Simplify 35x raise to the power 5 y raise to the power 3 ÷ 7xy raise to the power 2

The unit tangent vector T is (1/√10)i + (3/√10)k

The principal unit normal vector N is j.

vector function r(t) = ti + at²j + 3tk.
Step 1: Find the derivative of r(t) with respect to t, which gives us the tangent vector.
r'(t) = (1)i + (2at)j + (3)k
Step 2: Evaluate r'(t) at t=0.
r'(0) = (1)i + (2a*0)j + (3)k = i + 3k
Step 3: Find the magnitude of r'(0).
|r'(0)| = √(1^2 + 3^2) = √10
Step 4: Normalize r'(0) to find the unit tangent vector T.
T = r'(0) / |r'(0)| = (1/√10)i + (3/√10)k
Step 5: Find the second derivative of r(t) with respect to t.
r''(t) = (0)i + (2a)j + (0)k
Step 6: Evaluate r''(t) at t=0.
r''(0) = (0)i + (2a)j + (0)k = 2aj
Step 7: Find the magnitude of r''(0).
|r''(0)| = √(2a)^2 = 2a
Step 8: Normalize r''(0) to find the principal unit normal vector N.
N = r''(0) / |r''(0)| = (2a/2a)j = j
So, at t=0, the unit tangent vector T is (1/√10)i + (3/√10)k, and the principal unit normal vector N is j.

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Answer:

3 m/s²

Step-by-step explanation:

We can use Newton's Second Law of Motion.  The Second Law of Motion states that acceleration is calculated by dividing the force by the mass.

[tex]A=\frac{F}{m}[/tex] with f being the force and m being the mass

We know that the force is 1,500 N and the mass is 500 kg.

So, let's substitute:

[tex]A=\frac{1500}{500}\\A=3[/tex]

So the acceleration of the cart is 3 m/s²

Hope this helps :)

No, it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet.

The reason it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet is thanks to the quantity. At some point, the perimeter of a rectangle is larger than the area.

However, as the dimensions increase, it becomes impossible for the perimeter to keep up such that the area keeps increasing. For a rectangle with 100 feet as perimeter, it would not be possible to have an area that is 100 square feet.

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a. The elasticity function: E(x) = -8x²/(1536-2x²)

b. The elasticity at x = 20 is -2.78.

c. At x = 20, demand is elastic.

d. The value of x for which total revenue is a maximum is $12.

a. The elasticity function, E(x), can be calculated using the formula:

E(x) = (dQ/Q) / (dx/x)

where Q is the quantity demanded and x is the price. In this case, we have:

Q = D(x) = 1536 - 2x²

Taking the derivative with respect to x, we get:

dQ/dx = -4x

Using this, we can calculate the elasticity function:

E(x) = (dQ/Q) / (dx/x) = (-4x/(1536-2x²)) * (x/Q) = -8x²/(1536-2x²)

b. To find the elasticity at x = 20, we substitute x = 20 into the elasticity function:

E(20) = -8(20)²/(1536-2(20)²) = -3200/1152 = -2.78

So the elasticity at x = 20 is -2.78.

c. To determine whether demand is elastic, unit elastic, or inelastic at x = 20, we can use the following guidelines:

If E(x) > 1, demand is elastic.

If E(x) = 1, demand is unit elastic.

If E(x) < 1, demand is inelastic.

Since E(20) = -2.78, demand is elastic at x = 20.

d. To find the value(s) of x for which total revenue is a maximum, we use the formula for total revenue:

R(x) = xQ(x) = x(1536 - 2x²)

Taking the derivative of R(x) with respect to x, we get:

dR/dx = 1536 - 4x²

Setting this equal to zero to find the critical points, we get:

1536 - 4x² = 0

Solving for x, we get:

x = ±12

To determine whether these are maximum or minimum points, we take the second derivative of R(x):

d²R/dx² = -8x

At x = 12, we have d²R/dx² < 0, so R(x) is maximized at x = 12. Therefore, the value of x for which total revenue is a maximum is $12.

