Position vector = 3 ti + tj + 1/4t^2k
Time = 2
Find the velocity vector, speed, and acceleration vector of the object.

After the duration of 2 hours the distance between the first pair and the second pair is 3.07 km, under the condition that the second pair decide to head 60° west of north travelling at the same pace.

In order to evaluate the distance between two points with given coordinates, we can apply the distance formula. The distance formula is

d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]

Here,

(x₁, y₁) and (x₂, y₂) = coordinates of the two points.

For the given case, we can consider that the first pair of team members start at the origin (0, 0) and cover the distance towards  north for 2 hours at a pace of 4 km/h.

Hence, their final position is (0, 8).

The second pair of team members take  the origin (0, 0) and travel 60° west of north for 2 hours at a pace of 4 km/h.

Now to evaluate their final position, we have  to find their coordinates. Let us consider their final position (x, y).

We can apply trigonometry to find x and y.

The angle between their direction of travel and the y-axis is 60°.

sin(60°) = y / d

cos(60°) = x / d

Here,

d = distance travelled by the second pair of team members.

It is given that they travelled for 2 hours at a pace of 4 km/h.

d = 2 hours × 4 km/h

= 8 km

Staging this value into the above equations

y = d × sin(60°) = 8 km × sin(60°)

≈ 6.93 km

x = d × cos(60°) = 8 km × cos(60°)

≈ 4 km

Hence, the final position regarding the second pair of team members is approximately (4 km, 6.93 km).

Now we can apply the distance formula to evaluate the distance between the two pairs of team members

d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]

d = √ [ (4 − 0)² + (6.93 − 8)² ]

d ≈ 3.07 km

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Part a: f(x) = (x-3)^2 + 5

Part b: f(x) = (x+10)^2 + 5

Part a: To shift the function f(x) = x^2 + 5 right 3 units, we need to subtract 3 from the x-coordinate of the vertex. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex. Thus, the function in vertex form that shifts f(x) right 3 units is:

f(x) = (x-3)^2 + 5

Part b: To shift the function f(x) = x^2 + 5 left 10 units, we need to add 10 to the x-coordinate of the vertex. Using the same vertex form as before, the function in vertex form that shifts f(x) left 10 units is:

f(x) = (x+10)^2 + 5

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the rock will be going 89.9 m/s just before it hits the bottom of the chaste on a certain plaats moon.

To answer your question, we need to use the formula for the acceleration due to gravity, which is:

a = g

where a is the acceleration, and g is the gravitational constant. In this case, we know that the acceleration due to gravity on the moon is 2.9 m/sec^2, so we can substitute that into the formula:

a = 2.9 m/sec^2

Now we need to use the formula for calculating the speed of an object that is falling under the influence of gravity, which is:

v = gt

where v is the speed, g is the gravitational constant, and t is the time. We know that the rock takes 31 seconds to hit the bottom of the chivaste, so we can substitute that into the formula:

t = 31 s

Now we can calculate the speed of the rock just before it hits the bottom:

v = gt
v = 2.9 m/sec^2 x 31 s
v = 89.9 m/s

So the rock will be going 89.9 m/s just before it hits the bottom of the chivaste on the certain plaats moon.

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Of course! Please let me know what you need help with and I'll do my best to assist you within the given time frame.

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The total cost of the trip in U.S. dollars as per given rates and conversion is equal to approximately USD 3,232.58.

Total cost of the trip in U.S. dollars,

Convert the Australian dollars to U.S. dollars.

Using the exchange rate of 0.7752 USD per 1 AUD.

The cost of the hotel is,

7 nights × A$110/night = A$770

To convert this to U.S. dollars, multiply by the exchange rate,

A$770 × 0.7752 USD/AUD

= USD 596.904

Expected cost of meals, tours, souvenirs, etc. is,

A$3,400

Convert this to U.S. dollars, we again multiply by the exchange rate,

A$3,400 × 0.7752 USD/AUD

= USD 2,635.68

Total cost of the trip in U.S. dollars is the sum of these two amounts is,

USD 596.904 + USD 2,635.68 = USD 3,232.584

Rounding to two decimal places = approximately USD 3,232.58.

Therefore, the cost of the trip in the U.S. dollars is equal to approximately USD 3,232.58.

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The above question is incomplete, the complete question is:

You are planning a trip to Australia. your hotel will cost you a$110 per night for seven nights. you expect to spend another a$3,400 for meals, tours, souvenirs, and so forth. How much will this trip cost her in U.S. dollars if the USD equivalent is .7752?

Therefore, the measure of line segment XC is 3.75 cm.

In geometry, two lines or planes are said to be perpendicular if they intersect each other at a right angle (90 degrees). The term "perpendicular" is also commonly used to describe the relationship between a line and a surface, where the line is at a right angle to the surface at the point of intersection. In general, the concept of perpendicularity is fundamental to many mathematical and scientific fields, such as trigonometry, physics, and engineering. It is also a commonly used term in everyday language to describe objects or structures that intersect at right angles, such as the corners of a square or the legs of a chair.

Here,

In the given diagram, let O be the center of the circle and let XC = a.

Since AB is perpendicular to XY at C, we have AC = BC = 8 m (using Pythagoras theorem). Also, since AB is a radius of the circle, we have AB = r, where r is the radius of the circle.

By the power of a point theorem, we have:

AC × XC = BC × XY

Substituting the given values, we get:

8 m × a = 8 m × 30 cm

Simplifying and converting units, we get:

a = 3.75 cm

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A bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.

The kinetic energy (E) of a moving object varies directly with the square of its velocity (v). To write the equation relating E to v, we can use the formula: E = k * v^2, where k is a constant of proportionality. Given a bowling ball traveling at 15 meters per second with 1000 joules of energy, we can find the value of k:

1000 = k * (15^2)
1000 = k * 225
k ≈ 4.44

So, the equation relating the kinetic energy and velocity is: E ≈ 4.44 * v^2.

Now, we want to find the energy of the bowling ball when it's moving at 11 meters per second. Using the derived equation:

E ≈ 4.44 * (11^2)
E ≈ 4.44 * 121
E ≈ 537.64

Therefore, a bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.

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Complete question:

The kinetic energy of a moving object varies directly with the square of its velocity. A bowling ball traveling at 15 meters per second has about 1000 joules of energy.

Write the equation that relates the kinetic energy, E, to its velocity, v.

Round your answer to the nearest hundredth.

About how much energy will a bowling ball have if it is moving at 11 meters per second?

Use your answer from part one. Round your answer to the nearest hundredth

The relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

You can compare various data sets using bar graphs.

In a line graph, the data is represented by tiny dots, and the line that connects them indicates what happens to the data.

So, we have the coordinates:

(-1, 3); (-2, 4); (1, 2); (2, 4)

Now, plot it on the graph as follows:

(Refer to the graph attached below.)

(-1, 3) and (-2, 4) are in the 2nd quadrant, and (1, 2) and (2, 4) are in the 1st quadrant.

Therefore, the relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).

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Correct question:

Express the relation (-1, 3); (-2, 4); (1, 2); (2, 4) on the graph.

The area of the parallelogram is 8 units², which is option (b).

To find the area of a parallelogram, we need to use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we can use the distance formula to find the base and height.

Base = distance between points P and Q
= √[(5-3)² + (3-3)²]
= √4
= 2 units

Height = distance between point P and the line containing points R and S. We can find the equation of this line by first finding its slope:

slope = (y2 - y1)/(x2 - x1)
= (7 - 7)/(9 - 7)
= 0

Since the slope is 0, the line is horizontal and has an equation of y = 7. Therefore, the height is the distance between point P and this line, which is:

Height = distance from point P to line y = 7
= |3 - 7|
= 4 units

Now we can plug in the values of b and h into the formula A = bh:

A = 2 x 4
= 8 units²

Therefore, the area of the parallelogram is 8 units², which is option (b).

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Answer:

Step-by-step explanation:

The length of the sides AB, BC and AC are √13, √13 and √26, hence the triangle is a isosceles triangle.

a. Points (-2, 3), (1, 1), (-1, 2) in the triangle are vertex. The distance formula for any two points is,

AB = √[(d-b)²+(c-a)²]

= √[(1 - (-2))² + (1 - 3)²]

= √[3² + (-2)²]

= √13

BC = √[(d-b)²+(c-a)²]

= √[(-1-1)²+(-2-1)²]

= √[(-2)² + (-3)²]

= √13

AC = √[(d-b)²+(c-a)²]

= √[(-1 - (-2))² + (-2 - 3)²]

= √[1² + (-5)²]

= √26

b. The triangle is an isosceles triangle because AB = BC.

