ILL GIVE BRAINLIEST !!!!!!

To determine the minimum speed of a particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k, we need to find the magnitude of the velocity vector, which is the derivative of the position vector with respect to time.

v(t) = r'(t) = 2ti + 6j + (2t - 24)k

The speed of the particle at any given time t is the magnitude of the velocity vector, which is:

|v(t)| = √(4t^2 + 36 + (2t - 24)^2) = √(4t^2 + 4t^2 - 96t + 576) = √(8t^2 - 96t + 576)

To find the minimum speed, we need to find the minimum value of |v(t)|. We can do this by finding the vertex of the parabolic function 8t^2 - 96t + 576, which corresponds to the minimum value of the function.

The vertex of a parabola of the form ax^2 + bx + c is at x = -b/2a. In this case, a = 8, b = -96, and c = 576, so the vertex is at t = -b/2a = 96/16 = 6.

So the minimum speed of the particle is:

|min speed| = |v(6)| = √(8(6)^2 - 96(6) + 576) = √(288) = 12√2

Therefore, the minimum speed of the particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k is approximately 16.97 units/sec (rounded to two decimal places). Option 4, min speed = 17 units/sec, is the closest answer.

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Answer:

i know this is really late but it's B

Step-by-step explanation:

Answer:B

Step-by-step explanation:

trust meh

This is an example of a seasonal component in a time series. A seasonal component refers to regular, predictable patterns that are associated with the time of year, such as increased sales during the summer months.

Selling products or services to clients in exchange for cash or other types of payment is known as ale. The sales process consists of a number of elements, such as:

Product: The items or services being sold are referred to here. A corporation must have a comprehensive grasp of its product offerings and how they fit the demands of its target market.

Price: The sum of money that a consumer must fork over in order to purchase the item or service. Price should be set to maximise profit while maintaining market competitiveness.

Locations where higher the good or service is sold are referred to here as "place." Physical storefronts, internet marketplaces, or a network of distributors may all fall under this category.

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The integral for the mass of a thin wire in the shape of a parabola density is \(\int[-1,1]\int[0,x^2] x^2 y^2 dy dx\)

To find the mass of the thin wire in the shape of a parabola with density function ρ(x, y) = \(x^2 y^2\),

we can set up a double integral over the region that describes the parabola. The mass M is given by the following integral:

M = ∬ρ(x,y) dA

where dA represents the area element in the xy-plane. To set up this integral, we need to first determine the limits of integration for x and y.

The parabola can be described by the equation y =\(x^2\), where x ranges from -1 to 1. Therefore, the limits of integration for x are -1 to 1.

For each value of x, the y-values range from the parabola to the x-axis, which is the region between y = 0 and y = \(x^2\). Therefore, the limits of integration for y are 0 to\(x^2\).

Using these limits of integration, the integral for the mass of the thin wire is:

M = ∫∫ρ(x,y) dA

=\(\int[-1,1]\int[0,x^2] x^2 y^2 dy dx\)

This integral can be evaluated using standard integration techniques.

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The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the industry's output is Y = 3, and the profit of each firm  = -2.

a) Supply curve of an individual firm

The price received by the individual firm will be P. Its demand curve is given by

D(p) = 20 - p.

Each firm chooses output to maximize its profit. Profit maximization occurs when the price is equal to the marginal cost. Mathematically,

P = MC(y)

4y = P

y = P/4

Thus the supply curve of the firm is y = P/4

b) The smallest price at which the product can be sold. The product can be sold at the minimum of the supply curve, which is y = 0, given P ≥ 0. Therefore the smallest price is P = 0.

c) Equilibrium price and output

Equilibrium occurs when each firm is producing at its profit-maximizing output given the output of other firms. Let the number of firms in the industry be n. The output of the industry is Y = ny. The industry supply curve is given by

S(P) = nP/4

The equilibrium price intersects the industry supply curve with the demand curve. Thus the equilibrium price satisfies

S(P) = Y

nP/4 = 20 - P

=> P = 80/(4 + n).

The equilibrium number of firms is the number that makes the industry supply curve equal to the demand curve. Thus

20 - P = nP/4

=> P = 80/(4 + n)

=> n = (80 - 20P)/P

= 20/P - 4.

Thus the equilibrium number of firms is a function of P and can range between 1 and infinity, but it must be an integer. The equilibrium output of each firm is given by

y = P/4 = 20/(4n + n²)

The equilibrium output of the industry is given by

Y = n

y = 5/P = (n² + 4n)/80.

d) Equilibrium number of firms with new demand curve D(p) = 21 - p.

The intersection of this curve with the marginal cost curve is at p = 21/5. This is greater than the minimum possible price of 0. Thus there is a positive profit to be earned in this industry, and new firms can enter the market.

e) Equilibrium price and output with new demand curve with the new demand curve D(p) = 21 - p, the industry supply curve and the equilibrium price are as given in part (d). The equilibrium output of each firm is given by y = P/4 = 21/20, and the equilibrium output of the industry is given by Y = 21/4.

f) Equilibrium number of firms, price, output, and profit with demand curve D(p) = 24 - p. This demand curve intersects the marginal cost curve at p = 6. The minimum possible price is P = 0. Thus there is a range of prices from 0 to 6 where firms can profit positively.

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the output of the industry is Y = 3, and the profit of each firm is (6)(3/2) - (2)(2(3/2)² + 8) = -2.

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Answer:

It should be 75.4

Step-by-step explanation:

The formula for a cylinders volume is V=\(\pi\)r^2h

so plugging those in would be

V=\(\pi\)(2)^2(6)= 75.4

Hope this helps!

Answer:

3ad-5ad

Step-by-step explanation:

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

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

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

The explanatory variables and response variables for this relationship are;

b. Explanatory variable: high school GPA

   Response variable: college GPA

What are explanatory variables?

When it comes to an experiment, a researcher-manipulated variable is an explanatory variable. It acts as a gauge of the transformation the response variable underwent.

Explanatory variables are frequently referred to as predictor variables or independent variables. A response variable is the variable that a researcher is asking a specific question about.

Numerous variables, referred to as explanatory variables, might have an impact on the response variable.

Therefore, the correct option is b, Explanatory variable: high school GPA, Response variable: college GPA.

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Complete question:

College administrators at a small, private college

noticed that students who had higher high school

GPAs tend to have higher college GPAs.

What are the explanatory variable and response

variable for this

relationship?

Explanatory variable: size of college

Response variable: college GPA

Explanatory variable: high school GPA

Response variable: college GPA

Explanatory variable: college GPA

Response variable: high school GPA

Explanatory variable: type of college (public)

Response variable: college GPA

For given experiment, the probability of getting a multiple of 3 and 4 is 1/7

In this question we have been given an expreiment of rolling  two number cubes and multiply the numbers.

We need to find the probability of getting a multiple of 3 and 4

If two number cubes are rolled and multiply the numbers, the maximum output of multiplication would be 36

So, the sample space:

n(S) = 21

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

And the multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36

The number of outcomes for getting a multiple of 3 and 4 are:

12, 24, 36

n(A) = 3

so, the required probability would be,

p(A) = n(A)/n(S)

p(A) = 3/21

p(A) = 1/7

Therefore, the probability of getting a multiple of 3 and 4 = 1/7

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Answer:

fraction form: 1/4x

decimal form: 0.25x

Step-by-step explanation:

Step-by-step explanation:

The interval is -2 <= x <= 3 (A).

Answer:

7A, 8D

Step-by-step explanation:

The compound interest formula is as followed

\(A = P(1+\frac{r}{n} )^{nt}\\\)

A = accumulated amount

P = principle

r = interest rate

n = compounding

t = time

The accumulated amount is represented by f(x).

The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000

The interest rate is 5%. This needs to be converted into a decimal.

5% = 0.05 = r

The money is compounded annually, thus n = 1.

The time is represented by x. x = t.

thus

\(f(x) = 2000(1+0.05)^{x}\)

After six years, you simply find f(6), or substitute 6 into x.

f(6) = 2000(1.05)^6 = $2,680.19

Answer:

Associative property

Step-by-step explanation:

you can group factors in any order and the answer will be the same

Answer:

B.35 words per minute

Step-by-step explanation:

To get the rate per minute you have to divide the words type by the amount of minutes it took to type them. Since 105/3=35 and 175/5=35, the answer is B.35 words per minute

Answer:

a

Step-by-step explanation:

step 1:

for x is less than -5 the f(x) = -3

step 2:

for x is greater than or equal to -5 and less than or equal to 15, f(x)=x+2 and since x contains the value of 15 the Value of x=15 results in f(x)=x+2 15+2=17.

step 3

for x is greater than 15, f(x)= -x+2.

only exists in the graph a.

Answer: a

Step-by-step explanation:

Answer:

and

Step-by-step explanation:

Answer:

Hold on let me seee!!!!!!!

Answer:

13388

Step-by-step explanation:

12600 will be 100% so we want to get at what price its sold when there is a 15%dicount

So will minus 15% from the 100% of the Mp

100%-15%=85%

so if 100%=12600

what about 85%=?

we crossmultiply

85%×12600/100%=10710

so10710 is what the radio will be sold if a 15% dicount is given but we want to get wat price the shopkeeper got in that he made a profit of25%

so if 100%=10710

what about 125%

125%×10710/100%=13387.5 which is 13388/=

L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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Angle IKH must be right angle since line IH is the diameter of the circle.

A right angle is an angle that measures exactly 90 degrees, or a quarter of a full turn.

In the given diagram, we can see that line IH is the diameter of the circle.

Also if line IH is the diameter, then the angle at the circumference formed by the lines joining the diameter of the circle must be 90 degrees.

So angle KHI + angle KIH + angle IKH = 180 (sum of angles in a triangle)

angle KHI + angle KIH + 90 = 18

Thus, angle IKH must be right angle since line IH is the diameter of the circle, and angle IBH must also be 90 degrees.

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Answer:

I think that the ratio is 1:1

Step-by-step explanation:

Because since the ratio is 6:6, you have to divide both side by 6 and get 1:1. You can't divide it no more (unless if you want it as a decimal). Hope this helped. This is an update.

we assume the height of the triangle is x,

so the base length will be x+4

the triangle area will be area = 1/2 ( base * height)

48 = 1/2 (x + 4) x

96 = x2 + 4x

96 + 4 = x2 + 4x + 4

100 = (x + 2)2

10 = x + 2 (for the square 100, we ignore the -10, minus is meaningless in length )

x = 8

x + 4 = 8 + 4 = 12

so the height for the triangle is 8 unit, base is 12 unit,

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Answer:

The ratio of original area to enlarged area is 1/4.

Step-by-step explanation:

Area of original circular garden is

\(\pi {( \frac{d}{2} )}^{2} = \pi \frac{ {d}^{2} }{4} \)

Area of enlarged circular garden is

\(\pi ( { \frac{2d}{2}) }^{2} = \pi {d}^{2} \)

So the ratio of original area to enlarged area is 1/4.

Answer:

the answer is -6

Step-by-step explanation:

if you have -5 and you take away another number, you end up with -6

Answer:

-6

Step-by-step explanation:

-5 - 1 ISNT -4

-5 + 1 IS -4

Answer:

Choice a 10 cm

Step-by-step explanation:

Volume of a sphere; 4/3 x 3.14(r^3)

Since we dont know the radius aka r, we can put in the different values until we get what we are looking for :)

!!!used an online calculator for this!!!

Choice a: 4188.79

Choice b: 50965.01

Choice c: 38792.39

Choice d: 5575.2

Since none of the answers are coming out as 4846.59, I would go with the closest one, choice a.

I really hope this helps!!

Please rate!!

Have a wonderful day!!

The points where q first crosses the t-axis in the given equation need to be highlighted.

To find the points where q first crosses the t-axis in the equation x = x0e^(-βt)(cos(ωt) + (β/ω)sin(ωt)), we need to determine the values of t when q equals zero.

Let's calculate the values of q versus t using the given equation over the interval 0 ≤ t ≤ 0.5 with Δt = 0.01 sec.

We can start by assigning the given values: q0 = 1 × 10^3 coulombs, R = 0.5 × 10^3 ohms, L = 10 henry, and C = 1 × 10^-4 farads.

By substituting these values into the equation, we can calculate the corresponding values of q for each value of t in the given interval. It is important to clearly label all the variables and use scientific notation with three decimal places.

Next, we examine the calculated values of q to identify the points where q first crosses the t-axis.

These points correspond to the values of t when q equals zero. By looking at the table, we can highlight or mark the corresponding t-values where q becomes zero for the first time.

These highlighted points represent the instances when q first crosses the t-axis in the given equation.

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The equation that can be used to determine the sales price of the bracelets is $22.5

Amount in her account = $150

Amount in her account after sales = $235

Change in account balance = $235 - $150

= $85

cost of necklace = $22.5

let

bracelet = x

necklace = y

The equation:

Total sales = 5x + y

85 = 5x + 22.5

85 - 22.5 = 5x

62.5 = 5x

x = 62.5/5

x = $12.5

Therefore, the cost of each bracelet is $12.5 and the cost of necklace is $22.5

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So if an equation was f(x)=x+4

you would automatically change f(x) into y

so it would y-y=x(x-x)

so you plug in the x and 4 which is the first y and x

y-4=x(x-x)

you switch the numbers around

so your final answer would be x-4