Find the foci for each equation of an ellipse.

36 x²+8 y²288

Answer:

Step-by-step explanation:

Let's open the brackets,

12z - 21 = -21 + 12z (distributive property)

12z - 12z = -21 + 21

0z = 0

z = 0

Answer:

x=12

Hope this helped! :) If its right, please give me brainliest!

The mathematical model of an abstract syntax tree (AST) for a programming language's block (BL) statement typically involves representing the syntax of the statement using a tree structure.

This tree structure consists of nodes that correspond to different components of the statement, such as keywords, variables, operators, and expressions. The AST provides a way to parse and interpret the syntax of the statement, allowing for efficient compilation and execution of the code.

The model can be represented using various algorithms and data structures, such as recursive descent parsing or top-down parsing. Ultimately, the AST serves as a tool for developers to analyze, optimize, and debug their code, and is an essential component of many modern programming languages.

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The particle's motion along the parabola from x = -1 to x = 2 results in a work done of 13.5 units.

To find equations of parabola we compute the work done by the force field in moving a particle along a curve, we can use the line integral formula:

Work = ∫C F · dr

where F is the force field and dr is the differential displacement vector along the curve C.

Given the force field F(x, y, z) = xi + yj + zk, and the curve defined by y = 3x² and z = 0, we need to express F and dr in terms of the parameter x.

The differential displacement vector dr can be written as:

dr = dx i + dy j + dz k

Since z is constant (z = 0), dz = 0, so dr simplifies to:

dr = dx i + dy j

We can express dy in terms of dx using the equation of the parabola

y = 3x²:

dy = 6x dx

Now we can rewrite dr as:

dr = dx i + 6x dx j

Substituting F and dr into the line integral formula:

Work = ∫C (xi + yj + zk) · (dx i + 6x dx j)

Now we calculate the dot product between F and dr:

F · dr = (xi + yj + zk) · (dx i + 6x dx j)

= x dx + 6x² dx

Integrating the dot product over the curve C from x = -1 to x = 2:

Work = ∫C (x dx + 6x² dx)

= ∫[from -1 to 2] (x + 6x²) dx

Integrating with respect to x:

Work = [1/2 x² + 2x³] | from -1 to 2

= [1/2 (2)² + 2(2)³] - [1/2 (-1)² + 2(-1)³]

= [1/2 (4) + 2(8)] - [1/2 + 2(-1)]

= 2 + 16 - 1/2 - 4

= 13.5

Therefore, the work done in moving the particle along the parabola from x = -1 to x = 2 is 13.5 units.

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Answer:

im pretty sure $80

Step-by-step explanation:

Answer:

3, 3x+5

Step-by-step explanation:

DIFFERENTIATE W.R.T. X

3

EVALUATE

3x+5

For the following  equation, L.H.S = R.H.S is proved by solving the left-hand side and equating with it with the right-hand side equation :

\(\frac{tan x}{1-cot x} + \frac{cot x }{1-tan x} = 1+ tan x+ cot x\)

L.H.S =  \(\frac{tan x}{1- cot x} + \frac{cot x }{1 - tan x}\)

\(\frac{- tan^{2}x }{1- tan x} + \frac{cot x }{1 - tan x}\)

\(\frac{-tan^{2} x + cot x}{1 - tan x}\)

Multiply \(\frac{tan x}{tan x}\) we get,

\(\frac{1- tan^{3} x}{tan x (1- tan x)}\)

\(\frac{(1 - tan x ) (1 + tan x + tan ^{2}x) }{tan x (1 - tan x )}\)

\(\frac{( 1- tan x + tan^{2}x) }{tan x}\)

Divide each term separately,

\(\frac{1}{tan x} + \frac{tan x}{tan x} + \frac{tan^{2}x }{tan x}\)

cot x + 1 + tan x

therefore, 1+ tan x + cot x = R.H.S

L.H.S = R.H.S, hence the theory is proved.

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The company should use a warranty period that is equal to 67,467.5 miles.

To determine the warranty period, we need to find the value of the tire life that corresponds to 95% of the tires. We can use the standard normal distribution table to find the value of the z-score that corresponds to the 95th percentile. This value is approximately 1.645.

Now, we can use the formula for the normal distribution to find the tire life value that corresponds to the z-score of 1.645. This formula is:

X = μ + zσ

Where X is the tire life value, μ is the mean of the distribution (65,000 miles), z is the z-score (1.645), and σ is the standard deviation of the distribution (1500 miles).

Plugging in the values, we get:

X = 65,000 + 1.645(1500)

X = 67,467.5

This means that 95% of the tires will have a life of at least 67,467.5 miles.

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The factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

For the polynomial x³ - 7x² - 16x + 112, the following statements are true:

1. The factors of the polynomial are (x - 4)(x - 4)(x + 7).

2. The polynomial is completely factored.

To factor the polynomial completely, we can use different factoring techniques such as grouping, factoring by grouping, or synthetic division.

In this case, we observe that the number 4 is a root of the polynomial since when we substitute x = 4 into the polynomial, we get zero.

