What is a box plot? Explain in words how it looks,

The

equation of tangent and normal

to the surface z^2=4(1+x^2+y^2)at (2,2 ,6)  is

2x+2y+2z-24=0

and

2x+2y+6z-24=0

respectively.

Step-by-step explanation:

To find the equation of the

tangent and normal planes

at the point (2, 2, 6),  we first need to

find the gradient vector of the surface

, which is the vector pointing in the direction of the steepest ascent.

The gradient vector of the surface is grad(z^2)=<2x,2y,2z>

The equation

of the tangent plane

at the point (2, 2, 6) is given by

<2x,2y,2z> . (x-2,y-2,z-6) =0

so the

equation of tangent plane

is 2x+2y+2z-24=0

The

equation of the normal plane

at the point (2, 2, 6) is given by

<x,y,z> . (2,2,6) = constant

so the

equation of normal plane

is 2x+2y+6z-24=0

Note

: The

dot product

of the position vector <x,y,z> and the gradient vector <2x,2y,2z> gives the equation of the tangent plane. The position vector <x,y,z> gives the equation of the normal plane.

For more on

Tangent and Normal

Questions:

https://brainly.com/question/29185805

Answer:

If f(x) = +4, which of the following is the inverse of f(x)?

O A. ƒ˜¹(x) = 2(2+4)

B. ƒ˜¹(x) = 7(2-4)

C. ƒ˜¹(x) = 7(2+4)

D. f¯¹(x) = ²(2-4)

Step-by-step explanation:

The inequality value that would be able to show/x/ ≤ 5 is option A

In mathematics, inequality refers to a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than, less than, or not equal to the other.

The symbol that we have  is telling us that the value of the x would be less than  or it would be seen to be equal to five.

We can see that /x/ ≤ 5 would exclude the negative values and this can be seen in the option that is marked option A

Learn more about inequality:https://brainly.com/question/20383699

#SPJ1

Answer:

(0,2)

(3,0)

Step-by-step explanation:

Answer:

1.78f

Step-by-step explanation:

7/4=1.78 and then you add f

The scale factor is 4/5.

In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.

Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.

A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.

An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.

A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.

Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.

To find the scale factor, we can compare the ratios of the corresponding side lengths of the congruent triangles.

Scale factor = (corresponding side length in triangle FQX) / (corresponding side length in triangle CVI)

Let's first identify the pairs of congruent angles:

Angle FQX = angle CVI (both are right angles)

Angle XQF = angle ICV (corresponding angles)

Angle FXQ = angle CVI (corresponding angles)

Now let's write the ratios of the corresponding side lengths in a proportion:

FQ / CV = QX / VI = XF / IC

Substituting the given values, we have:

28 / 35 = 36 / 45 = 24 / 30

Simplifying each fraction, we get:

4 / 5 = 4 / 5 = 4 / 5

Therefore, the scale factor is 4/5.

To know more about corresponding visit:

https://brainly.com/question/7071992

#SPJ1

Answer:

∠b=82°

Step-by-step explanation:

143°=∠c+∠b (exterior angle property)

143°=61°+∠b

∠b=143-61

∠b=82°

Answer:

7(45)=7(40)+7(5)

Step-by-step explanation:

We need to represent 7(45) using the distributive property to simplify.

We can write 45 as 40+5

So it becomes,

7(45) = 7(40+5)

Distributive property is : a(b+c)=ab+ac

a=7, b = 40 and c = 5

7(40+5)=7(40)+7(5)

So, the correct option is (4).

Answer:

79.25

Step-by-step explanation:

8*5=40

40-3/8=39.625

39.625*2=79.25

Hope this helps

Answer:

I think it would be a rhombus.

Answer:

the number of students that enrolled after 15 year is 317

Step-by-step explanation:

The computation of the number of students that enrolled after 15 year is shown below;

We know that

Future value = Present value × (1 +rate of interest)^number of years

 = 100 × (1+8%)^15

= 100 × 1.08^15

= 317

Hence, the  number of students that enrolled after 15 year is 317

The same should be considered and relevant

Answer:

y = 0.8

Step-by-step explanation:

Answer:

P’(-1, 1), I’ (1, 2), G’(1,0)

Step-by-step explanation:

Step-by-step explanation:

1) let the number=x

six times a number=6x

Condition:

6x+4=22

2) eleven times a number=11x

Condition:

11x-5=50

3) 9 times a number=9x

Condition:

9x-7=-16

Note:if you need to ask any question please let me know.

Answer:

The second answer option

Step-by-step explanation:

Lmk if you need explanation

∠1 = 68°

∠2 = 22°

side 3 = 5 cm

side 4 = 19.5 cm

5: perimeter of ΔABC = 45 cm

6: perimeter of ΔPQR = 30 cm

7: Area of ΔPQR = 30 cm²

Similar triangles are triangles that have the same shape but may have different sizes. This means that corresponding angles of similar triangles are equal, and corresponding sides are in proportion.

The hotspots can be completed as follow:

∠1 = 180° - 22° - 90° = 68°  (angle sum in a triangle)

∠2 = 22° (similar triangle)

side 3 = √(13²-12²) = 5 cm (Pythagoras)

side 4 = √(18²+7.5²) = 19.5 cm (Pythagoras)

5: perimeter of ΔABC = AB + BC + AC = 7.5 + 19.5 + 18 = 45 cm

6: perimeter of ΔPQR = PQ + QR + PR = 5 + 13 + 12 = 30 cm

7: Area of ΔPQR = 1/2 * base * height = 1/2 * 12 * 5 = 30 cm²

Learn more about similar triangles on:

brainly.com/question/1675117

#SPJ1

The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

Learn more about fractions on:

brainly.com/question/78672

#SPJ1

Only the opposite edges of a rectangle's parallel and congruent angles are congruent. Although the sides and angles of a trapezoid may not always be identical, at least one set of its sides must be parallel.

In geometry, parallel lines are coplanar unlimited lines that never cross. In a particular three-dimensional space, the parallel planes represent the ones that never cross. Parallel curves are those with a constant minimum separation between them and no places of contact or intersection. In geometry, parallel lines are two lines which run in the exact same plane, evenly spaced apart, and hadn't cross. Both vertical and horizontal can be used. In commonplace items like train tracks, stacks of notebooks, and crossings for pedestrians, straight lines can be seen.

The form of Jackson's poster is best described as a rhombus. A quadrilateral with a rhombus has opposing sides that are parallel and all of its sides are equal. Additionally, it has congruent opposing angles. In addition to having parallel opposing sides, a parallelogram also has non-congruent sides and angles. Only the opposite edges of a rectangle's parallel and congruent angles are congruent. Although the sides and angles of a trapezoid may not always be identical, at least one set of its sides must be parallel.

To know more about parallel lines visit:

https://brainly.com/question/16701300

#SPJ1

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

learn more about velocity from

https://brainly.com/question/80295

#SPJ1

Answer:

18, 7.4 (if its 12.6) and 52, 92 (if its 12x6)

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The chi-square test statistic = 24.68.

The critical value for df = 11.34.

Since the calculated value of the chi square  falls in the critical region it is concluded that the two variables are dependent.

1) The null and alternative hypotheses are

H0: candy preferences of  students is independent of age.

Ha: candy preferences of  students is  not independent of age.

As the calculated value χ² = 24.68 lies in the critical region  χ² ≥χ² =11.34, null hypothesis is rejected.

Therefore, we conclude that there is not enough evidence to accept the null hypothesis .

Answer:

-0.4k + 14

Step-by-step explanation:

hope that helped!

The answer is 1/3

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer: 1/3

Step-by-step explanation: To subtract mixed numbers, first subtract the fractions.

Notice here however that we have 1/6 - 5/6

which will give us a negative fraction.

Since this will cause us a lot of trouble, instead,

let's rewrite the first mixed number.

We can do this by thinking of 3 and 1/6 as 2 + 1 and 1/6 or 2 + 7/6

by changing 1 and 1/6 into an improper fraction.

So 3 and 1/6 can be written as 2 and 7/6.

So we have 2 and 7/6 -  2 and 5/6.

Now, subtract the fractions.

So we have 7/6 - 5/6 which is 2/6.

Then subtract the whole numbers.

2 - 2 is 0.

However, we don't need to include 0 in our answer.

We can write our answer as 2/6.

However, 2/6 is not in lowest terms.

So divide the numerator and denominator by 2 to get 1/3.

So 3 and 1/6 - 2 and 5/6 is 1/3.

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

Learn more on scale factors here: https://brainly.com/question/28822248

#SPJ1

A. The current flowing through the inductor at time T is given by i(T) = (2/250) * (1 -\(e^{-4t}\))A B. The total stored energy in the inductor from t = 0 to t = T is given by W(T) = 2( \(e^{-4t}-e^{-8t}\)) J.

Finding the region beneath a curve or the entire accumulation of a quantity over a given period is the goal of the mathematical procedure known as integration. It is the inverse operation of differentiation and is frequently employed in a number of scientific, mathematical, and engineering disciplines.

Finding an antiderivative—a function that, when separated from the original function being integrated—is a necessary step in the integration process. The symbol for this antiderivative is frequently ∫f(x) dx, where f(x) is the function being integrated and dx denotes an incredibly minute change in x. The outcome of the integration is a family of functions that differ from one another by a constant quantity called the integration constant.

A. We know that v(t) = L di(t)/dt, where L is the inductance of the inductor and i(t) is the current flowing through it at time t. We can rearrange this equation to get di(t)/dt = v(t)/L, and then integrate both sides with respect to time from t = 0 to t = T to get:

∫[0, T] di(t)/dt dt = ∫[0, T] v(t)/L dt

After integrating the left side, we get:

i(T) - i(0)

This becomes i(T) as the starting current is zero. When the right side is integrated, we get:

(1/L) ∫[0, T] v(t) dt

When we replace the given phrase for v(t), we obtain:

(1/L) ∫[0, T] 8 -\(e^{-4t}\) dt

When we incorporate this expression, we get:

(1/L) * (-2  \(e^{-4t}\) ) |[0, T]

When the integration and simplification limitations are swapped out, we obtain:

i(T) = (2/L) * (1 -  \(e^{-4t}\) ) A

As a result, the current through the inductor at time T can be calculated as follows:

i(T) = (2/250) * (1 -  \(e^{-4t}\) ) A

B. As of time T, the inductor's total stored energy is given by:

W(T) = (1/2) L i²(T)

We obtain the following by substituting the expression for i(T) from section A:

W(T) = (1/2) * 250 * [(2/250) * (1 -  \(e^{-4t}\) )]²

Simplifying, we get:

W(T) = 2.5 * [(1 -  \(e^{-4t}\) )²] J

We integrate this expression with regard to time from t = 0 to t = T to determine the total energy stored from t = 0 to t = T:

W(T) = ∫[0, T] 2.5 * [(1 -  \(e^{-4t}\) )²] dt

We can rewrite this integral as follows by replacing the supplied expression for p(t):

W(T) = (1/8) ∫[0, T] p(t) dt

Integrating p(t) in relation to time results in:

p(t) = 64 ( \(e^{-4t}-e^{-8t}\))

∫[0, T] p(t) dt = 16 ( \(e^{-4t}-e^{-8t}\)) J.

When we use this expression to solve for W(T), we obtain:

W(T) = 1/8 * 16 ( \(e^{-4t}-e^{-8t}\)) J.

Simplifying, we get:

W(T) = 2 ( \(e^{-4t}-e^{-8t}\)) J.

As a result, the formula for the total energy stored in the inductor from t = 0 to t = T is as follows:

W(T) = 2 ( \(e^{-4t}-e^{-8t}\)) J.

To know more about current, visit:

https://brainly.com/question/1100341

#SPJ1

Answer:

Shelia is

Step-by-step explanation:

hope this helps plz mark brainlessly

Answer:

First problem: x = 5.7√2 = (57√2)/10

Second problem: x = 10√3

The number of decibels of sound emitted by the animal is approximately 145.05 dB.

To find the number of decibels (D) of sound emitted by the animal, we will use the formula D = \(10 * log10(I / I0)\), where I is the intensity of the sound (320 watts/cm2) and I0 is the reference intensity (10^-12 watts/cm2).

First, calculate the ratio I / I0 = \(320 / (10^-12) = 3.2 * 10^14.\)

Then, find the base-10 logarithm of this ratio: \(log10(3.2 * 10^14) ≈ 14.5051.\)

Finally, multiply this result by 10: D = \(10 * 14.5051\) ≈ 145.051 decibels.

So, the number of decibels of sound emitted by the animal is approximately 145.05 dB.

Read more about sound intensity here:

https://brainly.com/question/30101270

#SPJ1

Answer:

(C) Multiply first equation by -2 and second equation by 3, solution (1, 1)

Step-by-step explanation:

Simultaneous equations are set of equations which possess a common solution. The equations can be solved by eliminating one of the unknowns by multiplying each of the equations in a way that a common coefficient is obtained in the unknown to be eliminated.

Given the simultaneous equations:

3x - 5y = -2

2x + y = 3

First step:

Multiply first equation by -2 and multiply second equation by 3,

-6x + 10y = 4

6x + 3y = 9

Second step:

Add the two equations together,

13y = 13

Divide both sides by 13

y = 1

Third step:

Put y = 1 in the first equation

3x - 5(1) = -2

3x - 5 = -2

3x = 5 - 2

3x = 3

Divide both sides by 3:

x = 1

solution (x,y) = (1,1)

Option C

Learn more about simultaneous equations: https://brainly.com/question/30293776

#SPJ1