The discriminant of the function is

The equation of the tangent line to the curve x+y-1=ln(x^6+y^6) at the point (1,0) is x - 1 = 0

The equation of the tangent line to the curve given by the equation x+y-1=ln(x^6+y^6) at the point (1,0) can be found using implicit differentiation.

Step 1: Differentiate both sides of the equation with respect to x:

d/dx (x+y-1) = d/dx (ln(x^6+y^6))

Step 2: Apply the chain rule to the right side of the equation:

1 + dy/dx = (1/(x^6+y^6)) * (6x^5 + 6y^5 * dy/dx)

Step 3: Rearrange the equation to isolate dy/dx:

dy/dx = (6x^5 + 6y^5)/(x^6 + y^6 - 1)

Step 4: Substitute the coordinates of the point (1,0) into the equation to find the slope of the tangent line at that point:

dy/dx = (6(1)^5 + 6(0)^5)/(1^6 + 0^6 - 1) = 6/0

Note: The slope of the tangent line is undefined, indicating that the tangent line is vertical.

Step 5: Using the point-slope form of a line, we can write the equation of the tangent line:

y - 0 = (6/0)(x - 1)

The equation of the tangent line to the curve x+y-1=ln(x^6+y^6) at the point (1,0) is x - 1 = 0. However, it's important to note that the slope of the tangent line is undefined, indicating that the line is vertical.

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Answer:

I think it would be the addition property of equality

Step-by-step explanation:

the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2 is \vec n = <0,0,-1>

A unit normal vector is a normal vector with magnitude 1, and it points in the direction that is perpendicular to the tangent to the curve at a given point.

To determine the unit normal vector to a curve, it's important to find the tangent first and then find the normal. In this case, we're looking for the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2.

To find the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2, it is necessary to find the tangent to the curve and then find the normal. This is a crucial step in understanding the geometry of curves in 3D space.

To find the tangent to the curve, we'll differentiate the vector equation with respect to t and evaluate it at t = 2. The derivative of \vec r (t) is given by:

d\vec r/dt = <1, -2t^-3, -4e^-t^-4>

So the tangent to the curve at t = 2 is:

d\vec r/dt = <1, -2(2)^-3, -4e^-2^-4> = <1, 1.5, -1.648721>

Next, we'll find the normal to the tangent by taking the cross product of the tangent with a fixed vector, for example, the unit vector i = <1,0,0>. The cross product of two vectors results in a vector that is perpendicular to both of them.

The cross product of the tangent and the unit vector i is given by:

\vec T x \vec i = <1, 1.5, -1.648721> x <1,0,0> = <0,0,-1.5>

Since the magnitude of the normal is not 1, we'll normalize it by dividing it by its magnitude:

\vec n = \vec T x \vec i / ||\vec T x \vec i|| = <0,0,-1.5> / ||<0,0,-1.5>|| = <0,0,-1>

So the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2 is given by:

\vec n = <0,0,-1>

This is the unit normal vector that points in the direction that is perpendicular to the tangent to the curve at t = 2. The magnitude of 1 ensures that it's a unit vector and the direction points towards the normal direction.

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Answer:

1 1/4

Step-by-step explanation:

3 - 1 = 2

2 - 3/4 = 1 1/4

The probability that three points chosen uniformly and independently on a circle fall on a semicircle is 1/2 or 50%.

The probability of three points chosen randomly and independently on a circle falling on a semicircle is 1/2, or 50%. This is because the probability of a point landing on either side of the semicircle is equal. The points are chosen on a circle, so each point has an equal probability of being on either side of the semicircle. Therefore, the probability of three points randomly chosen on a circle landing on a semicircle is 1/2 or 50%.

Let A, B, and C be the three points chosen on a circle.

The probability that A, B, and C fall on the semicircle is:

P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

= (1/2) x (1/2) x (1/2)

= (1/2)^3

= 1/8

Therefore, the probability that three points chosen randomly and independently on a circle fall on a semicircle is 1/8 or 12.5%.

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The probability that three points chosen uniformly and independently on a circle fall on a semicircle is written as 1/8.

The term probability in math is defined as the chances of something materializing based upon the ratio of its number of outcomes to the number of outcomes of the whole sample space the event relies upon.

While we looking into the given question, here let us consider that A, B, and C be the three points chosen on a circle.

Then the probability that A, B, and C fall on the semicircle is calculated as,

=> P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

Now, we have to apply the value of each probability, then we get

=> (1/2) x (1/2) x (1/2)

Therefore, the resulting value is

=> (1/2)³ = 1/8

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Answer: (1,2)

Step-by-step explanation:

1)

x+y=3

y=-x+3

x | 0 | 3 |

y | 3 | 0 |

2)

3x+y=5

y=-3x+5

x | 0 | 2 |

y | 5 | -1 |

Answer:

a) 3 cubes

b) 6 cubes

c) 15 cubes

d) 16 cubes

The number of small cubes in each cuboid is:

(a) 3, b) 6, c) 27, and d) 16.

Given are four cuboids.

It is required to find the number of small cubes that are used to make these cuboids.

a) There are only 3 small cubes.

b) There is only one step of cubes.

Number of cubes = 3 + 3 = 6

c) There are 3 cubes arranged horizontally and 3 cubes arranged vertically through each surface.

Number of cubes in one step = 3 × 3 = 9

There are 3 steps like that.

So, total number of cubes = 3 × 9 = 27

d) There are 4 cubes in the horizontal position.

And there are 4 cubes going down.

Total number of cubes = 4 × 4 = 16

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The first 10 terms sum in the geometric series is 5115.

The first term of geometric series = 5

Common ratio = 2

First, let us discuss how to calculate the sum of n terms of GP. Assume the sum of the first n terms of a GP with first term a and common ratio r. Then the first 'n' terms of GP are of form a, ar, ar², ... ar^(n-1). Let S be the sum of the GP of n terms. Then:

Sₙ = a + ar + ar² + ... + ar^(n-1) ... (1)

Multiply both sides by r:

rSₙ = ar + ar² + ... + arⁿ ... (2)

Subtracting equation (1) from equation (2):

rSₙ - Sₙ = (ar + ar² + ... + arⁿ) - [a + ar + ar² + ... + ar^(n-1)]

Sₙ (r - 1) = arⁿ - a

Sₙ (r - 1) = a(rⁿ - 1)

Sₙ = a(rⁿ - 1)/(r - 1)

Note that, here, r ≠ 1.

Sₙ = -a(1 - rⁿ)/(-(1 - r)) = a(1 - rⁿ)/(1 - r).

Sₙ = a[1-rⁿ]/[1-r]

S₁₀ = 5[1-2¹⁰]/[1-2]

S₁₀ = 5[1023]

S₁₀ = 5,115

--The given question is incorrect, the correct question is

"The first term in a geometric series is 5 and the common ratio is 2. Find the sum of the first 10 terms in the series."--

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After performing the linear regression evaluation, the equation of the regression line is:

(i) y = 1.40x + 1.45

To locate the linear regression line for the given records, we will use a statistical software program or a calculator. By analyzing the data points, we can decide the equation of the road that satisfactorily represents the connection between the hours of the stand being open (x) and the profit (y).

After performing the linear regression evaluation, the equation of the regression line is:

y = 1.40x + 1.45

This equation shows that for each extra hour the stand is open, the profit increases by using $1.40. The y-intercept, represented with the aid of the regular term 1.45, shows that although the stand isn't always open, there may be nevertheless a base income of $1.45.

The linear regression line for the given statistics indicates a positive relationship between the hours of the stand being open and the earnings earned. As the hour's increase, the earnings have a tendency to increase as nicely.

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The correct question is:

The linear regression line for the given data is y = 1.28x + 2.93. This equation represents the relationship between the hours the stand is open (x) and the corresponding profit (y).

To find the linear regression line for the given data, we can use statistical software or a calculator. The linear regression line represents the best fit line through the data points.

First, we list the given x and y values:

x: 1, 2, 3, 4, 5, 6, 7

y: 3.58, 5.18, 6.24, 7.97, 7.09, 8.31, 11.33

Using the software, we calculate the linear regression line. The result is y = 1.28x + 2.93, rounded to two decimal places.

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QUESTION

gabriel and raj were running a lemonade stand at the local park. they decided to pay their sister to operate the stand. the following values represent the profit y after x hours of the stand being open. using a calculator or statistical software, find the linear regression line for the data. enter your answer in the form y =mx+b, with m and b both rounded to two decimal places.

X    Y

1   3.58

2   5.18

3   6.24

4    7.97

5   7.09

6    8.31

7    11.33

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

Answer:

-37/6

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Assume Stefan won x games,

Marion would win: 5(x-4) games,

5(x-4)= 15

5x-20= 15

5x= 15+20

5x= 35

x= 7.

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

below

Step-by-step explanation:

three cards angles are greater than 100°

total cards = 8

probability = 3/8

Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

The writer's profit is $84.00. To calculate the writer's profit, you need to consider the premiums collected from selling the call options, the interest earned on those premiums, and the cost of buying the shares to complete the call contract.The premiums collected from selling the call options are:$0.91 x 100 = $91.00The interest earned on those premiums over 30 days at 5% is:($91.00 x 0.05 x 30) / 365 = $0.38The total amount of cash available to the writer at expiry is therefore:$91.00 + $0.38 = $91.38The cost of buying the shares to complete the call contract is:100 x $42 = $4,200.00Since the underlying asset is worth $39 at expiry, the writer can buy the necessary shares for:100 x $39 = $3,900.00The writer's profit is therefore:$91.38 - $3,900.00 = $84.00Since the writer made a profit, the answer is $84.00.

Hope I helped you...

The students are most likely studying percentages or proportions related to the data being represented in the circle graph.

To know the students most likely to study:

The group of students are most likely studying a circle graph that represents data using sectors labeled with numbers and symbols.

This type of graph is commonly used to show proportions or percentages of a whole.

Therefore, the students are most likely studying percentages or proportions related to the data being represented in the circle graph.

The options "frequency distribution" and "bar graph" are less likely to be studied in this context as they are different types of graphs that represent data differently.

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Answer:

y=6/5x+3

Step-by-step explanation:

Get into y=mx+b from

Subtract 6x

-5y=-6x+12

Divide by -5

y=6/5x-12/5

Use y-y1=m(x-x1)

y-(-3)=6/5(x-(-5))

Negative times a negative is a positive

y+3=6/5(x+5)

Distribut

y+3=6/5x+6

Subtract 3

y=6/5x+3

Hope this helped!

Answer:500

Step-by-step explanation:

√250000=500

Answer:

\( \sqrt{250000} \\ \sqrt{500} \times \sqrt{500 } \\ { \sqrt{500 } }^{2} \\ 500\)

Thank you ☺️☺️

Explanation:

x = some unknown number

"A number less than 12" translates to x < 12

This number x is also more than -16, so x > -16 which is the same as -16 < x

Combine -16 < x with x < 12 to end up with -16 < x < 12

x is between -16 and 12, excluding both endpoints.

A number line diagram might help picture what is going on.

Answer:

-16<x< 12

Step-by-step explanation:

it's simple algebra. -16 is less than x which x is less than 12. X is more than -16 but less than 12

ans. (c) 1/2

given line,

y = 1/2 x -2

we know that the slope form of the line is given by

y =mx+c

comparing both equations we get

m= 1/2

hence, the slope is 1/2

The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

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Answer:

both are correct

Step-by-step explanation:

the 4th raw of the keisha's one same to first raw of david's.david's one is simple & keisha's isn't

y= a(x - 5)^2 - 2.This equation represents a parabola with its vertex at the point (5, -2) and opens upward if a > 0 or downward if a < 0.

To translate the vertex of a quadratic function right 5 units and down 2 units, we can use the vertex form of the quadratic equation:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and a is the coefficient of the quadratic term.

To translate the vertex right 5 units, we need to replace x with (x - 5). This will shift the entire parabola 5 units to the right.

To translate the vertex down 2 units, we need to subtract 2 from the value of k. This will shift the entire parabola 2 units downward.

Therefore, the equation that translates the vertex right 5 units and down 2 units is:

y= a(x - 5)^2 - 2

where a is the coefficient of the quadratic term. This equation represents a parabola with its vertex at the point (5, -2) and opens upward if a > 0 or downward if a < 0.

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Step-by-step explanation:

input is C and D and output is A and B

The volume of the object is 3164 ft³.

We have,

The object has two shapes.

Sphere:

Radius = 7 ft

Volume.

= 4/3 πr³

= 4/3 x π x 7³

= 4/3 x 3.14 x 343

= 1436 ft³

Box:

Volume.

= 12 x 12 x 12

= 1728 ft³

Now,

The volume of the object.

= 1728 + 1436

= 3164 ft³

Thus,

The volume of the object is 3164 ft³.

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Answer:

Step-by-step explanation:

Answer:

The first choice is the answer of course