Using synthetic division or long division, we can divide the polynomial by (x - 4) twice to obtain the factored form (x - 4)(x - 4)(x + 7).

Hence, the factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

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Answer I blive is is 8

Step-by-step explanation:

Answer: #The tank holds 80,000 gallons of water when filled to capacity.

Step-by-step explanation:

4/5 - 3/4 = 1/20

The fraction (1/20) represents the 4000 gallons of water.

     1/20 = 4,000

       1    =?                  

then u cross multiply

1*4,000*20/1

= 80,000 gallons of water

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The statement "Construct a line from A perpendicular to the y-axis, determine the distance from A to the y-axis along this perpendicular line, find a new point on the other side of the y-axis that is equidistant from the y-axis" accurately describes how to reflect point A (3, -1) over the y-axis

To reflect a point over the y-axis, you need to find a new point that is the same distance from the y-axis as the original point, but on the other side of the y-axis.

This can be done by constructing a perpendicular line from the original point to the y-axis, determining the distance from the original point to the y-axis along this line, and then finding a new point on the other side of the y-axis that is the same distance from the y-axis as the original point.

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The amount of interest that the customer will pay is given as follows:

$31.88.

The balance of an account after t periods is given as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

Hence the interest accrued is given as follows:

I(t) = Prt.

The parameters for this problem are given as follows:

P = 2530.16, r = 0.00042, t = 30.

Hence the interest is given as follows:

I(30) = 2530.16 x 0.00042 x 30

I(30) = $31.88.

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Answer:

n = 4

Step-by-step explanation:

\(\sqrt{64} \cdot \sqrt[3]{8} = \sqrt{8 \times 8} \cdot \sqrt[3]{2 \times \ 2 \times 2 }\)

            \(= 8 \cdot 2\\=2^3 \cdot 2\\=2^4\\\)

Answer:

Step-by-step explanation:

\(\sqrt{64}\) .\(\sqrt[3]{8}\)

8.\(8^{1/3}\)

\(8^{1+1/3}\)

\(8^{4/3}\)

\(2^{2*4/3}\)

\(2^{8/3}\)

therefore n=8/3

Answer:

0.2156

Step-by-step explanation:

if we assume that the volume is 1L

then: density=mass(in kg) /volume(which is 1)=0.1256/1=0.1256

A Triangle is a polygon with three sides.

Foremost, a polygon is a plane figure or a two-dimensional shape with a definite number of line segments, which are connected to form a closed chain.

Thus, if a triangle has three sides, then it is a polygon

The correct answer is option B

Answer:(−5x3−6x2−5)(−5x2−2x) = 25x5+40x4+12x3+25x2+10x

Step-by-step explanation:

Answer:

x = 0.5 to the nearest 1/10.

Step-by-step explanation:

3^-x = x^3 + x

y = x^3 - 3^-x + x = 0

Using a graphing calculator to draw the graph of the above:

The graph crosses the x-axis at x = 0.4798

Answer:

x≈ .5

Step-by-step explanation:

x ≈ 0.479822322350589

Rounding to the nearest tenth

x≈ .5

There is either an error in the equation or the solution key

Answer:

Step-by-step explanation:

This is a Pythagorean Theorem Question

c^2 = a^2 + b^2

c= sqrt(5)

a = x

b = x            This is an isosceles right triangle. The vertical side and the horizontal side are equal.

x^2 + x^2  =  sqrt(5)^2

2x^2 = 5                           Divide both sides by 2

x^2 = 5/2                          Take the sqrt of both sides.

√x^2 = √5 / √2                Multiply right side by √2 on both top and bottom

x = √5*√2 / √2*√2

x = √10 /2

Theorem 3.9 states that if two lines are perpendicular, then they intersect to form four right angles. In this proof, we are given that lines m and n are perpendicular to line l.

Two-column proof of Theorem 3.9:

Statement                                      Reason

m ⊥ l, n ⊥ l<br>                                        Given

∠1 is a right angle<br>                 Definition of perpendicular lines

∠2 is a right angle<br>                               Same as 2

∠1 ≅ ∠2<br>                             Right angles have equal measure

m || n<br>                            If two lines are cut by a transversal such that                    corresponding angles are equal then the lines are parallel

Theorem 3.9 states that if two lines are perpendicular, then they intersect to form four right angles. In this proof, we are given that lines m and n are perpendicular to line l.

We then show that angles 1 and 2 are both right angles, and that angles 1 and 2 are congruent. Finally, we use the Parallel Postulate to conclude that lines m and n are parallel.

The first step in the proof is to use the definition of perpendicular lines to show that angle 1 is a right angle. We then use the same reasoning to show that angle 2 is a right angle.

In the third step, we use the fact that right angles have equal measure to show that angles 1 and 2 are congruent. Finally, in the fourth step, we use the Parallel Postulate to conclude that lines m and n are parallel.

The Parallel Postulate states that if two lines are cut by a transversal such that corresponding angles are equal, then the lines are parallel. In this case,

the transversal is line l, and the corresponding angles are angles 1 and 2. Since angles 1 and 2 are congruent, the Parallel Postulate tells us that lines m and n are parallel. This completes the two-column proof of Theorem 3.9.

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The product of 8759 x 2391 x 2391 x 7759 is 388,895,526,171,961.

To find the product of 8759 x 2391 x 2391 x 7759, we can use the associative property of multiplication. This property states that the way in which we group the factors does not affect the result of the multiplication.

So, we can group the factors in pairs and multiply each pair together before multiplying the products. Let's start with 8759 x 7759 and then multiply the products of 2391 x 2391.

8759 x 7759 = 67,907,881
2391 x 2391 = 5,716,881

Now, we can multiply these two products together to get the final result.

67,907,881 x 5,716,881 = 388,895,526,171,961

Therefore, the product of 8759 x 2391 x 2391 x 7759 is 388,895,526,171,961.

Using the associative property of multiplication can make it easier to find the product of a large number of factors. By grouping the factors in pairs and multiplying each pair together, we can simplify the problem and make it more manageable.

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a) The magnitude of Pˉ is P.  b) The direction cosine of Pˉ with respect to the x-axis is 110/P.  c) The directional angle of Pˉ with respect to the z-axis is arctan(60/√(110^2+(-0.58P)^2)).

a) To find the magnitude of vector Pˉ, we use the formula for the magnitude of a vector in three dimensions, which is the square root of the sum of the squares of its components.

b) The direction cosine of a vector with respect to a specific axis is the ratio of the component of the vector along that axis to its magnitude. In this case, the x-component of Pˉ is 110, so the direction cosine with respect to the x-axis is 110 / P.

c) The directional angle of a vector with respect to a specific axis can be found using the arctan function. In this case, we use the y-component and z-component of Pˉ to find the angle between Pˉ and the z-axis.

Therefore, the magnitude of Pˉ is given by P, the direction cosine with respect to the x-axis is cos(θ_x), and the directional angle with respect to the z-axis is θ_z.

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The statement that proves the congruency of the two triangles is (c) ASA

The given parameter is the two triangles in the figure

For the angles or the sides of the triangles to be congruent, the sides or the angles must be marked with the same identifier

Using the above as a guide,

Two corresponding angles in the triangles are marked with the same symbol

This is represented as AA i.e. Angle-Angle

Also, the triangles share a common side length

This is represented with S i.e. Side

This common side length is between the angles

So, we have

ASA i.e. Angle Side Angle

Hence, the congruency of the two triangles is by the ASA congruent theorem

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After log2n rounds, you may expect one coin to remain

There are n coins, then. According to probability, half of them will display tails, and the other half heads when you flip all of them. We now have n/2 coins after setting aside n/2 coins. We set the n/2/2 coins aside since this time they will all show tails, and the trend continues.

There is only one coin remaining, hence the sum of this GP must equal n-1.

After the first round, n/2 coins are anticipated to be withdrawn.

After the second round, n/4 coins are anticipated to be withdrawn.

Therefore, one coin should be left after log2n rounds.

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Answer:

\(\frac{1}{25}\)

Step-by-step explanation:

to find slope: \(m = \frac{y_2 - y_2}{x_2 - x_1}\)

\(m = \frac{6 - (-2)}{500-300} = \frac{8}{200\\}\\m = \frac{1}{25}\)

The time Billy should get up to be right on time for school is 6:52 am.

The formula to calculate the time Billy should get up to be right on time for school is as follows: Time Billy Should Get Up = School Start Time - (Time to Get Dressed + Time to Eat Breakfast + Time to Walk to School). In this case, the formula is: Time Billy Should Get Up = 8:35 am - (32 minutes + 13 minutes + 17 minutes). In order to solve this equation, first we must convert the minutes to hours. 32 minutes is equal to 0.53 hours and 13 minutes is equal to 0.22 hours. 17 minutes is equal to 0.28 hours. Thus, the formula is: Time Billy Should Get Up = 8:35 am - (0.53 hours + 0.22 hours + 0.28 hours). Now, we can solve for the time Billy should get up. 8:35 am minus 0.53 hours is 7:42 am. Then, 7:42 am minus 0.22 hours is 7:20 am. Finally, 7:20 am minus 0.28 hours is 6:52 am. Therefore, the time Billy should get up to be right on time for school is 6:52 am.

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The relationships between x and y that satisfy the curve defined by 2sin(x−3y)+ln(x+y)=2x2y3 at vertical and horizontal tangents are:

Vertical tangent: x = 3y.

Horizontal tangent: y = 1.

A vertical tangent occurs when the derivative of the function is equal to infinity. The derivative of the function is given by

dy/dx = (2x^2 y^2 - 2sin(x - 3y))/(x + y)

If x = 3y, then dy/dx = infinity, so there is a vertical tangent at x = 3y.

A horizontal tangent occurs when the derivative of the function is equal to 0. If y = 1, then dy/dx = 0, so there is a horizontal tangent at y = 1.

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Answer:

12

Step-by-step explanation: