find the differential of the function. t = v 3 uvw dt = du dv dw

The velocity vector u is 0 and the acceleration vector up is 0.

To find the velocity and acceleration vectors in terms of u and up, given r=8e' and a=3, follow these steps:

Identify the position vector r and acceleration a.
The position vector r is given as r=8e', and the acceleration a is given as a=3.

Differentiate the position vector r with respect to time t to find the velocity vector u.
Since r=8e', differentiate r with respect to t:
u = dr/dt = d(8e')/dt = 0 (because e' is a unit vector, its derivative is 0)

Differentiate the velocity vector u with respect to time t to find the acceleration vector up.
Since u = 0,
up = du/dt = d(0)/dt = 0

So, the velocity vector u is 0 and the acceleration vector up is 0.

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The absolute maximum value of the function \(f(x) = x^2 - 4\) for x between 0 and 4 inclusive and f(x) = -x + 16 for x greater than 4 is 12.

To find the absolute maximum value of the function, we need to evaluate the function at critical points within the given range and compare them to the function values at the endpoints of the range.

First, let's find the critical points by setting the derivative of the function equal to zero:

For the function \(f(x) = x^2 - 4\), the derivative is f'(x) = 2x. Setting f'(x) = 0, we find x = 0.

Next, let's evaluate the function at the critical point and the endpoints of the given range:

\(f(0) = 0^2 - 4 = -4\\\\f(4) = 4^2 - 4 = 12\\\\f(4+) = -(4) + 16 = 12\)

Comparing the function values, we see that the maximum value occurs at x = 4, where the function value is 12.

Therefore, the absolute maximum value of the function f(x) within the given range is 12.

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The equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To write the equation of a parabola with focus (-2, 5) and directrix y = 3, we can use the standard form of the equation of a parabola:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus or directrix.

First, let's determine the vertex of the parabola. The vertex lies halfway between the focus and the directrix, so its y-coordinate is the average of the y-coordinates of the focus and the directrix:

Vertex y-coordinate = (5 + 3) / 2 = 8 / 2 = 4

Since the directrix is a horizontal line, the vertex has the same y-coordinate as the directrix. Therefore, the vertex is (h, k) = (-2, 4).

Next, let's determine the value of p. The distance from the vertex to the focus (or directrix) is p. In this case, the focus is (-2, 5), so the distance from the vertex to the focus is:

p = 5 - 4 = 1

Now we can write the equation of the parabola using the vertex and the value of p:

\((x - (-2))^2 = 4(1)(y - 4)\)

\((x + 2)^2 = 4(y - 4)\)

Expanding the square on the left side:

(x + 2)(x + 2) = 4(y - 4)

(x^2 + 4x + 4) = 4y - 16

Simplifying the equation:

\(x^2 + 4x + 4 = 4y - 16\)

x^2 + 4x + 20 = 4y

Rearranging the terms:

4y = x^2 + 4x + 20

Finally, dividing both sides by 4 to isolate y, we get the equation of the parabola:

\(y = (1/4)x^2 + x + 5\)

So, the equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To sketch the parabola, plot the focus (-2, 5) and the directrix y = 3 on a graph. The vertex is also located at (-2, 4). The parabola opens upwards because the coefficient of x^2 is positive. Use the equation to plot additional points and sketch the curve symmetrically around the vertex.

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The radius of the circular ripple created by the stone can be expressed as a function of time using the formula r(t) = 55t cm. The formula A = πr² represents the area of the circle as a function of the radius.

(a) The radius of the circular ripple can be determined by multiplying the speed of the ripple (55 cm/s) by the time elapsed (t seconds). Therefore, the radius as a function of time is given by r(t) = 55t cm.

(b) The formula A = πr² represents the area of a circle as a function of the radius. Applying this formula to the circular ripple, we substitute r(t) into the formula to get A = π(55t)² cm². Simplifying further, we have A = 3025πt² cm².

Interpretation:

The formula A = 3025πt² cm² gives the extent of the rippled area in square centimeters at any given time t. As time increases, the area of the ripple expands, and the rate of expansion is determined by the square of the time. The value of A represents the total surface area covered by the circular ripple at a particular moment in time.

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Step-by-step explanation:

r = 3 √ 3V / 4π

is the correct answer of this question .

The probability that a randomly selected day will have a group trades total within 85,000 of the mean is 0.1328.

What is the probability about?

In the question given, the Mean (u) is said to be = 3421439

Therefore since Standard deviation = 508638.08

Note that:

z = x-u/sd

So:

P(u - 85000 <= x <= u + 85000)

u = 3421439

We insert the formula into the equation and it will be

= P(3421439 - 85000, 3421439 + 85000)

= P(3336439,  3506439)

= (3336439 - 3421439) / 508638.08, 3506439-3421439) / 508638.08)

= prob(-0.1671 and 0.1671 (So check the column under the z table)

So:

= 0.5664 - 0.4336

= 0.1328

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Answer:

See Explanation

Step-by-step explanation:

Given

See attachment for complete question

First, we determine the cost function for all the three rides.

Ride A

From the graph, we have the following points

\((x_1,y_1) = (0,8)\)

\((x_2,y_2) = (2,12)\)

Calculate slope

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{12-8}{2-0}\)

\(m = \frac{4}{2}\)

\(m =2\) --- This represents the rate per ride

The equation is the calculated as:

\(y = m(x - x_1) + y_1\)

So, we have:

\(y = 2(x - 0) + 8\)

\(y = 2(x) + 8\)

\(y = 2x + 8\)

So, the cost function is:

\(C(x) =2x + 8\)

Calculate the cost of admission i.e. x=0

\(C(0) = 2*0+8 = 8\)

So, we have:

\(C(0) = 8\) --- Admission Charge

\(C(x) =2x + 8\) --- Cost function

\(m =2\) --- Rate per ride

Ride B

From the table, we have the following points

\((x_1,y_1) = (0,12)\)

\((x_2,y_2) = (4,15)\)

Calculate slope

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{15-12}{4-0}\)

\(m = \frac{3}{4}\)

\(m = 0.75\) --- This represents the rate per ride

The equation is the calculated as:

\(y = m(x - x_1) + y_1\)

So, we have:

\(y = 0.75(x - 0) + 12\)

\(y = 0.75(x) + 12\)

\(y = 0.75x + 12\)

So, the cost function is:

\(C(x) = 0.75x + 12\)

Calculate the cost of admission i.e. x=0

\(C(0) = 0.75*0 + 12=12\)

So, we have:

\(C(0) =12\) --- Admission Charge

\(C(x) = 0.75x + 12\) --- Cost function

\(m = 0.75\) --- Rate per ride

Ride C

No additional fee;

So, the cost function is;

\(C(x) = 30\)

In summary, we have:

Ride A

\(C(x) =2x + 8\) --- Cost function

\(m =2\) --- Rate per ride

Ride B

\(C(x) = 0.75x + 12\) --- Cost function

\(m = 0.75\) --- Rate per ride

Ride C

\(C(x) = 30\) --- Cost function

By comparison

Ride A has the highest rate per ride of (#2), followed by ride B with a rate  of #0.75 per ride.

Ride C has no charges per ride

The impact on the total cost is that:

Ride A: People that opt for ride A will pay the least to get admitted (i.e #8) but they pay the most (i.e. #2) per each ride they take

Ride B: People that opt for ride B will pay #12 to get admitted, but they pay 0.75 per each ride they take

For A and B, the overall cost depends on the number of rides taken.

Ride C: Irrespective of the number of rides taken, people that opt for ride C will pay the same flat fee of #30

Answer:-22/3

Step-by-step explanation:

its negative because it represents an irrational number

Answer: -22/3

Why: It's irrational since it's negative

There are \(72^{16\) valid passwords that can be created with the given constraints.

To calculate the total number of valid passwords, we need to consider the number of options for each character in the password.

1. Digits (0-9): There are 10 digits.

2. Uppercase letters (A-Z): There are 26 uppercase letters.

3. Lowercase letters (a-z): There are 26 lowercase letters.

4. Special characters: There are 10 special characters.

In total, there are 10 + 26 + 26 + 10 = 72 possible characters for each position in the password.

