Plsplzplzplzplz help

We can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.

Given the equation of the surface is xy + 15x + z^2 = 209.

Let's determine the shortest distance from the surface to the origin.

The shortest distance between the surface and the origin is given by the perpendicular distance, which can be calculated as follows:

Firstly, we need to determine the gradient of the surface, which is the vector normal to the surface.

For this purpose, we need to write the surface equation in the standard form, which is:xy + 15x + z^2 = 209 xy + 15x + (0)z^2 - 209 = 0 (the coefficients of x, y, and z are a, b, and c).

The gradient of the surface is given by the vector: ∇f = (a, b, c) = (y + 15, x, 2z) at the point P(x, y, z), which is a point on the surface.

Here, the normal vector is ∇f = (y + 15, x, 2z).

Now, let's consider a point A on the surface which is closest to the origin.

Let the coordinates of A be (a, b, c).

Therefore, the position vector of A is given by: OA = ai + bj + ck.

The direction of the position vector is in the direction of the normal vector, and therefore: OA is parallel to ∇f.

Thus, we can write: OA = λ∇f = λ(y + 15)i + λxj + 2λzkWhere λ is a scalar.

Since A lies on the surface, we have: a*b + 15a + c^2 = 209.

We also know that OA passes through the origin.

Therefore, the position vector of A is perpendicular to the direction vector OA.

This gives us: OA·OA = 0⟹ (ai + bj + ck)·(λ(y + 15)i + λxj + 2λzk) = 0

Simplifying this equation gives us:aλ(y + 15) + bλx + c(2λz) = 0

Also, we know that OA passes through the origin.

Therefore, the magnitude of OA is equal to the distance of A from the origin.

Hence, we can write: |OA| = √(a^2 + b^2 + c^2)

The value of λ can be obtained from the equation: aλ(y + 15) + bλx + c(2λz) = 0orλ = -2cz / (b + a(y + 15))

Substituting this value of λ in OA, we get: OA = λ(y + 15)i + λxj + 2λzk= -2cz/(b + a(y + 15)) (y + 15)i - 2cz/(b + a(y + 15)) xj - 4cz^2/(b + a(y + 15))k

Substituting this value of λ in |OA|, we get: |OA| = √[(2cz/(b + a(y + 15)))^2 + (2cz/(b + a(y + 15)))^2 + (4cz^2/(b + a(y + 15)))^2] = 2cz√[(y + 15)^2 + x^2 + 4z^2] / |b + a(y + 15)|

The distance of the point A from the origin is |OA|, which is minimized when the denominator is maximized. The denominator is given by |b + a(y + 15)|.

Thus, we have to maximize the denominator with respect to a and b. The condition for maximum value of the denominator is obtained by differentiating the denominator with respect to a and b separately and equating it to zero. The values of a and b obtained from these equations are substituted in the equation a*b + 15a + c^2 = 209 to obtain the coordinates of the point A, which is closest to the origin.

Hence, we can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

4

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻  

\(\boxed{\text{Calculating the Answer...}}\\\\8^{\frac{2}{3}}\\-----------\\\text{Recall the Exponent Rule: }} a^{\frac{b}{c}} = \sqrt[c]{a^b}\\\\\rightarrow {\frac{\text{Power}}{\text{Root Index}}\\\\\)

\(-----------\)

\(\rightarrow 8^{\frac{2}{3}}\\\\\rightarrow \sqrt[3]{(8^2)}\\\\\rightarrow\sqrt[3]{64}\\\\\rightarrow \boxed{4}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

4

Step-by-step explanation:

\(8^{\frac{2}{3} }\)

=\((2)^3*\frac{2}{3}\)

=\((2)^\frac{3*2}{2}\)

=\((2)^\frac{6}{3}\)

=\(2^2\)

=4

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

They are known as the two types of first is null hypothesis and the second is alternative hypothesis. These two hypotheses bear opposite viewpoints.

H0: also known as null hypothesis: It is a statement about the population that either is taken to be true or is used to put forth an argument until it can be shown to be incorrect behind a reasonable doubt.

Ha: also known as the alternative hypothesis: It is a state about the population that is contradictory to H0 and what we conclude when we reject H0.

H0 every time has a symbol with an equal in it. It never has a symbol with an equal in it. The option of the symbol depends on the wording of the hypothesis test.

Yet, be aware that many researchers use = in the null hypothesis, even with > (greater) or < (less) as the symbol in the alternative hypothesis.

We can accept this practice because we only decide to reject or not reject the null hypothesis.

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Hi there!

\(\large\boxed{y = 12, x = 3}\)

The two trapezoids are similar, so we can determine a common scale factor:

OL/UR = NM/TS

9/3 = 6/2

3 = 3

Trapezoid ONML is 3x larger than UTSR, so:

RS = 4, LM = y

3RS = LM

3 · 4 = y = 12.

Find x using the same method:

3UT = ON

3(2x+1) = 4x + 9

6x + 3 = 4x + 9

2x = 6

x = 3.

Answer:

  с  60,800,000

Step-by-step explanation:

Any scientific or graphing calculator can evaluate this expression for you.

__

When adding numbers in scientific notation, they need to have the same multiplier exponent. Here, it is convenient to use 10^6:

  8.0×10^5 = 0.8×10^6

  6.0×10^7 = 60×10^6

Then the sum is ...

  (0.8 +60)×10^6 = 60.8×10^6 = 60,800,000

we have

Reiner had $133

Joel had $57

let x = T-shirt

then, after buying T-shirts:

Reiner = 133 - x

Joel = 57 - x

and Reiner had 3 times Joel had, so

answer: each T-shirt cost $19

Polynomials can be classified by the number of terms they have.

A function with only one term, for example "3x⁵" is a monomial.

If you add/subtract two monomials you determine a "binomial"

If there are three terms (or monomials) is a "trinomial"

The given polynomial is

Since it has only one term, it can be classified as a "Monomial"

Answer:

1) 6041921252.76

2) 3783786034.9

Step-by-step explanation:

You move the decimal point 9 spaces to the right

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Answer:

2.4375 pounds

Answer:

My guess is $29

Step-by-step explanation:

So first I take the difference of the 10th and 6th month, which is 116.

I take that and divide it by 4, because that was the change in 4 months(10-6)

116÷4=29

Answer:10

Step-by-step explanation:

Answer:

it’s just 2x^2

it’s not factorable

120 + 4w is the expression to show the total number of songs on Iris's playlist after w weeks.

She total ahs 120 songs already

She downloads or adds 4 songs every week

An expression to show the total number of songs on Iris's playlist after w weeks is:

120 + 4w

An expression or mathematical expression is a limited combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

Many authors differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical objects.

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Answer:

The sum is 12.5

Step-by-step explanation:

Answer:

1. C

2. B

3. A

4. D

5. B

6. C

7. B

8. C

9. C

10. B

11. A

12. D

13. B

14. A

15. A

Step-by-step explanation:

Connexus Sequences and Series Online Practice

100%

Check the picture below.

notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.

Here is the solution process:

                     3 x² -  2 x  -   6                      

x² + 0x + 2 | 3 x⁴ -  2 x³ +  0  x² -     x -   4

                    3  x⁴ + 0 x³ +  6  x²                

                             - 2 x³  -  6  x² -      x -   4

                             - 2 x³  + 0  x² -   4 x        

                                        -  6  x² +  3 x  -  4

                                        -  6  x²  + 0 x  -  12

                                                        3 x  + 8

Long division:

Therefore, the correct option is "A".

Answer:

D

Step-by-step explanation:

so they ran the trial ten times so now you have to aks how many times did they get heads

which would be 2/10 times

you want the accuracy of which they got so divide 2/10

we know the probability of getting heads is 50%

so when you calulate it, it will give you 0.2 use the percent button and get 0.1

Answer:

a) 280 + 15x = cost

  240 + 25x = cost

b) 280 + 15x = 240 + 25x which is 4 months

c) Fitness Club CanFit

Step-by-step explanation:

Bruh moment

let me know if i was right.

history= 70

total = 400

now

student of history in college = student in history÷ total students of history×100%

= 70/400×100%

= 17.5 %. (A)

The absolute deviation of each of the data values are 4, 1 and 3 respectively.

The absolute deviatuon gives the distance of any given value in a dataset to the mean value. The absolute deviation is always positive as it does not consider the side to which the value belongs.

Absolute deviation = |value - mean|

Mean = 4

Absolute deviation of 0 = |0 - 4| = 4

Absolute deviation of 3 = |3 - 4| = 1

Absolute deviation of 7 = |7 - 4| = 3

Hence, The absolute deviation of each of the data values are 4, 1 and 3 respectively.

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Answer:

64

Step-by-step explanation:

The sum means addition

To put this into algebra :

x + 43 = 107

Subtract 43 from both sides:

x = 107 - 43

x = 64

Hope this helped and brainliest please.

Answer:

The missing number is 64.

{43 + 64 = 107}

Step-by-step explanation:

Given that,

→ Sum of a number and 43 is 107.

Let's form the equation,

→ 43 + x = 107

Now find the required value of x,

→ 43 + x = 107

→ x = 107 - 43

→ [ x = 64 ]

Hence, the number is 64.

Answer:

La expresion x² - 11x = -30 es un trinomio de segundo grado,¿ cual de los siguientes productos equivale a esta expresión?A) (x + 6)(×+5)

Step-by-step explanation:

Step-by-step explanation:

180° = 2x + 70 + 4x + 10

180° = 2x + 4x + 70 + 10

180° = 6x+ 80

180 - 80 = 6x

100 = 6x

6x = 100

x = 16.66

x ≈ 17°

Answer:

(4,-10)

Step-by-step explanation:

Graphing calculator

Answer:

The point represents a 36 months old Panda whose weight is 82kg

Step-by-step explanation:

Given

See attachment for plane

Required

What does the point shown represent

The point is: (36,82)

Age is plotted on the x-axis and weight on the y-axis:

This means that:

\(Age= 36\ months\)

\(Weight = 82\ kg\)

So, the point represents a 36 months old Panda whose weight is 82kg

Answer:

yes

Step-by-step explanation:

Answer:

ENGLISH PLZ

Step-by-step explanation:

I CANT UNDERSTAND spanish