Find out the type of curve : 164² + 204 = 164-4x² - 4xy-4 2) Express the equation 2²=X² +xy" in Parametric form.

Answers

Answer 1

The equation 164² + 204 = 164-4x² - 4xy-4 represents a conic section known as an ellipse.

The given equation can be rewritten as 164² + 204 + 4x² + 4xy - 164 = 0 by rearranging the terms. Simplifying further, we have 4x² + 4xy + (164² - 164) + 204 = 0.

Comparing this equation with the general form of an ellipse, Ax² + Bxy + Cy² + Dx + Ey + F = 0, we can identify A = 4, B = 4, and C = 0. Since B² - 4AC = 4² - 4(4)(0) = 16 - 0 = 16 > 0, we can conclude that the given equation represents an ellipse.

To express the equation 2² = X² + xy in parametric form:

Let's introduce two new variables, u and v, which will be our parameters. We can express x and y in terms of u and v.

From the given equation, we have:

2² = X² + xy

Substituting x = u and y = v, we get:

2² = u² + uv

Now, we can express x and y in terms of u and v:

x = u

y = 2 - uv

Therefore, the parametric form of the equation 2² = X² + xy is:

x = u

y = 2 - uv

In this parametric form, we can choose various values for u and v to obtain different points on the curve represented by the equation.

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Related Questions

A pair of headphones cost $43.95. The sales tax rate is 4.5%. What is the total cost for the headphones including tax?

Answers

Answer:

45.94

Step-by-step explanation:

43.95*0.045=1.97775 rounds to 1.98.

1.98+43.95=45.94.

Hope this was helpful.

~cloud

the answer is 45.94 ^ same thing

The price of crude oil, per barrel, in the year 2006 was estimated at $66.02. There was a 9.5% increase in the year
2007 and a 38.83% increase in the year 2008. Determine the approximate value for a barrel of crude oil in the year
2008. Round your answer to the nearest cent.
a. $128.74
c. $179.27
b. $91.66
d. $100.36

Answers

Answer:

D.) $100.36

Step-by-step explanation:

66.02/100 = 0.6602

0.6602 x 109.5 = 72.2919

72.2919/100 = 0.722919

0.722919 x 138.83 = 100.36

If we reject a null hypothesis at the 10% significance level, we will also reject it at the 5% significance level. Ο Nο Yes Depends

Answers

No, if we reject a null hypothesis at the 10% significance level, it does not necessarily mean that we will also reject it at the 5% significance level.

Explanation:

Rejecting or not rejecting a null hypothesis depends on the level of statistical significance chosen for the hypothesis test. The significance level, often denoted as α, determines the threshold for accepting or rejecting the null hypothesis.

When we reject a null hypothesis at the 10% significance level, it means that the p-value associated with the test is less than 0.10. This suggests that the observed data provides strong evidence against the null hypothesis, and we can reject it.

However, the 5% significance level is a more stringent criterion. If we test the same null hypothesis at a lower significance level (α = 0.05), we require stronger evidence to reject the null hypothesis. Therefore, if the p-value is greater than 0.05 but less than 0.10, we would fail to reject the null hypothesis at the 5% significance level.

In summary, rejecting the null hypothesis at the 10% significance level does not guarantee its rejection at the 5% significance level. The decision to reject or fail to reject the null hypothesis depends on the chosen significance level and the corresponding p-value obtained from the hypothesis test.

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Five students wrote a test and the scores were as follows:5,3,7,9 and x. If their total score was 30 find the value of x

Answers

Answer:

The value of X is 6.

Step-by-step explanation:

5 + 3 + 7 + 9 = 24

30 - 24 = 6

X = 6

The difference is 6.  

Ben rolls a number cube 50 times. He records the result of each roll in the table below. RESULTS OF ROLLING NUMBER CUBE Outcome 1 2 3 4 5 6 Frequency 7 6 5 11 10 11 Based on the data, which statement is true? Ben will roll an even number about 250 times if the number cube is rolled 500 times. Ben will roll an even number about 220 times if the number cube is rolled 500 times. Ben will roll an even number about 700 times if the number cube is rolled 1,000 times. Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.​

Answers

Answer:Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.

Step-by-step explanation:

Answer all or none! Ty!​

Answers

1) You can make about 6 bracelets because 43 divided by 6.8 is 6.3235 so you round it to 6.

2) The answer is 14.4 miles because that’s what 3.6x4 equals.

3) The answer would be $63.09 because 7.01x9=63.09

4) The answer is 1.35 , you just have to multiply 0.5 and 2.7

5) The answer is 9.432 seconds

6) For aluminum it would be $1.15 and for copper it would be $3.24

7) 0.21 x 10 = 2.1

8) 45.35 divided by 10,000 = 0.004535

9) 6.02 x 0.1 = 0.602

10) 9.4 divided by 0.01 = 940

11) 15.5

12) $695

What is the equation of the horizontal line?

Answers

Answer: y = 1

y = 2x+7 x = -3

y = 2(-3) + 7

y = 1

Write your own situation for the expression c = 9g

Answers

Ivy is going to the fair with a friend. They will buy cotton candy. They buy 9 bags of it. Each bag cost 2 dollars . What is C the total cost of all the cotton candy if G=2?

Hello. Please help if you can.

Answers

The answer is x=5 and z=70

Find the output, h, when the input, x, is -18
h = 17+x/6
h=?

Answers

Answer:

i think h=17

Step-by-step explanation:

-18h = 17 = xh/6

Subtract xh/6 from both sides of the equation.

-18 - xh/6 = 17

Answer:

Step-by-step explanation:8

Consider The Function And The Arc Of A Curve C From Point A (4,3) To Point B (5,5) Using The Fundamental Theorem For Line Integrals, G(X,Y)=2x²+3y² S Vg⋅Dr=

Answers

We know that the line integral of the curve C is equal to the difference between the anti-derivative at the final point B and the antiderivative at the initial point A.  Therefore, Vg⋅dr= F(B) - F(A)⇒ Vg⋅dr= [2(5)²(5) + 3(5)² + C] - [90 + C]⇒ Vg⋅dr= 184

The question states that the function g(x,y) = 2x² + 3y² and the curve C is the arc of a curve from point A(4,3) to point B(5,5). The task is to find the value of the line integral along curve C.

Therefore, we need to use the fundamental theorem for line integrals to evaluate the line integral. To use the fundamental theorem for line integrals, we must first evaluate the gradient vector field of the function. Then we need to find the antiderivative of the gradient vector field of the function. We can obtain the antiderivative by integrating the gradient vector field along the curve C using the initial and final points of the curve. The value of the line integral of the curve C is equal to the difference between the antiderivative at the initial point A and the antiderivative at the final point B, i.e., Vg⋅dr= F(B) - F(A).

Step-by-step solution: Given, the function g(x,y) = 2x² + 3y²Let us calculate the gradient vector of the function g(x,y).∇g(x,y) = [∂g/∂x, ∂g/∂y]⇒ ∇g(x,y) = [4x, 6y]Therefore, the gradient vector field of g(x,y) is V = [4x, 6y].

Now, we need to find the antiderivative of the gradient vector field of the function. Let us integrate V along the curve C from A(4,3) to B(5,5). The curve C is given by y = x + 1.We know that the line integral along curve C is given by the formula, Vg⋅dr= ∫C V . dr = F(B) - F(A)

Therefore, we need to find the antiderivative F of V.F(x,y) = ∫V dx⇒ F(x,y) = 2x²y + 3y² + C. Since we have two variables, we need to find the value of C using the initial point A(4,3).F(4, 3) = 2(4)²(3) + 3(3)² + C⇒ F(4, 3) = 90 + C

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Given that the function is G(x, y) = 2x² + 3y² and Arc of a curve C from point A(4, 3) to point B(5, 5). The value of the line integral [tex]\int _C[/tex] (2x² + 3y²) ds is 106.67.

Solution: In the given question, we have a function G(x, y) = 2x² + 3y² and an arc of a curve C from point A(4, 3) to point B(5, 5).

We are to use the fundamental theorem for line integrals to find the value of  [tex]\int _C[/tex] (2x² + 3y²) ds.

Step 1: First, we will find the parametric equations of the given curve.

The points A(4, 3) and B(5, 5) are given.

We can write the parametric equations of the curve C as: x = f(t) and y = g(t), where a ≤ t ≤ b, and f(a) = 4, g(a) = 3, f(b) = 5, g(b) = 5.

Here, the curve C is the straight line from A(4, 3) to B(5, 5), so we can choose any convenient parameterization.

A possible one is: t → r(t) = (4 + t, 3 + t), 0 ≤ t ≤ 1.

Step 2: Next, we will find dr/dt and ds/dt.

We have: r(t) = (4 + t)i + (3 + t)j

⇒ dr/dt = i + j.

Square of the magnitude of the tangent vector: |dr/dt|² = (1)² + (1)²

= 2.

Magnitude of the normal vector:

|n| = √(ds/dt)²

= √(2)

= √2.

Magnitude of the velocity vector:

|v| = √(dr/dt)²

= √2.

Step 3: Now, we will find the limits of integration and substitute the required values in the integral.

Given:  [tex]\int _C[/tex] (2x² + 3y²) ds.

We have: r(t) = (4 + t)i + (3 + t)j

⇒ r'(t) = i + j

⇒ |r'(t)| = √2.

We know that the length of the curve C from A to B is given by:

Length of the curve = [tex]\int _C[/tex] ds

= [tex]\int_a^b[/tex] |r'(t)| dt

= [tex]\int_0^1[/tex] √2 dt

= √2.

Now, we have the value of ds: ds = √2 dt.

Then, we can write the integral as follows:

[tex]\int _C[/tex] (2x² + 3y²) ds = [tex]\int_0^1[/tex] (2(4 + t)² + 3(3 + t)²) √2 dt

= [tex]\int_0^1[/tex] (32 + 32t + 10t²) √2 dt

= [32t + 16t² + (10/3)t³[tex]]_0^1[/tex]

= 32 + 16 + (10/3)

= 106.67.

Thus, the value of the line integral  [tex]\int _C[/tex] (2x² + 3y²) ds is 106.67.

The required answer is: 106.67.

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Determine the projection of u=1.6i+3.3j in the v=-2.1-.5j direction.

A.8i+.2j

B.2.3i+.5j

C. -.6i-1.3j

D. -1.2i-1.1j

Answers

Answer:

[tex]0.80i +0.2j[/tex]

Step-by-step explanation:

The projection of u on v is expressed as;

[tex]proj_{v} u = \dfrac{u*v}{|v|^2} * v[/tex]

Given

u=1.6i+3.3j

v=-2.1i-.5j

u*v = (1.6i+3.3j )*(-2.1i-0.5j )

u*v = 1.6i(-2.1i) + 3.3j(-0.5j)

u*v = -3.36 - 1.65

u*v = -5.01

|v|² = (√(-2.1)²+(-0.5)²)²

|v|² = (-2.1)²+(-0.5)²

|v|² = 4.41+0.25

|v|² = 4.66

Substitute into the formula;

[tex]= \frac{1.71}{-5.01} * (-2.1i - 0.5j)\\= -0.3413 (-2.1i - 0.5j)\\= 0.8i + 0.17j\\= 0.80i +0.2j[/tex]

Help... do it now if you can pls...

Answers

Answer:

1.A,B,C,D

2. AB, CD

3. AC, BD

4. Line AD (don't take my word for this one)

Step-by-step explanation:

guys what is m=4 i really need help

Answers

Answer:

m equals four means that you need to multiply the 4 by what is infront of the m aka the 4

Find the inverse of this function. Show your steps.

Hi, so, I'm like halfway done, but can you show me the steps to get to the inverse of this function, please? Also, is was what I have so far correct?
Thanks so much if you help!

Answers

Answer:

1cesrutherford and Global business is the next 3.some 7th round and 50th 3 7th round ♥ in my car is a

please help, I need help understanding this. May someone explain this?

Answers

Ok so first let find what we know so far
We can see that one point is located at (3,-2)
And the slope is = -1
This means that the line must be passing thought -1
We have (k,4) so we must find out k

Lets graph (-4,4) to (3,-2)
it passes though -1 on the point line
And -1 is our slope
So k would be = -4

pls help and show work

Answers

Answer:

Step-by-step explanation:

3x^2 + 24x + 48 + 43 - 48

3(x^2 + 8x + 16) - 5

3(x + 4)^2 - 5

vertex at (-4,-5)

Answer:

vertex = (- 4, - 5 )

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

y = 3x² + 24x + 43 ← factor out 3 from the first 2 terms

  = 3(x² + 8x) + 43

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 8x

y = 3(x² + 2(4)x + 16 - 16) + 43

y = 3(x + 4)² - 48 + 43

y = 3(x + 4)² - 5 ← in vertex form

with vertex = (- 4, - 5 )

 

Mary has a toy which is in the shape of a right prism with triangular bases. The sides of its bases are each 4 feet and its approximate height is 3.5 feet. The length of the prism between the bases is 10 feet. What is the approximate surface area of this right prism? A. 134 B. 150.5 C. 210 D. 323.5

Answers

Answer:

B

Step-by-step explanation:

Answer:

C

Step-by-step explanation: 210 ft. 2

ATHEMATICS CURRICULUM
Lesson 3 Homework
time Zachary starts playing with his action figures.
the start playing with his action figures?
Start
1
12
11
1
31
10
on figures for 23 minutes.
Ish playing?
Finish

Answers

Answer:

guru gossip and you can you invite me to the heading

Assume that the population is normally distributed. Construct a 95% confidence interval estimate of the mean numbers. Round to at least two decimal places.

17 14 16 13 15 15 14 11 13

Margin of Error:

Confidence Interval:

Answers

Based on the given data, a 95% confidence interval estimate of the mean number falls between 12.22 and 16.78.

To construct a confidence interval for the mean, we need to calculate the sample mean and the margin of error. The formula for the margin of error is:

Margin of Error = Z * [tex]\frac{standard deviation}{\sqrt{n} }[/tex]

where Z is the critical value corresponding to the desired confidence level (for 95% confidence level, Z ≈ 1.96), Standard Deviation is the sample standard deviation, and n is the sample size.

From the given data, we calculate the sample mean to be 14.33 and the sample standard deviation to be 1.91. Since the population is assumed to be normally distributed, we can use the Z-distribution.

Using the formula for the margin of error, we find:

Margin of Error = 1.96 * (1.91 / √9) ≈ 1.39

The confidence interval is calculated by subtracting and adding the margin of error to the sample mean:

Confidence Interval = (14.33 - 1.39, 14.33 + 1.39) = (12.94, 15.72)

Rounded to at least two decimal places, the 95% confidence interval estimate of the mean number is approximately (12.22, 16.78). This means that we can be 95% confident that the true mean number falls within this interval.

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Slove the system of linear equations by graphing y=-x+7 y=x-1

Answers

x = 4, y = 3


add the two linear equations together: 2y = 6

now that we know y = 3, solve for x by substituting it in

800 jerseys 6 medium jerseys what percent of the jerseys is medium?

Answers

The percent of the jerseys :

6 : 800 = 0,75%

On a school field trip, there will be one adult for every 12 students. Which equation could be used to find a, the number of adults, if s, the number of students, is unknown?

Answers

There is no good answer for this.

You would do s/12, since there is 1 adult for every 12 kids. Then, round the number to the nearest 1. (if it is a decimal, there is a number and remainder of students.)

-7 = 2x - 7
A. 0
B. 4
C. Infinite Solutions
D. No solutions

Answers

Answer:

A

Step-by-step explanation:

the variable is how many times the two will be multiplied, so 2 times 0 equals 0, there by making the problem. -7= - 7

Answer:

that will be A. 0

Step-by-step explanation:

first, i flip the equation

2x - 7= -7

next, i add both side by 7

2x−7+7=−7+7

2x=0

and finally, you divided by 2

2x/2 = 0/2

you get x = 0

Find the inverse Laplace transform of f(t) = (Use step(t-c) for uc(t).) F(s) = 8² -98 e 2s - 15

Answers

The inverse Laplace transform of f(t) is given by f(t) = t - 98δ(t - 2) - 15.

To find the inverse Laplace transform of F(s) = 8s^2 - 98e^(2s) - 15, we can use the linearity property and the table of Laplace transforms. Let's break down the expression into three terms.

The inverse Laplace transform of 8s^2 is obtained by looking up the corresponding entry in the table of Laplace transforms. From the table, we find that the inverse transform of s^2 is t.

The inverse Laplace transform of -98e^(2s) can also be found in the table. The entry for e^(as) is δ(t - a), where δ(t) represents the Dirac delta function. Therefore, the inverse transform of -98e^(2s) is -98δ(t - 2).

Lastly, the inverse Laplace transform of -15 is simply -15.

By applying the linearity property, we can add up the individual inverse transforms:

Inverse Laplace transform of F(s) = t - 98δ(t - 2) - 15.

Therefore, the inverse Laplace transform of f(t) is given by f(t) = t - 98δ(t - 2) - 15.

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2.- Al frente de cada uno de los siguientes números, realiza su escritura. Lo debe hacer en
su cuaderno y en orden.
a) 274.345
e) 324.456
i) 89.731.000
b) 3.472.416
f) 12.945.856
j) 99.125.001
C) 2.323.579
g) 24.674.208
k) 100.286.777
d) 8.456.759
h) 56.405.480​

Answers

I dont know BUT DONT BE MAD have a puppy

12 + 6 − 4 ÷ (2 + 5)

Answers

Answer:

2

Step-by-step explanation:

14 / (7)

Just find the figure of the rectangle plss

Answers

Answer:

x= 21

y= 3

z= 21

Step-by-step explanation:

Let the center be O,

=> Triangle AOD is an Isosceles triangle so AO≅DO, "21 = x"

=> Line AC is divided in two equal parts by the center so if AO= 21 then

    7y = 21, and thus "y = 3"

=> BOC is also an Isosceles triangle so CO ≅ BO, if CO = 21 (7y → 7*3) then so will be BO. Therefore "z = 21"

2^2 y^-6
-------------
8^1 z^0 x^-7

How do you solve this?

Answers

4x^7
——-
8y^6

this is the simplified answer. you flip negative powers.

It costs $3 per hour to park in a parking lot, with a maximum cost of $12.

Explain why the amount of time a car is parked is not a function of the parking cost.

Answers

Answer:

It is not a function because there is a maximum.

Step-by-step explanation:

With 12 as the maximum it will not go on forever and functions do.

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E(Y|X=2)= and V(Y/X=2)= King Corporation began operations in January of the current year. The charter authorized the following stock:Preferred stock: 10 percent, $11 par value, 41,600 shares authorizedCommon stock: $6 par value, 86,600 shares authorizedDuring the current year, the following transactions occurred in the order given:a. Issued 23,700 shares of common stock for $10 cash per share.b. Sold 7,500 shares of the preferred stock at $21 cash per share.c. Sold 2,400 shares of the preferred stock at $21 cash per share and 3,300 shares of common stock at $11 cash per share.Required:Provide the journal entries required to record each of the transactions in (a) through (c). Given a RL circuit consisting of a battery, providing electromotive force , connected to a coil, or inductor with self inductance L which has a resistance R from the coil, the connecting wires and the battery. Show that the energy delivered by the battery up to an arbitrary time t equals the energy stored in the magnetic field plus the energy dissipated in the resistor. a python int can represent indefinitely large numbers. group of answer choices true false GEORGE (Exasperated; rising)I know [you love to talk] and I don't mind it sometimes...I want you to cut it out, see - The moody stuff, I mean. I don't like it. You're a nice-looking girl...all over. That's all you need, honey, forget the atmosphere. Guys aren't going to go for the atmosphere - they're going to go for what they see. Be glad for that. Drop the Garbo routine. It doesn't go with you. As for myself, I want a nice - (Groping) - simple (Thoughtfully) - sophisticated girl... not a poet - O.K.? (2.2.5) The following tabulations are actual demand of units for six months and a starting forecast in January. ACTUAL FORECAST January 100 80 February 94 March 106 April 80 May 68 June 94 a. Calculate demand Waterway's Bakery makes a variety of home-style cookies for upscale restaurants in the Atlanta metropolitan area. The company's best-selling cookie is the double chocolate almond supreme. Waterway's recipe requires 80 ounces of a commercial cookie mix, 7 ounces of milk chocolate, and 2 ounces of almonds per batch of cookies. The standard direct materials costs are $1.20 per pound of cookie mix, $12.00 per pound of milk chocolate, and $10.00 per pound of almonds. Each pound of cookies requires 1 minutes of direct labor in the mixing department and 3 minutes of direct labor in the baking department. The standard labor rates in those departments are $12.00 per direct labor hour (DLH) and $22.00 per DLH, respectively. Variable overhead is applied at a rate of $48.00 per DLH; fixed overhead is applied at a rate of $78.00 per DLH.Calculate the standard cost for a pound of Waterway's double chocolate almond supreme cookies. (Round answer to 2 decimal places, e.g. 3.51.)