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The greatest possible width the land strip, in miles with the amount of material that has is 1/250 miles wide.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.

A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of each rectangle serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Let's say that her landing strip is x miles long, then its area would be:

1/6.x

We also know how big it is:

so,

1/6.x = 1/1500

x = 6/1500

x = 3/750

x = 1/250 miles

Therefore, possible width of the landing strip is 1/250 miles.

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Complete question:

Michelle is building a rectangular landing strip for airplanes .She has material to cover 1/1,500 of a square mile. The landing strip must be 1/6 of a mile long. With the amount of material that has , what is the greatest possible width the land strip, in miles?

The scatterplot  that would describe is Option A.

A scatter plot is described as  a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.  

The slope - intercept form of the equation of a line is:

y = mx + c

where m =  the slope

c = the y-intercept

Only in the first scatterplot can the line of best fit intersect the y-axis at 2 if a line of best fit is drawn on each of the scatterplots. Only when a line of best fit is established on the first scatterplot is a slope of 1/2 conceivable.

That is, c = 2

m = 1/2

In conclusion, only the first scatterplot would have the line of best fit represented by the equation y = 1/2 x + 2.

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The given statement "In an equation with two x’s, the solution is the number that makes the two sides equalwhen put in for both x’s is false because  in an equation with two x's, the solution is the number that makes the two sides equal when put in for one or both of the x's.

For example, consider the equation 2x + 3 = 5x - 1. To find the solution, we need to find the value of x that makes both sides of the equation equal. We can do this by simplifying the equation:

2x + 3 = 5x - 1

2x - 5x = -1 - 3

-3x = -4

x = 4/3

So the solution to this equation is x = 4/3. Notice that we only substituted the value of x once in the equation, but we still found the solution.

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The model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.

To find the amount of tea in each teacup, you need to divide the total amount of tea (0.8 liters) by the number of teacups (4). The model for this is 0.8 ÷ 4. Follow these steps:

1. Divide 0.8 by 4:
0.8 ÷ 4 = 0.2

2. Interpret the result:
Each teacup will have 0.2 liters of hot tea.

So, the model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.

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The mass of the Antarctic iceberg is approximately 2.56 × 10¹more kilograms than the mass of the Rock of Gibraltar.

To find out, we can subtract the mass of the Rock of Gibraltar from the mass of the Antarctic iceberg:

4.55 × 10¹³ kg - 1.78 × 10¹² kg = 4.37 × 10¹³ kg

Therefore, the mass of the Antarctic iceberg is about 2.56 × 10¹ (or 25.6) times greater than the mass of the Rock of Gibraltar.

This is because the mass of the Antarctic iceberg is much larger than the mass of the Rock of Gibraltar, as it is a massive block of ice floating in the ocean while the Rock of Gibraltar is a solid rock formation on land.

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If a white dwarf in a binary star system gains mass beyond the Chandrasekhar limit (approximately 1.4 solar masses), it undergoes a runaway nuclear reaction, causing it to collapse and explode in a Type Ia supernova.

A white dwarf is a dense stellar remnant that is left behind after a star has exhausted all its nuclear fuel and has shed its outer layers. In a binary star system, the white dwarf may gain mass from its companion star, either through accretion or a merger. If the mass of the white dwarf exceeds the Chandrasekhar limit, the gravitational forces become so strong that the electrons in the atoms are forced to combine with the atomic nuclei, forming neutrons. This process is called electron capture, and it releases a tremendous amount of energy.

The energy released is enough to ignite a runaway nuclear reaction, causing the white dwarf to collapse and explode in a Type Ia supernova. Type Ia supernovae are important cosmic events because they are used as standard candles to measure the distance to distant galaxies. These explosions are also believed to play a significant role in the chemical evolution of the universe, as they produce heavy elements such as iron and nickel that are scattered into the interstellar medium.

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Answer:

u = 2

Step-by-step explanation:

To find the other possible vertices of the square, we need to determine the coordinates of the other three vertices. Since we know that the length of each side is 3 units, we can use this information to determine the distance between the given vertex (5, 4) and the other vertices.

First, we can determine the direction of the square by looking at the given vertex and knowing that the sides of a square are equal in length and perpendicular. Since we know that the side length is 3 units, we can move 3 units to the right to find one possible vertex. This gives us the point (8, 4).

Next, we can move 3 units up to find another possible vertex. This gives us the point (5, 7).

Finally, we can move 3 units to the left to find the last possible vertex. This gives us the point (2, 4).

Therefore, the letter that should be circled by all the ordered pairs that could be another vertex is D, which represents the point (2, 4).

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The solution to the expression -(-4) (-6)-3/5(10+5)/1/3 is 15.

To solve this expression, we need to follow the order of operations, which is also known as PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction):

Start with the parentheses: (-4) (-6)= 24, so we can rewrite the expression as:

24-3/5(15)/(1/3)

Now we need to simplify the expression inside the parentheses by adding 10 and 5, which equals 15. Then we need to simplify the division by multiplying the numerator by the reciprocal of the denominator, which is the same as dividing by 1/3. We can rewrite this expression as:

24-3/5*15*3

Multiply 3/5 and 15 first, then multiply that result by 3: 24-9.

Finally, subtract 9 from 24 to get the final answer: 15.

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Answer:

n = 6.

Step-by-step explanation:

The slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1) and (x2, y2).

So, (-8 - (-7)) / (n - 0) = -1/6

-1/n = -1/6

n = 6.

A cube is a three dimensional figure with six square faces that are all congruent, meaning they are identical in shape and size.

Each face of the cube is perpendicular to the adjacent faces, forming right angles where they meet. The cube is a highly symmetrical shape, with all edges and angles equal in length and measure respectively. Its regularity and symmetry make it a popular shape in mathematics and engineering, often used as a model for buildings, containers, and other structures.

The cube's unique properties also make it an ideal shape for games, puzzles, and art, showcasing its versatility and significance in various fields.

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The angle of elevation of the hill to the nearest degree is 44°.

The angle of elevation is the angle formed between the horizontal and an observer's line of sight to an object that is located above the observer. In this case, Tina is standing at the bottom of the hill and looking up at Matt who is standing on the hill. When Tina's line of sight is perpendicular to her body, she is looking at Matt's shoes.

This means that the line of sight forms a right angle with the ground.

To find the angle of elevation, we can use trigonometry. We know that the opposite side is the height of the hill (from Matt's shoes to the top of the hill), which is not given in the problem. However, we can use the Pythagorean theorem to find it.

Let h be the height of the hill. Then,

h^2 = (14.5)^2 - (5)^2
h^2 = 198.25
h ≈ 14.1 feet

Now, we can use the tangent function to find the angle of elevation.

tan θ = opposite/adjacent = h/14.5
tan θ = 14.1/14.5
θ ≈ 44.2°

Therefore, the angle of elevation of the hill to the nearest degree is 44°. This means that the hill slopes upward at an angle of 44° from the ground, as viewed from Tina's position at the bottom.

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Answer:

The third choice is the correct answer.

The answer is option B: (0.221-0.27).

Using the formula for a confidence interval for a proportion:

p± z*√(p(1-p)/n)

where p is the sample proportion (12/45 = 0.267), z* is the z-score for the desired confidence level (99% corresponds to a z-score of 2.576), and n is the sample size (45).

Substituting the values, we get:

0.267 ± 2.576*√(0.267(1-0.267)/45)

which simplifies to:

0.267 ± 0.195

Therefore, the 99% confidence interval for the true proportion of times the number cube would land with a six facing up is (0.072, 0.462).

So the answer is option B: (0.221-0.27).

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The probability that Morgan will catch the train to Agon is 0.578.

To catch the train to Agon, one of the following conditions must be met:

The train to Bewford is not late and the train to Agon is not late.

The train to Bewford is not late and the train to Agon is late.

The probability of the first condition is:

(0.76) x (0.65) = 0.494

The probability of the second condition is:

(0.24) x (0.35) = 0.084

Therefore, the probability that Morgan will catch the train to Agon is:

0.494 + 0.084 = 0.578 (to three decimal places)

So the probability that Morgan will catch the train to Agon is 0.578.

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The surface area of the triangular prism is 4302 mm²

A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is expressed as;

SA = 2B + ph where B is the base area and h is the height of the prism and p is the perimeter of the base.

Base area = 1/2 bh

= 1/2 × 36 × 24

= 36 × 12

= 432 mm²

Perimeter of the base = 36 + 30+30 = 96 mm²

SA = 2 × 432 + 96 × 36

SA = 846 + 3456

SA = 4302 mm²

Therefore the surface area of the triangular prism is 4302 mm².

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Since X cannot be negative (as it is a side length), we only need to consider the inequalities X > 3 and 13 > X. Therefore, the range of possible lengths for the missing side, X, is between 3 inches and 13 inches (not inclusive).

To find the range of possible lengths for the missing side, X, we need to use the Triangle Inequality Theorem.

This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the two given side lengths are 5 inches and 8 inches.
Let's find the range of possible lengths for the missing side, X, using the theorem:
1. 5 + 8 > X
  13 > X
2. 5 + X > 8
  X > 3
3. 8 + X > 5
  X > -3.

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The height of the cone in terms of y is h = y / 4.

The cylinder and the cone have the same volume. The cylinder has radius x and height y. The cone has radius 2x.

Therefore,

volume of a cylinder = πr²h

where

Volume of a cone = 1 / 3 πr²h

where

Therefore,

πr²h = 1 / 3 πr²h

πx²y = 1 / 3 π (2x)²h

πx²y = 1 / 3 π 4x² h

multiply both sides by 3

πx²y = π 4x² h

divide both sides by  π 4x²

Hence,

h = πx²y  / π 4x²

h = y / 4

Therefore, the height of the cone is h = y / 4.

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The solid being referred to is a cuboid and the plane that intersects it creates a triangular shape, then the intersection of the plane and the solid would be described as Triangle. Option A is the correct answer.

If a cuboid is being sliced by a plane that creates a triangular shape within the solid, then the intersection of the plane and the solid would take the form of a triangle.

However, it's important to note that this answer only applies to the specific scenario in which a cuboid is being sliced and the resulting intersection appears triangular.

In general, the intersection of a plane and a solid could take on a variety of shapes, including rectangles, parallelograms, or trapezoids, depending on the specific solid and plane in question.

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The value of the addition of the functions:

F(x) + g(x) = (8x² + 34x - 56)/(x²-3x-40).

To add the two rational functions F(x) and g(x), we first need to find a common denominator. In this case, the common denominator is (x+5)(x-8), since both denominators can be factored in this way.

F(x) needs to be multiplied by (x-8) on the top and bottom to get a common denominator of (x+5)(x-8), and g(x) needs to be multiplied by (x+5) on the top and bottom to get the same common denominator.

So, we have:

F(x) = (x+7)/(x+5) * (x-8)/(x-8) = (x² - x - 56)/(x² - 3x - 40)

g(x) = 7x/(x²-3x-40) * (x+5)/(x+5) = 7x(x+5)/(x+5)(x-8) = 7x(x+5)/(x²-3x-40)

Now that both functions have the same denominator, we can add them together:

F(x) + g(x) = (x² - x - 56)/(x² - 3x - 40) + 7x(x+5)/(x²-3x-40)

To simplify this expression, we need to combine the two fractions over the common denominator:

F(x) + g(x) = (x² - x - 56 + 7x² + 35x)/(x²-3x-40)

Combining like terms in the numerator:

F(x) + g(x) = (8x² + 34x - 56)/(x²-3x-40)

So, F(x) + g(x) = (8x² + 34x - 56)/(x²-3x-40).

