What is 3/4+1/4+1/2=

The directional Derivative of the given function is; -4/√37

Formula for directional derivative is given by;

D_u g(a, b) = ∇g(a, b) * u

where u is a unit vector

We are given;

g(p, q) = p⁴ - p²q³

∇g(p, q) = (dg/dp, dg/dq) = ((4p³ - 2pq³), (p⁴ - 3p²q²))

∇g(1, 1) =  ((4(1)³ - 2(1 * 1³), (1⁴ - 3(1² * 1²))

∇g(1, 1) = (2, -1)

We are given v = i + 6j

Thus, unit vector of v is;

u = (i + 6j)/√(1² + 6²)

u = (i + 6j)/√37 = [1/√37, 6/√37]

Applying the directional derivative formula we have;

D_u g(1, 1) = ∇g(1, 1) * u

⇒ (2, -1) * [1/√37, 6/√37]

⇒ (2/√37) - (6/√37)

⇒ -4/√37

Read more about Directional Derivative at; https://brainly.com/question/9064150

Answer:

1/24

Step-by-step explanation:

1/8 divided 3/1

1/8 x 1/3=1/24

Answer: -4

Step-by-step explanation:

Let the integer be x.

\(8(x+1)-x=-20\\\\8x+8-x=-20\\\\7x+8=-20\\\\7x=-28\\\\x=-4\)

So, the integers are -4 and -3.

Answer:

|x|

Step-by-step explanation:

The answer is |x| because it can either be -x or x.

Hope this helps :)

Have a nice day!

Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

To know more about algebraic equations,

https://brainly.com/question/24875240

Answer: V≈9.42 yd^3

the formula to use for a cylinder is V=πr^2h. The radius is 0.5 since the diameter is 1. The height is 12. