The force on a particle is described by 3x³ + 1 at a point x along the x-axis. Find the work done in moving the particle from the origin to x = 9.

There are 720 different leadership assignments possible for the student organization.

To determine the number of different leadership assignments possible, we need to calculate the number of permutations for selecting the president, vice-president, and treasurer from a group of 10 students.

For the first position of president, there are 10 students to choose from. Once the president is selected, there are 9 remaining students for the position of vice-president. Finally, for the position of treasurer, there are 8 remaining students.

To find the total number of different leadership assignments, we multiply the number of choices for each position:

Total number of assignments = 10 * 9 * 8 = 720

Therefore, there are 720 different leadership assignments possible for the student organization.

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The distance between the observer and the hot air balloon is increasing at a rate of \(25\times \sqrt{5}\) feet/minute when the balloon is rising at a rate of 50 feet/minute and is 150 feet above the ground.

point A and the hot air balloon is at point B, 200 feet away horizontally and 150 feet above the ground vertically. We want to find how fast the distance AB is increasing at the moment when the balloon is rising at a rate of 50 feet/minute.

Let's call the distance AB "d" and the time "t". We are given that:

\(d = \sqrt{(200^2 + (200 - 150)^2)} = \sqrt{(50000)} = 100\times \sqrt{5}\) feet (using the Pythagorean theorem)

h = 150 feet (the height of the balloon above the ground)

dh/dt = 50 feet/minute (the rate at which the height of the balloon is increasing)

To find dd/dt, we can use the chain rule of differentiation:

dd/dt = (dd/dh) × (dh/dt)

We can find dd/dh by taking the derivative of the distance formula with respect to h:

\(dd/dh = 1/\sqrt{(200^2 + (200 - h)^2)} \times d/dh(\sqrt{(200^2 + (200 - h)^2)} )= (200 - h) \sqrt{(200^2 + (200 - h)^2)}\)

Plugging in h = 150, we get:

\(dd/dh = (200 - 150) / \sqrt{(200^2 + (200 - 150)^2) } = 50 / \sqrt{(50000) } = \sqrt{(5)/2}\) feet/foot

Now we can find dd/dt:

\(dd/dt = (dd/dh) \times (dh/dt) = (\sqrt{(5)/2) } \times 50 = 25\times \sqrt{5}\) feet/minute

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Answer:

-\(-\frac{1}{5} * (5+25x)\\-\frac{1}{5} *5-\frac{1}{5}(25x)\\-1-\frac{1}{5}(25x)\\-1 -1 (5x)\\01-5x\)

Step-by-step explanation:

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

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The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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The distance between the two skew lines that measure along the line Perpendicular to the two lines is \(\frac{13}{\sqrt{70}}\).

To find the distance between the skew lines and measure the distance along the line perpendicular to the two lines, it is necessary to find a vector n perpendicular to both lines. Then project rAC onto that vector.

Here's the step-by-step explanation:

Step 1 Finding vector AB and vector CD

Step 2 Finding the vector n perpendicular to both lines.

The vector that is perpendicular to both lines is the cross-product of the vectors AB and CD.

Step 3 Finding the projection of rAC onto the vector n.

Therefore, the distance between the two skew lines is \(\frac{13}{\sqrt{70}}\).

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METHOD

Next

The two possible side length of Lena square

is

L > 0 or L > W

The equation of the parabola can be determined using the given points (-1, 3), (0, 5.5), and (0, 3).

In general, the equation of a parabola in standard form is y = ax^2 + bx + c, where a, b, and c are constants. To find the specific equation, we substitute the given points into the equation and solve for a, b, and c.

Using the point (-1, 3):

\(3 = a(-1)^2 + b(-1) + c\)

3 = a - b + c

Using the point (0, 5.5):

\(5.5 = a(0)^2 + b(0) + c\)

5.5 = c

Using the point (0, 3):

\(3 = a(0)^2 + b(0) + c\)

3 = c

Therefore, c = 5.5 = 3.

Substituting c = 5.5 into the equation 3 = a - b + c, we get:

3 = a - b + 5.5

-2.5 = a - b

From the equation -2.5 = a - b, we can write b = a + 2.5.

Thus, the equation of the parabola is \(y = ax^2 + (a + 2.5)x + 5.5.\)

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There are 397.7 miles in a 640 km trip

To convert from kilometers to miles, we need to use a conversion factor. The conversion factor is the number of miles equivalent to one kilometer. In this case, the conversion factor is 0.621371 miles per kilometer.

To convert the distance of 640 kilometers to miles, we multiply it by the conversion factor:

640 km * 0.621371 miles/km = 397.68064 miles

This calculation gives us the distance in miles. However, since we are asked to round to one decimal place, we round the result to the nearest tenth:

397.68064 miles ≈ 397.7 miles

Therefore, the distance of a 640 km trip is approximately 397.7 miles.

