Plot the vertex, focus, and directrix for the parabola represented by this equation. X=-1/12(y-2)^2+1

Answer:

Circumference = 2πr

69.08 = 2× 3.14 × r

69.08 ÷ 6.28 = r

11m = r

Answer: 22

Step-by-step explanation: Divide the total by pi or 3.14 and the diameter is 22 and the radius is 11

The general solution to the differential equation is:

y = C x exp(2x² + x)

Where C is the constant of integration.

The given differential equation is

dy/dx = y/x + 4x + 1

By using the separation of variables,

Which involves separating the y and x terms on opposite sides of the equation and then integrating both sides.

So we have:

dy/dx = y/x + 4x + 1

dy/y = (1/x + 4x + 1)dx

Now we can integrate both sides:

∫ dy/y = ∫ (1/x + 4x + 1)dx

ln|y| = ln|x| + 2x² + x + C

Where C is the constant of integration.

Now we can solve for y by exponentiating both sides:

|y| = exp(ln|x| + 2x² + x + C)

|y| = exp(ln|x|) exp(2x² + x + C)

|y| = |x| exp(2x² + x + C)

y = ± x exp(2x² + x + C)

So the general solution to the differential equation is:

y = C x exp(2x² + x)

Where C is the constant of integration.

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The complete question is attached below:

Answer: 4.1

Step-by-step explanation:

Answer:

4 1/10

hope this helps have a good day :)

Answer:

The Triangles are congruent by Angle-Side-Angle.

x would equal 4 because the triangles are congruent.

Step-by-step explanation:

In the function call, the argument tax_percentage is assigned the value of 0.07.

In the function call split_check(60.52, 5, .07, tip_percentage=0.18), the value passed as the tax_percentage argument is 0.07.

The function split_check is being called with the following arguments:

60.52 as the amount of the check

5 as the number of people to split the check among

0.07 as the tax percentage

0.18 as the tip percentage (provided as a keyword argument tip_percentage=0.18)

Therefore, the value 0.07 is passed as the tax_percentage argument in the function call.

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1. (a) pq - "If it is an eagle, then it is a bird."

(b) qp - "If it is a bird, then it is an eagle."

(c) pa - "It is an eagle and it is a bird."

All statements are true.

2. (a) pq - "If it is a wild animal, then it is a mammal."

(b) a →p - "All animals are wild, then they are mammals."

(c) p > - "All mammals are wild animals."

All statements are not true. Counterexample can be a bird, which is a wild animal but not a mammal.

In task 1, we are given two statements and asked to express them using symbolic logic notation, and then evaluate whether they are true or false. In the first statement, "It is an eagle, it's a bird," we can represent it as "p ∧ q," where p stands for "It is an eagle" and q stands for "It's a bird." All the statements are true as an eagle is a bird.

In the second statement, "All wild animals are mammals," we can represent it as "p → q," where p stands for "It is a wild animal" and q stands for "It is a mammal." The statement is false as there are wild animals that are not mammals, such as snakes, lizards, and birds.

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--The complete question is, Learning Task 1

Do the following:

1. Statement: It is an eagle, it's a bird.

Write the following in words:

(a) pa (b) qp (c) pa

Are all statements true?

If not give a counter example.

2. Statement: All wild animals are mammals.

SON

Write in words:

(a) pq (b) a →p (c) p >

Are all statements true?

If not give a counter example.​--

The measure of the shortest side of the larger sail is 12 ft

We can use the property that similar triangles have corresponding sides in proportion to solve this problem.

Let the length of the shortest side of the larger sail be x.

Since the two sails are similar, we can set up the proportion:

12 : 28 : 32 = x : 28 : y

where y is the length of the remaining side of the larger sail.

We can then use cross-multiplication to solve for y:

12 * 28 = 28 * x

336 = 28x

x = 12

So the length of the shortest side of the larger sail is 12 feet.

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The 'x' coordinate is negative and 'y' coordinate is positive.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

We know that :

π = 180

Therefore,

3π/4 = (3×180)/4 = 3 × 45

3π/4 = 135

In second quadrant, we have negative value if x coordinate and positive value of y coordinate.

Hence, the angle lies in the second quadrant. Second quadrant is enclosed by the negative x axis and positive y axis.

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Answer:

x is negative, and y is positive.

Step-by-step explanation:

The answer above is correct.

The relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

Let the velocity and acceleration of the first car be v1 and a1 respectively.The velocity of the second car be v2 and acceleration be a2.Let the distance between the two cars at any time after t=0 be given by S.If the initial distance between them is 50 feet, then S=S0+50ft where S0 is the distance between them at time t=0.

From the given conditions, we can set up the following relationships for the two cars.1) For the first car:S=ut+(1/2)at^2 where u is the initial velocity.