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The volume of the fish tank is approximately 3,693,142,608 cubic inches

To find the volume of the rectangular prism-shaped fish tank, we need to multiply its width, length, and height.

Given the dimensions are 2014 inches wide, 1012 inches long, and 1812 inches tall, the calculation is as follows:

Volume = Width × Length × Height

Volume = 2014 in × 1012 in × 1812 in

Upon calculating the product, we get:

Volume ≈ 3,693,142,608 cubic inches

The volume of the fish tank is approximately 3,693,142,608 cubic inches

N.B: None of the answer choices has the correct answer.

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In triangle ABC with angle B as a right angle, if the measure of angle A is greater than 75 degrees (e.g., 80 degrees), side BC can be approximately 9.848 units, and the hypotenuse AC can be 10 units.

In triangle ABC with angle B as a right angle, to find measures of side BC and hypotenuse AC such that the measure of angle A is greater than 75 degrees, we can use the sine function.

Determine the sine of angle A. Since angle A needs to be greater than 75 degrees, let's choose 80 degrees as an example.
sin(80°) = opposite side (BC) / hypotenuse (AC)

Choose a convenient value for the hypotenuse (AC). Let's choose AC = 10 units.

Solve for the opposite side (BC).
sin(80°) = BC / 10
BC = 10 * sin(80°)
BC ≈ 9.848

If the measure of angle A is more than 75 degrees (for example, 80 degrees), side BC and the hypotenuse AC in the triangle ABC with a right angle can both be 10 units.

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Answer:

when it's maintain supplimentary , it means that the sum of the angles given is 180° , In this case let one of the angle be x and the other is given as 125° .

therefore

125° + x = 180°

x = 180° - 125° = 55°

the compliment of x is the angle which when added to x givens 90° , Let the angle be y.

therefore

x + y = 90°

y = 90° - x = 90° - 55° = 35°

35° is the answer

The answer is B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.

To solve this problem, we are given a function h(x) and asked to find its antiderivative or indefinite integral, which is denoted by H(x) and is defined as the function whose derivative is h(x). We are also given a specific value of H(x) at x = 6 and asked to use it to find the constant of integration, denoted by C.

The given function is h(x) = 22x - 3x² - 6/x, and we want to find H(x), which is the antiderivative of h(x). Using the power rule of integration, we can integrate each term of h(x) separately:

where C is the constant of integration. Note that we need to include an absolute value sign around x in the natural logarithm term because the function is not defined for x = 0.

Next, we are given that H(6) = 31, which means that when x = 6, the value of H(x) is 31. Substituting x = 6 and H(x) = 31 into the above equation, we get:

Simplifying, we get:

Therefore, the antiderivative of h(x) is:

We can simplify the expression by using the identity ln|a/b| = ln|a| - ln|b|:

where C is the constant of integration. Thus, the final answer is:

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Therefore , the solution of the given problem of unitary method  comes out to be space between Mars' and Jupiter's orbits contains rock-like objects.

To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.

Here,

What makes up the majority of the sun?

hydrogen a

The names of the planets nearest to the sun are:

Inner planets, B

A. 2n² is the general formula for the main shell.

Except for one planet, all of them revolve in the same direction. What planet is that?

(1) Venus

Which of the following is the solar system's inner planet?

Mercury, a.

The region of space between Mars' and Jupiter's orbits contains rock-like objects, which are known as:

Asteroid C.

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

a. There would be  at least 20 students must go on the trip for the average cost per student to fall to $175.

b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases.

a. To find out how many students must go on the trip for the average cost per student to fall to $175, we can use the formula:

Total Cost = $500 + $150 x Number of Students

Average Cost per Student = Total Cost / Number of Students

Setting the average cost per student to $175 and solving for the number of students, we get:

$175 = ($500 + $150 x Number of Students) / Number of Students

Multiplying both sides by Number of Students, we get:

$175 x Number of Students = $500 + $150 x Number of Students

Simplifying, we get:

$25 x Number of Students = $500

Number of Students = $500 / $25 = 20

Therefore, at least 20 students must go on the trip for the average cost per student to fall to $175.

b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases. This is because the fixed cost of $500 is spread over more students, making the cost per student lower. So, as more students go on the trip, the average cost per student will continue to decrease.

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I must have left home at 4:54 PM in order to arrive at the park at 4:30 PM after 24 minutes of travel time.

Given the parameters in the question: if i went to park at 4:30 and it took me 24 minutes

Arrival time = 4 : 30PM

Travel time = 24 minutes

I can determine when i left home by simply subtracting the travel time from the time I arrived.

Hence,

Add the travel time to the time you arrived at the park.

4:30 PM (arrival time) + 24 minutes (travel time) = 4:54 PM

Therefore, I must have left home at 4:54 PM.

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Answer: 9/64

Step-by-step explanation:

First, we find the probability of blue in one spin.

One spin: 3/8

Next, we also know that the second spin will also have a probability of 3/8.

To combine these probabilities in both spins, we multiply. This will combine the two independent events. It can be similar to Permutation.

Probability of both spins: 3/8 x 3/8

=9/64

9/64 is the combined probability of both spins.

The reduction form is [tex]I_4 i= cot^3 x =ln |sin x| - 3 cot x + 3x + C[/tex].

To find the reduction formula for ∫cot^n x dx, we can use integration by parts. Let u = cot^(n-1) x and dv = cot x dx, then[tex]du = (n-1)cot^(n-2) x csc^2[/tex]x dx and v = ln |sin x|. By the formula for integration by parts, we have:

∫cot^n x dx = ∫u dv = uv - ∫v du

= [tex]cot^(n-1) x ln |sin x| - (n-1) ∫cot^(n-2) x csc^2 x ln |sin x| dx.[/tex]

This gives us the reduction formula:

[tex]I_n = ∫cot^n x dx = cot^(n-1) x ln |sin x| - (n-1) I_(n-2).[/tex]

Using this formula, we can find I_4 as follows:

[tex]I_4 = ∫cot^4 x dx = cot^3 x ln |sin x| - 3 I_2\\= cot^3 x ln |sin x| - 3 ∫cot^2 x dx\\= cot^3 x ln |sin x| - 3 (cot x - x) + C,\\[/tex]

where C is the constant of integration. Therefore, the solution for I_4 is [tex]cot^3 x ln |sin x| - 3 cot x + 3x + C.[/tex]

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To help you with the journal entries and preparation of the stockholders' equity section for Sikie Shoe Manufacturing Co, let's start with the journal entries for the given transactions:

On January 15, the authorization date:

Journal entry:

Common Stock (200,000 shares * $2 par value) $400,000

Preferred Stock (100,000 shares * $25 par value) $2,500,000

Authorized Capital Stock $2,900,000

On January 20, 50,000 preferred stock were sold for cash at $70 per share:

Journal entry:

Cash $3,500,000

Preferred Stock (50,000 shares * $25 par value) $1,250,000

Common Stock $1,250,000

Paid-in Capital in Excess of Par - Preferred Stock $2,250,000

On February 1, 70,000 common shares were issued with a market price of $8:

Journal entry:

Cash $560,000

Common Stock (70,000 shares * $2 par value) $140,000

Paid-in Capital in Excess of Par - Common Stock $420,000

On February 15, 4,000 common shares were issued to Delkab Consulting Co. in settlement of professional services provided at a fee of $100,000:

Journal entry:

Common Stock (4,000 shares * $2 par value) $8,000

Paid-in Capital in Excess of Par - Common Stock $92,000

Accounts Payable/Professional Services $100,000

On March 20, Mr. Park exchanged a piece of land with a fair value of $150,000 for 10,000 common shares:

Journal entry:

Land (fair value) $150,000

Common Stock (10,000 shares * $2 par value) $20,000

Paid-in Capital in Excess of Par - Common Stock $130,000

On July 1, 45,000 common shares were issued for cash at a market price of $25:

Journal entry:

Cash $1,125,000

Common Stock (45,000 shares * $2 par value) $90,000

Paid-in Capital in Excess of Par - Common Stock $1,035,000

Now let's move on to the questions regarding common shares issued and outstanding:

As of July 31, the number of common shares issued is:

Calculation: 70,000 (February 1) + 4,000 (February 15) + 10,000 (March 20) + 45,000 (July 1) = 129,000 common shares

As of July 31, the number of common shares outstanding is the same as the number of common shares issued since there are no repurchases or retirements mentioned.

