If
xn = (n−1)cos(n2 +n+1) 2n−1
EXERCISES
then xn has a convergence subsequence.

Answer:

sqrt(601)/2 ft

Step-by-step explanation:

The legs of the right triangle are 12 and 2.5. by the Pythagorean Theorem, the length of the ladder is sqrt(12^2 + 2.5^2) = sqrt(150.25). Simplified is sqrt(601)/2 ft.

The length of ladder used is 12.25 ft.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

example:

The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.

Solution:

Given : Hypotenuse = 16 units

Let us consider the given side of a triangle as the perpendicular height = 8 units

On substituting the given dimensions to the Pythagoras theorem formula

Hypotenuse^2 = Base^2 + Height^2

16^2 = B^2 + 8^2

B^2 = 256 - 64

B = √192 = 13.856 units

Therefore, the measure of the third side of a triangle is 13.856 units.

given:

base=  2.5 ft,  

perpendicular= 12 ft

Using Pythagoras theorem,

H² =  B² + P²

H² = 2.5² + 12²

H² = 6.25+ 144

H= 12.25 ft

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Answer:

Hope you like it. I have just wrote answers

a) The resultant force on the particle is equal to - 225 · x, where x is measured in meters.

b) The particle moves with simple harmonic motion.

c) The motion has a period of approximately 1.257 seconds.

d) The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.

e) The equation for the position of the particle is x(t) = 0.5 · cos 25t, where t is in seconds.

In this case we have a system with a particle under periodic motion due to two reactive forces from two springs. a) The system is represented by the following formula based on Newton's laws:

∑F = - k₁ · x - k₂ · x = m · a      (1)

Where:

If we know that k₁ = k₂ = 112.5 N/m, then the resultant force on the particle is equal to - 225 · x, where x is measured in meters.

b) The particle is under simple harmonic motion has a differential equation of the form:

x'' + ω² · x = 0       (2)

Where:

By some algebraic handling on (1), we find the following differential equation:

x'' + [(k₁ + k₂) / m] · x = 0     (3)

Thus, the particle moves with simple harmonic motion.

c) The period of the motion (T), in seconds, is determined by T = 2π / ω. Then, the period is described by the following expression:

T = 2π · √[m / (k₁ + k₂)]

T = 2π · √(9 kg / 225 N /m)

T ≈ 1.257 s

The motion has a period of approximately 1.257 seconds.

d) The speed of the particle (v), in metres per second, can be found by the principle of energy conservation:

(1 / 2) · k · A² = (1 / 2) · k · x² + (1 / 2) · m · v²      (4)

v = √[k · (A² - x²) / m]

Where:

If we know that k = 225 N / m, A = 0.5 m, x = 0.05 m and m = 9 kg, then the speed of the particle is:

v = √[(225 N / m) · [(0.5 m)² - (0.05 m)²] / (9 kg)]

v ≈ ± 2.488 m / s

The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.

e) The function position for a particle under simple harmonic motion:

x(t) = A · cos ω · t      (5)

If we know that A = 0.5 m and ω = 25 rad / s, then the equation for the position of the particle is:

x(t) = 0.5 · cos 25t

The equation for the position of the particle is x(t) = 0.5 · cos 25t.

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Using translation concepts, the equation for function g(x) given in the graph is:

[tex]g(x) = 2^{x + 2}[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent function for this problem is given as follows:

[tex]f(x) = 2^x[/tex]

From the graph, function g(x) was shifted 2 units left, hence x -> x + 2 and the definition is:

[tex]g(x) = 2^{x + 2}[/tex]

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The minimum production rate of bushels per acre of corn needed this year is 97 for two year's production to reach the goal of 49,100.

To calculate the minimum production rate for this year, we must subtract the production rate of the previous year, with what is expected to be obtained this year.

Then we must divide the minimum that must be obtained by the total area, by the 300 acres that we have, to know how much corresponds to each acre.

According to the above, each acre must produce 97 bushels of corn to reach the goal of 49,100 for both years.

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The mean length of the 6 people's index finger is 11.55

The given parameters are:

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{3 * 9.9 + 3 * 13.2}{3 + 3}[/tex]

Evaluate

[tex]\bar x = \frac{69.3}{6}[/tex]

Divide

[tex]\bar x = 11.55[/tex]

Hence. the mean length of the 6 people's index finger is 11.55

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Using the interpretation of the confidence interval, the correct option is:

We are 95% confident that those who studied had a higher passing rate than those who did not study.

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

The confidence interval of the difference is:

(0.005, 0.125).

Since the entire interval is positive, the correct option is:

We are 95% confident that those who studied had a higher passing rate than those who did not study.

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The given function has symmetry about the y - axis.

Symmetry of the Function

If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.

The given function is,

f(x) = 2x² - 1

It is an even function since the function remains same for both x and -x.

Putting f(x) = 0, we get,

2x² - 1 = 0

2x² = 1

x² = 1/2

x = ±1/2

⇒ Axis of symmetry is, x=0

Hence, the function f(x) is symmetric about y-axis.

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Answer:

At maximum, she can buy 5 tomatoes.