Since the password must consist of 16 characters, we have 72 choices for each character. We can calculate the total

number of valid passwords using the formula

Total passwords = (number of choices per character)^(number of characters)

Total passwords = \(72^{16\)

So, there are\(72^{16\) valid passwords that can be created with the given constraints.

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The point reactor kinetics equations describe the rate of change of neutron population and the concentrations of delayed neutron precursors in a nuclear reactor.

The point reactor kinetics equations describe the behavior of a nuclear reactor. These equations are used to model the rate of change of neutron population (dn/dt) and the rate of change of concentrations of various delayed neutron precursors (dCᵢ/dt) over time.

In the first equation, dn/dt represents the rate of change of neutron population, which is influenced by the reactivity (rho₀) - the difference between the actual and critical reactivity, the delayed neutron fraction (β/Δ), and the sum (∑) of the decay constants (λᵢ) multiplied by the concentrations (Cᵢ) of delayed neutron precursors.

In the second equation, dCᵢ/dt represents the rate of change of concentration for each delayed neutron precursor (Cᵢ). This is influenced by the production rate of the precursor (βᵢ/Δ) multiplied by the neutron population, and the decay rate of the precursor (λᵢ) multiplied by its concentration.

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So, the last three digits of m*n is 001.

Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.

Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:

p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2

Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.

Therefore, the last three digits of m*n is 001.

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To determine the number you thought of, let's work backward from the given result of 156. We determined that the number you thought of was 490.

By following the steps in reverse order, we can calculate the original number. We start with the given result of 156. To reverse the subtraction, we add 7 18 to it, which gives us 8 7 4. Moving further, to reverse the division, we multiply 8 7 4 by 1 1 5, resulting in 1 0 0 5 6 0. Now, to reverse the multiplication, we divide 1 0 0 5 6 0 by 2 1 2, yielding 4 9 0. Hence, the number you initially thought of was 4 9 0.

In summary, by working backward from the given result of 156, we determined that the number you thought of was 490.

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The function f(17) represent your friend paid for 17 rides and had $42.75 left over.

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let f(x) represent the amount that the rider has left over after x rides.

f(x) = -1.25x + 64

f(17) = -1.25(17) + 64 = 42.75

f(17) = $42.75

f(17) represent the money left

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Answer:

1/2x-4

Step-by-step explanation:

Since we don't know the number (unknown) we simplify it as a variable, x.

Then since you're taking half of x, place 1/2 next to x. Finally subtract 4, and it concludes to 1/2x-4.

Answer:

6

Step-by-step explanation:

6*4=24

1/2*24=12

3+2=5

12/5=6

Parenthises

Exponets

Multiplication

Divide

Add

Subtract

Hope this helps!!

Answer:

6

Step-by-step explanation:

1/2 x (6 x 4) ÷ 3 + 2  

(We do the equation in the parenthesis 1st)

1/2 x 24 ÷ 3 + 2    

(Since it's multiplication and division, we just go from left to right)

4 + 2

6

Answer:

The salesman sold 120 kg in the morning and 2 times 120 = 2402⋅120=240 kg in the afternoon.

Answer

5=$3.75

3.75÷5=.75 ($.75 per banana)

.75x2=T

T=$1.50

Step-by-step explanation:

Answer:

T = 0.75(2)

Step-by-step explanation:

$3.75 ÷ 5 = 0.75

0.75 x 2 = 1.5

T = 0.75(2)

1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.

In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:

ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,

where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.

To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:

-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.

If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:

-c^2*dt^2 + dx^2 = k^2.

This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.

Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.