To solve a rational function, we generally follow these steps:

In the case of F(x) and g(x), we already simplified the sum of the functions. We can see that the denominator factors as (x+5)(x-8), which means that the function is undefined at x = -5 and x = 8. These are vertical asymptotes.

To find any horizontal asymptotes, we can use the fact that the degree of the numerator is greater than or equal to the degree of the denominator. This means that there is no horizontal asymptote; instead, the function approaches infinity as x approaches infinity or negative infinity.

Finally, we can graph the function using this information and any other relevant points, such as intercepts.

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Answer:

Set A: 1, 7, 10, 17, 20

Range: 19

Mean: 11

Set B: 10, 12, 16, 17, 18

Range: 8

Mean: 14.6

How to find...

Mean: Divide the sum of all values in a data set by the number of values.

Range: Find the largest observed value of a variable (the maximum) and subtract the smallest observed value (the minimum).

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Here is the expected number of broken machines or tanks and K is the total number of tanks. So (K-L) gives the number of tanks in working condition.

The number of repairmen (R) needed to have an average of at least 180 tanks working is to be determined. Thus as observed from the results obtained for one-way data table, the value of R such that (K-L) is at least 180 is R = 11 repairmen

The Expected number of broken or bad machines (L) is

[tex]L=\sum j\pi_i[/tex]

The Expected number of machines waiting for service (1) is

[tex]L=\sum (j-R)\pi_i[/tex]

An expected number of words is often used as a guideline to ensure that the content is neither too long nor too short. In this case, the expected number is 150 words. A 150-word piece of writing can be considered a short composition. It is long enough to convey a basic idea or message, but not so long that it becomes tedious to read. This length is often used in blog posts, news articles, and social media updates.

When writing a 150-word piece, it is important to make every word count. The writing should be clear and concise, with each sentence contributing to the overall message. It may also be helpful to outline the main points before starting to write to ensure that the piece stays focused.

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8:10

subtract 20min from 30 min

30-20=10

Answer: He should move at 8:10

Explanation:  10 + 20 = 30  /  30 - 20 = 10

Therefore he should leave at 8:10

The equation of the parabola is:

The two points that define the latus rectum are (±9/64, 4).

The equation of the parabola with vertex at (0,0) and axis of symmetry the y-axis can be written in the form x = ay^2, where a is a constant. Since the parabola contains the point (6,4), we can substitute these values to solve for a:

6 = a(4²)

6 = 16a

a = 6/16 = 3/8

So the equation of the parabola is x = (3/8)y².

To find the two points that define the latus rectum, we need to determine the focal length, which is the distance from the vertex to the focus.

Since the axis of symmetry is the y-axis, the focus is located at (0, f), where f is the focal length. We can use the formula f = a/4 to find f:

f = a/4 = (3/8)/4 = 3/32

So the focus is located at (0, 3/32). The two points that define the latus rectum are the intersections of the directrix, which is a horizontal line located at a distance of f below the vertex, with the parabola. The directrix is located at y = -3/32.

To find the intersections, we can substitute y = ±(16/3)x^(1/2) into the equation of the directrix:

y = -3/32

±(16/3)[tex]x^(^1^/^2^)[/tex]= -3/32

x = 9/64

So the two points that define the latus rectum are (±9/64, 4).

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The particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.

To find when the particle is at rest, we need to find the values of t where the velocity of the particle is zero.

The velocity function is obtained by taking the derivative of the position function: v(t) = x'(t) = x²(t) - 5x(t) + 6

Setting v(t) = 0, we get a quadratic equation in x(t): x²(t) - 5x(t) + 6 = 0. Factoring the quadratic, we get: (x(t) - 2)(x(t) - 3) = 0

Therefore, x(t) = 2 or x(t) = 3. We now need to check which values of t correspond to these values of x(t).

At x(t) = 2, we get: v(t) = x²(t) - 5x(t) + 6 = 4 - 10 + 6 = 0. Thus, the particle is at rest at t = 2. At x(t) = 3, we get: v(t) = x²(t) - 5x(t) + 6 = 9 - 15 + 6 = 0

Thus, the particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.

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