Step-by-step explanation:

If you solve the inequality, as so:

1.2x+1.8 <=7.8

1.2x <= 6

x <= 5

Answer:

f(n)={n/2     = if n is even=   n={2/2

       {3n+1                                 {3(2)+1   =7

Step-by-step explanation:

if n is even u can put any even no in that place and u can get odd no or even no.(i think)

Answer:

$.56

Step-by-step explanation:

To find the cost of one pen, take the total cost and divide by the number of pens

$1.68/ 3

$.56 per pen

The resulting coordinates for each row are (-2, 2), (0, 4),()2, 6), (6, 10) and (8,12) respectively

Given the linear function expressed as;

y = x + 4

where

x are the input values and y are the output values

If x = -2

y = -2+4

y = 2

The coordinate (x, y) will be (-2, 2)

If x = 0

y = 0+4

y = 4

The coordinate (x, y) will be (0,4)

If x = 2

y = 2+4

y = 6

The coordinate (x, y) will be (2, 6)

If x = 6

y = 6+4

y = 10

The coordinate (x, y) will be (6,10)

If x = 8

y = 8+4

y = 12

The coordinate (x, y) will be (8, 12)

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The total surface area of the tower composed of a prism with a square base and a pyramid is 3600 + 400√2 m²

Total surface area of the tower = area of the base + 4(area of the rectangular surface) + 4(area of the triangular surface)

Therefore,

area of the base = 20² = 400 m²

4(area of the rectangular surface)  = 4(40 × 20) = 3200 m²

4(area of the triangular surface) = 4(1 / 2 × 10√2 × 20) = 4(100√2) = 400√2 m²

Therefore,

total surface area = 400 + 3200 + 400√2

total surface area = 3600 + 400√2 m²

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Answer:

a)400V2 plus 3,600 m2

Step-by-step explanation:

Answer:

1.The center of the circle lies on the x-axis

2.The radius of the circle is 3 units.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answer:

x = -34

Step-by-step explanation:

-3x + 2x -34 = 0

sum the x

-3x + 2x = -x

replace -x in the equation

-x -34 = 0

move -34 to other side

-x = 34

divide the two sides by -1 to get x value

x = -34

now replace x value in the equation:

-3(-34) + 2(-34) -34 =

102 -68 -34 =

102 -102 = 0

Answer:

30 km

Step-by-step explanation:

Distance = rate x time

Distance = 20 x 1.5

Distance = 30

[tex]20*1.5=30[/tex] [tex]km[/tex]

Correct answer:-

Avg. speed = [tex]20km/h[/tex]

Time = [tex]1.5 hour[/tex]

Distance traveled in 1.5 hours is Distance = Speed x Time

So,

[tex]D = 20 * 1.5 = 30.[/tex]

reference link-

a cyclist travels at a speed of 20 km per hour how far will he ...https://brainly.in › Math ›

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Answer:

180°

cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°

Answer: [tex]\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

Step-by-step explanation:

[tex]a \cdot b=(3)(0)+(-4)(5)+(-1)(2)=-22\\\\|a| |b|=\sqrt{3^2 +4^2 +1^2} \sqrt{5^2 +2^2}=\sqrt{754}\\\\\therefore \cos \theta=\frac{-22}[\sqrt{754}}\\\\\theta=\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

Answer: Option 1

Step-by-step explanation:

[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]

Solve Absolute Value.

| x + 4 | = 2

We know either x + 4 = 2 or x + 4 = −2

x + 4 = 2 (Possibility 1)

x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)

x = -2

x + 4 = −2 (Possibility 2)

x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)

x = -6

Answer: x = - 2 or x = -6

Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.

[tex]x + y = 55 \\ x - y = 15 \\ \\ 2x = 70 \: \: \: \: \: \: x = 35 \\ y = 55 - x = 55 - 35 = 20[/tex]

Answer: B

Step-by-step explanation:

The line y=2 is solid and shaded above, so it represents [tex]y \geq 2[/tex].

This allows us to eliminate all the options except for B.

Answer: A

Step-by-step explanation:

The polynomial has roots at [tex]x=-4, -2, 4[/tex].

So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].

This eliminates everything except for A.

Answer: [tex]f^{-1}(x)=\frac{x-3}{3}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=3y+3\\\\x-3=3y\\\\y=\frac{x-3}{3}\\\\\therefore f^{-1}(x)=\frac{x-3}{3}[/tex]

Answer:

Step-by-step explanation:

This is classic right triangle trig, cos specifically. Our reference angle is the one marked 26°, the hypotenuse is given as 12, and the side adjacent to the reference angle is our unknown. This is the cosine ratio. Setting up to solve for x:

[tex]cos26=\frac{x}{12}[/tex] and

12cos(26) = x  Plug this into your calculator in degree mode to get that

x = 10.8

The point which would lie on the graph of f(x) = log2x is; (1, 0.301).

Since it follows from the task content that the given point (–1, 0.5) lies on the graph of f –1(x) = 2x.

The subsequent graph of f(x) = log2x would result from taking logarithms in which case, we have the graph passing through points determined as follows;

f(x) = log2^x

f(x) = x log2

Hence, when x = 1;

f(1) = 1log 2

Hence, we have point; (1, 0.301).

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Reason:

Set A = {0,1,2,3,4,5,6,7,8,9}

Set B = {0,1,2,3,4,5,6,7}

The probability of getting a "2" from set A is 1/10 since there is one copy of "2" that we want out of ten values total.

The probability of getting a "2" from set B is 1/8 for similar reasoning. This time there are eight numbers in this set.

Multiply those fractions mentioned (1/10)*(1/8) = 1/80

This fraction converts to the exact decimal value of 0.0125, meaning there's exactly a 1.25% chance of getting "2" twice in a row.

Answer is (n + 3) + (n - 7)

Simplified to 2n - 4

Using “n” for number

This snow flake-like figure can be generated by rotating an end 60° five times around the center of the hexagon. There are two forms: (i) clockwise, (ii) counterclockwise.

Geometrically speaking, snow flakes represent regular hexagons. Regular hexagons can divided into six concentric regular triangles, whose central angles have a measure of 60°. This fractal figure can be generated by rotating 60° five times around the center.

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Answer:

80°

Step-by-step explanation:

Congruent means the same size, so we know that the angle of the shapes made by the lines HK and GJ are the same, meaning that the angle of GOJ is simply 80°.