Moving on to the treasury stock transactions:

On August 1, purchased 5,000 shares of its own $2 par value common stock at $20 per share:

Journal entry:

Treasury Stock $100,000

Cash $100,000

On September 1, sold 1,500 shares of treasury stock purchased on August 1 for $30 per share:

Journal entry:

Cash $45,000

Treasury Stock $30,000

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The correct option is (a). The man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.

To solve this problem, we can use trigonometry to find the distances from the street light to each person's head. Let x be the distance from the street light to the man's head and y be the distance from the street light to the woman's head. Then, we can set up two equations using the tangent function:

tan(42) = x / d and tan(50) = y / d

where d is the distance between the two people (60 ft). Solving for x and y, we get:

x = d * tan(42) = 78.3 ft

y = d * tan(50) = 89.6 ft

Therefore, the man’s head is 78.3 ft away from the street light and the woman’s head is 89.6 ft away from the street light.

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The population growth rate for 2019 would be 800 people.

The population size at the start of 2020 would be 149, 800 people.

The formula is:

Growth rate = rmax × Population × ( 1 - ( Population / Carrying Capacity ) )

Growth rate = 0.8 × 149,000 × ( 1 - ( 149, 000 / 150, 000) )

Growth rate = 0.8 × 149, 000 × 0. 0067

Growth rate = 800 people

The population size at the start of 2020 would therefore be:

=  Initial Population + Growth Rate

= 149, 000 + 800

= 149, 800 people

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Answer: 5 hours of service

Step-by-step explanation:

25 + x(15) = 20x

⇒ 25 = 20x - 15x

⇒ 25  = 5x

⇒ x = 5

Brianna can buy up to 5 books without spending more than her gift certificate amount.

We can set up the inequality: 9x + 5 <= 50. where x is the number of books Brianna can buy. To solve for x, we can start by subtracting 5 from both sides of the inequality: 9x <= 45

Divide both sides by 9: x <= 5. The inequality 9x + 5 <= 50 represents the fact that the total cost of Brianna's order (the cost of the books plus the shipping charge) should not exceed the amount of her gift certificate, which is $50.

We subtracted 5 from both sides to isolate the term 9x and then divided by 9 to solve for x, which represents the number of books she can buy. The solution, x <= 5, indicates that Brianna can buy up to 5 books without going over her gift certificate amount.

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The solution of the trigonometric equation

cos(2x) = cos(x) + 2

is x = 180°

Here we want to solve the equation:

cos(2x) = cos(x) + 2

First, we know that:

cos(2x) = 2cos(x)²  - 1

Then we can rewrite:

2cos(x)²  - 1 = cos(x) + 2

We can define:

cos(x)= y

2y² - 1 = y + 2

Then we need to solve the quadratic:

2y² - 1 - y - 2  =0

2y² - y - 3 = 0

Using the quadratic formula we will get:

[tex]y = \frac{1 \pm \sqrt{(-1)^2 - 4*2*2*-3} }{2*2} \\\\y = \frac{1 \pm 5}{4}[/tex]

so the solutions are:

y = (1 + 5)/4 = 6/4

y = (1-  5)/4 = -1

And remember that y = cos(x), then y =  6/4 can be discarded.

Then the solution comes from:

cos(x) = -1

then x = pi = 180°

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The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.

In this problem we find must determine the image of two points by translation, whose formula is introduced below:

T(x, y) = P'(x, y) - P(x, y)

Where:

First, determine the translation vector:

T(x, y) = (1, 4) - (0, 0)

T(x, y) = (1, 4)

Second, determine the images of points B and C:

B'(x, y) = (- 3, 2) + (1, 4)

B'(x, y) = (- 2, 6)

C'(x, y) = (- 2, 3) + (1, 4)

C'(x, y) = (- 1, 7)

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Answer:

5x=380

x = 76

Carla made 76 cookies each hours

Step-by-step explanation:

Just make an equation, so the total number of cookies is 380 and she works for 5 hours, so it is just 380/5.

Answer:

Step-by-step explanation:

2 x 36 ÷ 3 + 9 - 4

= 72 ÷ 3 + 9 - 4 (perform multiplication first)

= 24 + 9 - 4 (perform division)

= 29 (perform addition and subtraction)

Therefore, 2x36 ÷ 3 + 9 - 4 = 29.

Answer:

29

Step-by-step explanation:

2×36=72

72/3=24

24+9=33

33-4=29