2) For the second car:S=vt+(1/2)at^2 where v is the initial velocity.In the first equation, we can substitute u=0 (since it started from rest) and a=a1.

In the second equation, we can substitute v=50ft (since it is 50ft behind) and a=a2.

Substituting the above values in the above two equations, we get:S= (1/2)a1t^2 and

S= 50ft + v2t + (1/2)a2t^2

From the problem statement, we are also given that the lead car is accelerating in such a way that the distance S in feet between the two cars at any time t after t=0 seconds is 50 more than twice the square of t.

Therefore,S = 2t^2 + 50ft

We can now equate the above two expressions for S, and solve for t, to get the relationship between the distance S and time t:

S = 2t^2 + 50ft = (1/2)a1t^2 + 50ft + v2t + (1/2)a2t^2

Simplifying the above expression, we get:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2

Therefore, the relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

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Answer:

siesta  bien

Step-by-step explanation:

Answer:

213.042  km

Step-by-step explanation:

We need to convert 213 km 42 m to km.

We know that,

1 km = 1000 m

or

1 m = (1/1000)km

So,

42 m = (42/1000) km

It means,

\(213\ km\ 42\ m=213\ km+\dfrac{42}{1000}\ km\\\\=213.042\ km\)

So, the required answer is 213.042  km.

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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the answer to the question is one mile

Answer:

20.7 and 500.200

Step-by-step explanation:

Answer:

20/7 = 2.8571

500/22000 = 0.0227

Step-by-step explanation:

The integral for finding the area of the region is:

A = ∫[lower bound]^[upper bound] [rightmost bound] dy

A = ∫[1/6]^∞ [6] dy

To sketch the region enclosed by the curves and determine whether to integrate with respect to x or y, let's analyze the given equations:

y = 1/x

y = 1/x^2

x = 6

To begin, let's plot these curves on a coordinate plane:

First, we can observe that both equations involve hyperbolas. The equation y = 1/x represents a hyperbola that passes through the points (1,1), (2,0.5), (-1,-1), etc. The equation y = 1/x^2 represents a hyperbola that passes through the points (1,1), (2,0.25), (-1,1), etc.

Next, the equation x = 6 represents a vertical line passing through the point (6,0) on the x-axis.

Now, to determine the enclosed region, we need to find the limits of integration.

Since the curves intersect at certain points, we need to find these points of intersection. Equating the two equations for y and solving, we get:

1/x = 1/x^2

Multiplying both sides by x^2 yields:

x = 1

Hence, the curves intersect at x = 1.

Therefore, the region enclosed by the curves is bounded by the following:

The curve y = 1/x,

The curve y = 1/x^2,

The vertical line x = 6, and

The x-axis.

To determine whether to integrate with respect to x or y, we need to consider the orientation of the curves. In this case, the curves are defined in terms of y = f(x). Thus, it is more convenient to integrate with respect to y.

To find the area of the region, we need to set up the integral bounds. Since the region is bounded by the curves y = 1/x and y = 1/x^2, we need to find the limits of y.

The lower bound is determined by the curve y = 1/x^2, and the upper bound is determined by the curve y = 1/x. The vertical line x = 6 acts as the rightmost boundary.

Therefore, the integral for finding the area of the region is:

A = ∫[lower bound]^[upper bound] [rightmost bound] dy

A = ∫[1/6]^∞ [6] dy

Now, we can proceed with evaluating this integral to find the area of the enclosed region.

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Toni had 17 points, Effie had 25 points and Linda had 18 points.

The question is asking to find the number of points each girl had in a girl's basketball game. To find out how many points Effie had, you must multiply Toni's points by 3, subtract 8, and then multiply the difference by 2. To find out how many points Linda had, you must add 9 to Toni's points and divide the sum by 3. The given information is that Effie scored 9 more than Toni and Linda combined.

Formula and Calculation:

Toni's Points = x

Effie's Points = 3x-8

Linda's Points = (x+9)/3

Effie scored 9 more than Toni and Linda combined, so:

3x-8 = x+9/3 + 9

2x-8 = x+9

x = 17

Therefore, Toni had 17 points, Effie had 25 points and Linda had 18 points.

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Answer:

cube root of 9. the third option

Step-by-step explanation:

x^3 = 9

we take the cube root of both sides.

so x = cube root of 9

As per given by the question,

There are given that a length of three sides of the triangle.

The length of sides are, 14cm, 22cm, and 30cm.

Now,

For finding the measure of the smallest angle,

The smallest angle in a triangle is always opposite the shortest side. and also the bigest angle is always opposite the longest side.

So,

Suppose length A is 14cm, B is 22 cm and C is 30cm.

Then,

From the law of cosines,

Let A be the smallest angle.

So,

Now,

Find the value of angle A,

Now,

Then,

Hence, the measure of the smallest angle is 25.84 degree.

(a)The corresponding accumulation function a(t) is obtained by integrating A(t) with respect to t. Integration is the reverse process of differentiation, i.e., it undoes the effect of differentiation.

= ∫(t²+2t+4)dt

= [t³/3+t²+4t]+C         , where C is the constant of integration.

Thus, the accumulation function a(t) is given by         a(t) = ∫(t²+2t+4)dt = t³/3+t²+4t+C

(b)To find ㏑, we integrate the difference between a and b with respect to t and evaluate it between the limits n and 0.

=∫₀ⁿ

=〖(a(t)-b(t)) dt= a(n)-a(0)-[b(n)-b(0)] 〗

= [n³/3+n²+4n]-[0+0+0]-[n²/2-2n-4]

= n³/3+3n²/2+6n-4

Thus, ㏑= n³/3+3n²/2+6n-4.

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Answer:

500

Step-by-step explanation:

i think. i have down syndrome dont hate my answers.

Answer: 500

Step-by-step explanation:

a) the mean of this distribution is 20

b) the mean of the distribution is 20 and the standard deviation of the distribution is 4.58.

a. Calculation of mean of the given distribution:

Mean = ∑(x * P(x))

where x = value of the outcome

P(x) = Probability of the outcome

∑ denotes the summation over all the possible outcomes

Mean = (10 * 0.10) + (15 * 0.30) + (20 * 0.20) + (25 * 0.30) + (30 * 0.10)= 1 + 4.5 + 4 + 7.5 + 3= 20

b. Calculation of standard deviation of the given distribution:

σ = √[∑(x - μ)² P(x)]

where x = value of the outcome

μ = mean of the distribution

P(x) = Probability of the outcome

∑ denotes the summation over all the possible outcomes

σ = √[((10 - 20)² * 0.10) + ((15 - 20)² * 0.30) + ((20 - 20)² * 0.20) + ((25 - 20)² * 0.30) + ((30 - 20)² * 0.10)]= √[100 * 0.10 + 25 * 0.30 + 0 + 25 * 0.30 + 100 * 0.10]= √[10 + 7.5 + 3.5]= √21= 4.58

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We are asked to show that the limit of the dipole moment function P(E) as E approaches 0 from the positive side is 0.

To prove the given statement, we need to evaluate the limit of the dipole moment function P(E) as E approaches 0 from the positive side.

Taking the limit as E approaches 0, we substitute E = 0 into the dipole moment function P(E):

lim(E→0+) P(E) = lim(E→0+) [(e^E + e^(-E))/(e^E - e^(-E))] - 1/E.

Substituting E = 0 into the expression, we get:

lim(E→0+) P(E) = [(e^0 + e^(-0))/(e^0 - e^(-0))] - 1/0.

Simplifying further, we have:

lim(E→0+) P(E) = [(1 + 1)/(1 - 1)] - 1/0 = (2/0) - 1/0.

Since the expression (2/0) - 1/0 is undefined, we cannot determine the limit using direct substitution.

However, in the context of electrostatics, as the electric field E approaches 0, the dipole moment P per unit volume approaches 0. This is because in the absence of an electric field, there is no net alignment of dipoles, resulting in a dipole moment of 0.

Therefore, we can conclude that lim(E→0+) P(E) = 0.

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Answer:

11

Step-by-step explanation:

The mile per gallon of that is covered by Nachelle will be equal to 15.1 gallons per mile.  

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the instructions in the question,

Total distance traveled by Nachelle = 196.3 miles

Total gas spent in traveling = 13 gallons.

So, the gas spent per mile will be,

196.3/13 = 15.1 gallons of gas per mile.

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Answer:

D) As the amount of nutrients in the soil increases, the rate of plant growth increases.

Step-by-step explanation:

When there is more nutrients in the soil it makes the plant healthier and grow more. Also all of the other ones have no correlation to eachother or effect on another.

Applying the side-splitter theorem, the value of x in the image given is calculated as: x = 5.

The Side-Splitter Theorem states that if a line is drawn parallel to one side of a triangle and intersects the other two sides, the ratio of the length of the two segments of the divided sides is equal to the ratio of the lengths of the sides that form the two smaller triangles.

Using this theorem, we van apply it to solve for x in the image given:

24x/(24x - 50) = 84/49

Solve for x:

24x(49) = 84(24x - 50)

1,176x = 2,016x - 4,200

1176x - 2016x = -4200

-840x = -4,200

x = -4200/-840

x = 5

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Step-by-step explanation:

hopefully it is clear and understandable

:)