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Answer:

B) √5, 5/2, 2.71 (repeating), 2 3/4

Step-by-step explanation:

1) For me, I convert the fractions and squared numbers into decimals

2) 2 3/4 = 2.75

3)  √5 (the square root of five) ≈ 2.236

4) 5/2 = 2.5

5) now list the numbers from least to greatest

5) Which number is the least? √5

6) Next? 5/2

7) Next? 2.71 repeating

8) Greatest? 2 3/4

Hope this helps you, good luck with your assignment, and if possible, please mark me brainliest.

Answer:

the number of dreams that include people you know out of 28 is 21

Step-by-step explanation:

Here is the complete question:

It is believed that about \(\frac{3}{4}\) of our dreams  involve people that we know.

So the expression to describe the number of  dreams that feature people you know if you have "d" dreams is:

\(\frac{3}{4} d\)

Now using the above expression we can predict number of dreams that include people you know out of 28. Here 28 represents number of dreams i.e. "d". So expression becomes:

\(\frac{3}{4} (28)\)

Now simplify the above expression:

\(\frac{3}{4} (28)\) = \(\frac{3*28}{4}\) = \(\frac{84}{4}\) = \(21\)

Hence the number of dreams that include people you know out of 28 is 21

The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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Answer: 95.0 square feet

A 1% increase in price will result in a less than 1% decrease in quantity demanded, and vice versa.

To determine the elasticity of demand at a price of p=4, we need to calculate the price elasticity of demand using the formula:

Price elasticity of demand = (% change in quantity demanded / % change in price)

Since we are given a specific price of p=4, we need to calculate the corresponding quantity demanded using the demand function:

q(4) = 600(5 - sqrt(4)) = 600(3) = 1800

Now, let's imagine that the price of drinking-water on campus increases from p=4 to p=5. The new quantity demanded would be:

q(5) = 600(5 - sqrt(5)) = 600(2.76) = 1656

Using these values, we can calculate the price elasticity of demand:

Price elasticity of demand = ((1656-1800)/((1656+1800)/2)) / ((5-4)/((5+4)/2)) = -0.95

Since the price elasticity of demand is less than 1 in absolute value, we can conclude that the demand for drinking-water on campus at PMU is inelastic at a price of p=4. This means that a 1% increase in price will result in a less than 1% decrease in quantity demanded, and vice versa.

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Answer:

\(-\frac{2}{3}/-\frac{7}{4}=\frac{8}{21}\)

Step-by-step explanation:

Given: \(-\frac{2}{3}/-\frac{7}{4}\)

Take the reciprocal of the divisor: \(-\frac{2}{3}/-\frac{4}{7}\)

Multiply the two fractions instead: \(-\frac{2}{3}*-\frac{4}{7}\)

Evaluate: \(\frac{8}{21}\)

Answer:

8 / 21

Step-by-step explanation:

Answer:

its 4.5ft

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

9:2=4.5

ჯსჯსჯაკამა

Answer:

y = -2x + 4

Step-by-step explanation:

y / 4  = x - 2 / -2

-2y = 4(x - 2)

-y = 2(x - 2)

-y = 2x - 4

y = -2x + 4

»(y + 0)/4 = (x - 2)/(0 - 2)

»y/4 = (x - 2)/(-2)

»-2y = 4(x - 2)

»-2y = 4x - 8

»y = -4x - 8/(-2)

»y = -2x + 4✅

Answer:

a

Step-by-step explanation:

Answer:

15 units

Step-by-step explanation:

√[ 17² - ( - 8)² ] = 15 ( on y-axis )

Coordinate of the point = ( 0 , 15 )

1. 1 loaf will costs $100.80 to make.

2. Our start up cost is $100

1 loaf = Initial cost for machine + Cost per bread or

Let x and y represent the items:

y=100+0.8x

Now, to find 1 loaf, just substitute 1 for x

y=100+.8(1)

y=100+0.8

y=100.80

Therefore, 1 loaf will costs $100.80 to make.

Our start up cost is $100 which is the cost of the bread machine you are interested in.

C. linear equation is

start up cost+cost per loaf times loaf or

y=100+0.8x

in y=mx+b form

y=0.8x+100

To find points, just substitute values for x and get values for y (I used multipliles of 10 so that you wouldn't have to plot a decimal coordinate)

If we put it 0 for x, we get 100 for y

If we put in 10 for x, we get 108 for y

If we put in 20 for x, we get 116 for y

Also, we don't use negative because you can't make negative amounts of bread

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Answer:

5j-15-2j+2=   3j-13

Step-by-step explanation:

5 times j

5 times 3

minus the ones with the letters

then the ones without

and u get the answer

hope this helps!

Three types of molds used in metal casting are sand molds, permanent molds, and ceramic molds. For a mold sprue with given dimensions, we can determine the velocity of the molten metal at the base of the sprue, the volume rate of flow, and the time it takes to fill the mold using relevant formulas.

1. In the foundry process, several basic requirements must be met. These include selecting a suitable mold material that can withstand the high temperature of the molten metal and provide proper dimensional accuracy and surface finish. Designing an appropriate gating and riser system is crucial to ensure uniform filling of the mold cavity and allow for the escape of gases. Sufficient venting is necessary to prevent defects caused by trapped gases during solidification. Effective cooling and solidification control are essential to achieve desired casting properties. Finally, implementing quality control measures ensures the final casting meets dimensional requirements and has the desired surface finish.

2. Three common types of molds used in metal casting are as follows:

  - Sand molds: These molds are made by compacting a mixture of sand, clay, and water around a pattern. Sand molds are versatile, cost-effective, and suitable for a wide range of casting shapes and sizes.

  - Permanent molds: Made from materials like metal or graphite, permanent molds are designed for repeated use. They are used for high-volume production of castings and provide consistent dimensions and surface finish.

  - Ceramic molds: Ceramic molds are made from refractory materials such as silica, zircon, or alumina. They can withstand high temperatures and are often used for casting intricate and detailed parts. Ceramic molds are commonly used in investment casting and ceramic shell casting processes.

3. For the given mold sprue, we can determine the following parameters:

  (i) Velocity of the molten metal at the base of the sprue can be calculated using the formula V = √(2gh), where g is the acceleration due to gravity (981 cm/s²) and h is the height of the sprue (22 cm).

  (ii) The volume rate of flow can be determined using the equation Q = V1A1 = V2A2, where Q is the volume rate of flow, V is the velocity of the molten metal, and A is the cross-sectional area at the base of the sprue (2.0 cm²).

  (iii) The time to fill the mold can be calculated using the formula TMF = V / Q, where TMF is the time to fill the mold, V is the volume of the mold cavity (1540 cm³), and Q is the volume rate of flow.

By substituting the given values into the formulas and performing the calculations, we can determine the required values for (i) velocity of the molten metal, (ii) volume rate of flow, and (iii) time to fill the mold.

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Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.

Acceleration is the rate of change of the velocity of an object with respect to time.

Jonathan's initial velocity, u = 12 m/s East

His final velocity, v = 5 m/s East

The time taken, t = 23 seconds

We can use the formula for acceleration:

a = (v - u) / t

Substituting the given values, we get:

a = (5 m/s - 12 m/s) / 23 s

a = -7 m/s / 23 s

a = -0.3043 m/s^2 East

Therefore, Jonathan's acceleration is -0.3043 m/s² East, which means he is slowing down.

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The volume of the solid obtained by rotating the region under the curve y=2-x about the x-axis over the interval [1, 2] is π units cubed.

In this case, the radius of each disc is r=2-x and the thickness of each disc is dx. The volume of each disc is then πr²dx=π(2-x)²dx.

The volume of the solid is then equal to the sum of the volumes of an infinite number of these discs, which is given by the following integral:

V = π∫_1² (2-x)²dx

V = π * 1

V = π

Evaluating this integral, we get V=π units cubed.

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Answer:

D

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

D

why must it be more than 20 characters???

Answer:

The correct answer is choice D.

Step-by-step explanation:

Since the parabola opens sideways, that means the function will feature \(y^2\) and not \(x^2\), so you can immediately rule out options B and C. Because the graph also opens right, that means the coefficient of \(y^2\) is positive. Using all of this information, you'll find that the correct answer is D: \(x = \frac{1}{12} y^2\).

Assonance and consonance are both literary devices that can greatly impact a poem. They contribute to the poem's overall mood, musicality, and structure.

Assonance refers to the repetition of vowel sounds in close proximity within a line or stanza, while consonance involves the repetition of consonant sounds.

These techniques create a sense of harmony and rhythm, making the poem more engaging and enjoyable for the reader.

Assonance can evoke particular emotions and feelings by focusing on specific vowel sounds.

For example, soft vowel sounds, such as "oo" or "ee," can create a calming and soothing atmosphere, while harsher vowels, like "a" or "o," can evoke tension or excitement.

This helps to establish the poem's tone and mood, allowing the reader to connect with the poet's intended message.

Consonance, on the other hand, can create a sense of cohesion within the poem by emphasizing particular consonant sounds.

This can strengthen the connection between lines and stanzas, helping to create a consistent theme throughout the poem.

Consonance can also add a musical quality to the verse, making it more memorable and engaging.

The assonance and consonance play crucial roles in shaping a poem's mood, musicality, and structure.

They help to create a more immersive and memorable reading experience, enabling the reader to connect with the poet's message and emotions on a deeper level.

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Answer:

Inequality: \(3b+1+2\leq 18\)

Toni can carry up to 5 books.

Step-by-step explanation:

"Up to" means you cannot exceed over the amount, meaning everything in her backpack has to be less than or equal to 18 lbs.

Add 1 and 2, to get 3 and subtract from both sides, which gets you \(3b\leq 15\)

Finally, divide both sides by 3, which gets you 5.

Answer:

-----------------

Find each area and then find their difference.

The difference is: