannot be simplified

Table B y / x

Place 6 as y and 8 as x

6 / 8 simplify by dividing both sides by 2

3 / 4

The points (1,3) and (-1,-3) are on the line given by the given equation.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=6x+7. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=6 and b=7.

The question gives the equation y=3x from the standard form equation, you can identify that: m=3 and b=0.

For solving the question, you should check if the given coordinates comply with the equation y=3x.  See below.

         y=3*1

         y=3

Therefore, the coordinate (1,3) is on the line given by the equation y=3x.

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She can choose 10 different pairs of fruits.

With five different fruits, the first (apple) can be matched with each of the other five. That’s 4 pairs.

The second fruit (orange) can also be matched with each of the other four fruits, except that it has already been matched with an apple, so that would not be a “different” pair. So that’s 3 more pairs.

The third fruit (pear) can make 2 more “different” pairs, the fourth fruit (strawberry) can make 1 more unique pairs.

This implies 4 + 3 + 2 + 1 = 10 pairs

Or we can use combinations for this:

⁵C₂ = 5! / 2! × 3!

= 5 × 4 × 3! / 2 × 3!

= 10 pairs

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