(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)

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You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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Answer:

92.99 units squared

Step-by-step explanation:

area of a circle is

\(\pi \times {r}^{2} \)

just multiply that by 74/360, the fraction of a full circle we got here

Answer:

1.44m

Step-by-step explanation:

:p

Answer:

Step-by-step explanation:

given the expression, we are expected to solve for the value of x

\(-(9x-4)+12+18x>79\)

we begin by opening the bracket

\(-(9x-4)+12+18x>79\\\\-9x+4+12+18x>79\\\\\)

collect like terms

\(-9x+4+12+18x>79\\\\-9x+18x+4+12>79\\\\9x+16>79\\\\\)

subtract 16 from both sides

\(9x+16>79\\\\9x>79-16\\\\9x>63\)

divide both sides by 9 we have

\(x>\frac{63}{9}\\\\ x>7\)

the greatest value of x that is not a solution is 7 since x is not equal to 7

The difference of the polynomials (8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4) simplifies to 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6.

To find the difference of the given polynomials, we subtract the second polynomial from the first polynomial term by term.

(8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4)

Removing the parentheses and combining like terms, we get:

8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6

Therefore, the difference of the polynomials is 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6. This is the simplified form of the polynomial expression obtained by subtracting the second polynomial from the first polynomial.

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The ph of a buffer that contains 0.41 m propanoic acid and 0.22 m propanoate is 5.505.

In the given question we have to calculate the ph of a buffer.

The ph of buffer contains 0.41 m propanoic acid and 0.22 m propanoate.

The value of ka for propanoic acid is 1.3 x 10^{-5}.

Since, we have to calculate the pH after 0.16 mole of solid NaOH is added to 1.00 L.

Moles of excess NaOH = 0.16-0.041 = 0.119

pH = P(ka)+log(salt/acid)

pH = -log(1.3×10^{-5})+log[(0.88+0.16)/(0.41-0.16)

pH = 4.886+log(1.04/0.25)

pH = 4.886+0.619

pH = 5.505

Hence, the ph of a buffer that contains 0.41 m propanoic acid and 0.22 m propanoate is 5.505.

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Given that sin(x) = 2/3 and x is in Quadrant II, we can use trigonometric identities to find the values of cos(2x), sin(2x), and tan(2x). In two lines.

To find cos(2x), sin(2x), and tan(2x), we can use the double-angle identities: cos(2x) = cos^2(x) - sin^2(x), sin(2x) = 2sin(x)cos(x), and tan(2x) = (2tan(x))/(1 - tan^2(x)). By substituting the given value of sin(x) = 2/3 into these formulas and applying the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can calculate cos(2x), sin(2x), and tan(2x) using trigonometric calculations. The values of cos(2x), sin(2x), and tan(2x) can then be determined.

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What is the question, is their answer options or...?

Answer:

See attached

Step-by-step explanation:

In the given expression, we have two factors: (x² + 5x + 1) and (4x - 1)(x - 2). To simplify the expression, we can apply the distributive property and multiply the factors. The correct answer is d. 4x² - 1(x - 2).

To simplify the expression, we can multiply the terms.

First, let's simplify the numerator: x² + 5x + 1.

Now, let's simplify the denominator: 4x(x² - 4).

Multiplying the numerator and denominator, we have:

(x² + 5x + 1) * (4x(x² - 4)) = 4x³(x² - 4) + 20x²(x²- 4) + 4x(x² - 4)

Expanding further, we get:

4x⁵- 16x³ + 20x⁴ - 80x² + 4x³ - 16x - 4x² + 16

Combining like terms, we have:

4x⁵ + 20x⁴ - 12x³ - 84x² - 16x + 16

Therefore, the expression in its simplest form is 4x^5 + 20x^4 - 12x^3 - 84x^2 - 16x + 16, which does not match any of the given options.

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Answer:

with what??????????????

As it's a parallelogram

\(\\ \sf\longmapsto 5y+3y=180\)

\(\\ \sf\longmapsto 8y=180\)

\(\\ \sf\longmapsto y=180/8\)

\(\\ \sf\longmapsto y=22.5\)

Now

\(\\ \sf\longmapsto 5x=3y\)

\(\\ \sf\longmapsto 5x=3(22.5)=67.5\)

\(\\ \sf\longmapsto x=67.5/5\)

\)

\(\\ \sf\longmapsto x=13.5\)

Answer:

x=13.5

y=22.5

Step-by-step explanation: