Someone can help me pleaseeee, for tonight with 2 or 3 will be fine
FIND THE LENGTH

Complete Question:

Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)

Answer:

Directional derivative at point (1,3),  [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Step-by-step explanation:

Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)

g(x,y) = [tex]x^2y^5[/tex]

[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]

[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]

Let P =  (1, 3) and Q = (3, 1)

Find the unit vector of PQ,

[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]

[tex]|\bar{PQ}| = \sqrt{8}[/tex]

The unit vector is therefore:

[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]

The directional derivative of g is given by the equation:

[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Answer:

  B

Step-by-step explanation:

You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).

The shading is below the line because y-values are less than (or equal to) values on the line.

Choice B matches the attached graph.

Answer:

it is graph b

Step-by-step explanation:

Answer:

$41,330

Step-by-step explanation:

To find the cost to asphalt a circular path, first, calculate the area of the circular path:

Area of circular path = area of big circle (A1) - Area of small circle (A2)

Area of circle = πr²

Radius of big circle (R) = 145 ft

Area of big circle (A1) = 3.14*145²

= 3.14*21,025

A1 = 66,018.5 ft²

Radius of small circle (r) = 80ft

Area of small circle (A2) = 3.14*80²

= 3.14*6,400

A2 = 20,096 ft²

=>Area of path =  66,018.5 - 20,096 = 45,922.5 ft²

If 100ft = $90

45,922.5 ft = x

Cross multiply and find x (cost to asphalt the circular path)

100*x = 45,922.5*90

100x = 4,133,025

Divide both sides by 100

x = 4,133,025/100

x = $41,330.25

To the nearest dollar, $41,330 is needed to asphalt the circular path

Answer:

4

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

JN* NK = LN * NM

3x = 2*6

3x = 12

Divide by 3

3x/3 =12/3

x =4

Answer: Volume = [tex]\frac{20\pi }{3}[/tex]

Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be

V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]

For this case, the region generated by the conditions proposed above is shown in the attachment.

Because it is revolting around the y-axis, the formula will be:

[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]

Since it is given points, first find the function for points (3,2) and (1,0):

m = [tex]\frac{2-0}{3-1}[/tex] = 1

[tex]y-y_{0} = m(x-x_{0})[/tex]

y - 0 = 1(x-1)

y = x - 1

As it is rotating around y:

x = y + 1

This is R(y).

r(y) = 1, the lower limit of the region.

The volume will be calculated as:

[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]

[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]

[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]

[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]

[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]

[tex]V=\frac{20\pi }{3}[/tex]

The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].

Answer:

The value will decrease.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;

[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]

[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]

If [tex]x_0 = 1\\[/tex]

We will iterate using the formula;

[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]

Given f(x) = x³ + 5x +2

f(x0) = f(-1) = (-1)³ + 5(-1) +2

f(-1) = -1 -5 +2

f(-1) = -4

f'(x) = 3x²+5

f'(-1) = 3(-1)²+5

f'(-1) = 8

[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]

f(-0.5) = (-0.5)³ + 5(-0.5) +2

f(-0.5) = -0.125-2.5+2

f(-0.5) = -0.625

f'(-0.5) = 3(-0.5)²+5

f'(-0.5) = 3(0.25)+5

f'(-0.5) = 0.75+5

f'(-0.5) = 5.75

[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]

The estimated solution is -0.3913 (to 4dp)

Answer:

Hey there! Your answer would be:  [tex]3x^2+4=x[/tex]

The quadratic formula is (-b±√(b²-4ac))/(2a), and helps us find roots to a quadratic equation.

All quadratic equations can be written in the [tex]ax^2+bx+c[/tex] form, and a, b, and c, are numbers we need for the quadratic equation.

Our given quadratic equation is 1±√(-1)²-4(3)(4)/2(3)

We can see that b is -1, as -b is positive 1.

That gives us  [tex]ax^2+-1x+c[/tex], which can be simplified to [tex]ax^2-x+c[/tex].

We can see that a is 3, because 2a=6, so a has to be 3.

That gives us [tex]3x^2-x+c[/tex]

Finally, we see that 4 is equal to b, clearly shown in the numerator of this fraction.

Which gives us a final answer of [tex]3x^2-x+4[/tex], or [tex]3x^2+4=x[/tex]

Answer:

173.20 ft

Step-by-step explanation:

[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]

Answer:

stratified random sampling technique

The sampling technique described, where sixteen students are randomly selected from each grade level, is called "stratified random sampling."

We have,

Stratification involves dividing the population (in this case, the high school students) into distinct subgroups or strata based on certain characteristics

By selecting a random sample from each stratum (each grade level), the sampling technique aims to ensure that each subgroup is represented in the sample in proportion to its size within the population.

This approach allows for a more representative sample and provides insights into the eating habits of students across different grade levels.

Thus,

The sampling technique described, where sixteen students are randomly selected from each grade level, is called "stratified random sampling."

Learn more about stratified random samplings here:

https://brainly.com/question/15604044

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Answer:

Q(x) = 4

R(x) = 0

Step-by-step explanation:

Q(x) = 2x + 2 ----- (1)

R(x) = x² - 1 -------- (2)

i) For (R * Q)(5)  and [(Q * R)], we have as follow:

[(x² - 1)(2x + 2)] (5)

= (2x³ + 2x² - 2x - 2)(5)

= x³ + x² - x - 1

When x = -1

x³ + x² - x - 1 = 0

∴ (x³ + x² - x - 1) ÷ (x + 1) = x² - 1

If x + 1 = 0

x = -1

and x² - 1 = 0

x = 1

From (1), when x= 1: Q(x) = 4

From (2), when x= 1 or -1: R(x) = 0

Answer:

Vertical Line

Step-by-step explanation:

A vertical line is x = [a number]

A horizontal line is y = [a number]

Answer:

vertical line

Step-by-step explanation:

A vertical line is of the form

x =

All the x values are the same and the y value changes

x = -4 is a vertical line

Answer:

B) [tex]x^2-3x+15[/tex]

Step-by-step explanation:

[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]

A) [tex]x^2+15x+15[/tex]

B) [tex]x^2-3x+15[/tex]

C) [tex]13x^2 + 3x + 15[/tex]

D) [tex]x^4-3x + 15[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

B. x² - 3x + 15

▹ Step-by-Step Explanation

7x² + 6x - 9x - 6x² + 15

Collect like terms

x² + 6x - 9x + 15

Subtract

x² - 3x + 15

Final Answer

x² - 3x + 15

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

198.5

Step-by-step explanation:

() = 200 - 1.5

() = 198.5

im not sure if this is what you are asking, but i hope it helps

Answer:

S=p(200-1.5)  

Answer:

(a) remainder is -40

(b) The remaining zeroes are (x+3) and (x-3)

Step-by-step explanation:

p(x) = x^4 - 2x^3 -7x^2 + 18x – 18

(a) Remainder of P(x) / (x+1) can be found using the remainder theorem, namely

let x + 1 = 0 => x = -1

remainder

= P(-1)

= (-1)^4 - 2(-1)^3 -7(-1)^2 + 18(-1) – 18

= 1 +2 -7-18-18

= -40

remainder is -40

(b)

If one zero is 1-i, then the conjugate 1+i is another zero.

in other words,

(x-1+i) and (x-1-i) are both factors.

whose product = (x^2-2x+2)

Divide p(x) by (x^2-2x+2) gives

p(x) by (x^2-2x+2)

= (x^4 - 2x^3 -7x^2 + 18x – 18) / (x^2-2x+2)

= x^2 -9

= (x+3) * (x-3)

The remaining zeroes are (x+3) and (x-3)

Answer:

30 m^3

Step-by-step explanation:

Answer:

B. 20m3

Step-by-step explanation:

i dont know if its correct, hope it is tho

Answer:

A pair of vertical angles are ADE and BDC. Vertical angles are located across from each other.

Answer:

D. Angle ADE and angle BDC

Step-by-step explanation:

Vertically opposite angles are equal.

Angle ADE and angle BDC are a pair of vertical angles.

Answer:

[tex]f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }\\[/tex]

Step-by-step explanation:

[tex]1/u=1/f-1/v\\\frac{1}{f} = \frac{1}{u} +\frac{1}{v}\\Divide- both- sides- by; 1\\\frac{1}{f} \div \frac{1}{1} = ( \frac{1}{u} +\frac{1}{v}) \div \frac{1}{1}\\\\f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }[/tex]

Answer:

  y

Step-by-step explanation:

The expression

  y = f(x)

tells you that y is the dependent variable, and that it depends on x, the independent variable. The independent variable is always the function argument. Any variable that depends on that is the dependent variable.

Answer:

given,

AB= 17

AC= 8

angle BCA =90°

as it is a Right angled triangle ,

taking reference angle BAC

we get,h=AB=17

b=AC=8

p=BC=?

now by the Pythagoras theorem we get,

p=

[tex] \sqrt{h { }^{2} - b {}^{2} } [/tex]

so,p=

[tex] \sqrt{17 {}^{2} - 8 {}^{2} } [/tex]

[tex] = \sqrt{225} [/tex]

=15 is the answer....

hope its wht u r searching for....

The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.

This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.

a(n) = a(1) + d( n- 1)

d = 3

This is the formula of an arithmetic sequence.

an = a(1) + d( n- 1)

Substitute in the values of

a(1) = 7 and

d = 3

a(n) = 7 + 3 ( n- 1)

Simplify each term.

a(n) = 7 + 3n- 3

Subtract 3 from 7.

a(n) =  3n + 4

The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Substitute in the value of n to find the nth term.

a(55) = 3 (55) + 4

Multiply 3 by 55 .

a(55) = 165 + 4

Add 165 and 4.

a(55) = 169

Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.

To learn more about Aritmetic sequence

https://brainly.com/question/6561461

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Answer:

  8 : 1

Step-by-step explanation:

The graph shows a point at the location corresponding to 8 cups of raspberry juice and 1 cup of lemon-lime soda. So the ratio is ...

  raspberry juice : lemon-lime soda = 8 : 1

Answer:

D

Step-by-step explanation:

raspberry : lemon lime soda::8:1

Answer:

The price of one reusable bottle is $8.12

Step-by-steetp explanation:

Ms stone wanted to purchase two reusable bottles but discovered she had only ⅝of the Mone and that ⅝ is equal to $ 10.15.

So the cost of what she wants to purchase will be called x.

Mathematically

⅝ * x = 10.15

X = (10.15*8)/5

X = 81.2/5

X= 16.24

The price of the two bottles is $16.24

So the price if one bottle will be calculated as follows.

2 bottles=$ 16.24

One bottle= $16.24/2

One bottle= $8.12

The price of one reusable bottle is $8.12

Answer:

3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.47, n = 460, \mu = 0.47, s = \sqrt{\frac{0.47*0.53}{460}} = 0.0233[/tex]

What is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Sample proportion lower than 0.47 - 0.05 = 0.42 or higher than 0.47 + 0.05 = 0.52.

Since they are equidistant from the mean of 0.47 they are equal. So we find one of them, and multiply by two.

Lower than 0.42:

pvalue of Z when X = 0.42. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.42 - 0.47}{0.0233}[/tex]

[tex]Z = -2.15[/tex]

[tex]Z = -2.15[/tex] has a pvalue of 0.0158

2*0.0158 = 0.0316

3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%

Answer:

x=4200, y=2700

Step-by-step explanation:

let x be first account

y the second

x+y=6900

0.03x+0.08y=342

solve by addition/elimination)

multiply first equation by 0.03

0.03x+0.03y=207  subtract from second

0.03x+0.03y-0.03x-0.08y=207-342

0.05y=135

y=2700, x=4200

Answer:

(A)  (-19,-8)

Step-by-step explanation:

Given that the graph is an inverse variation.

The equation of variation is:

[tex]x=\dfrac{k}{y}[/tex]

Since point (-8, -19) is on the graph

[tex]-8=\dfrac{k}{-19}\\k=152[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac{152}{y}[/tex]

[tex]\text{When y=-8},x=\dfrac{152}{-8}=-19\\\\\text{When y=19},x=\dfrac{152}{19}=8\\\\\text{When y=8},x=\dfrac{152}{8}=19\\\\\text{When y=-19},x=\dfrac{152}{-19}=-8[/tex]

Therefore, the point that is also on the graph is:

(A)  (-19,-8)

Answer:

D

Step-by-step explanation:

Answer:

b = (3V)/h

Step-by-step explanation:

You have to rearrange the equation so that it is equal to b.

V = hb/3

3(V) = (hb/3)(3)

3V = hb

(3V)/h = (hb)/h

b = (3V)/h

Answer:

2

Step-by-step explanation:

5÷2 1/5 = 2

Answer:

2 3/11

Step-by-step explanation:

To find the original number, we need to divide 5 by 2 1/5.

5/ 2 1/5

Convert 2 1/5 to an improper fraction:

11/5

5/ 11/5

When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.

5*5/11

25/11

2 3/11

Hey there! :)

Answer:

C. (0, -6).

Step-by-step explanation:

In slope-intercept form ( y = mx + b), the 'b' value represents the y-intercept.

In this instance:

y = 4x - 6

The 'b' value is equal to -6. This means that the y-intercept is at (0, -6).

-------------------------------------------------------------------------------------------

The y-intercept can also be solved for by substituting in 0 for x:

y = 4(0) - 6

y = 0 - 6

y = -6.

Answer:

C. (0, –6)

Step-by-step explanation:

y = 4x - 6

The equation is:

y = mx + b

where b is the y-intercept.

In this case, - 6 is the vertical intercept.

Do not confuse from (-6, 0) because that represents an x-intercept.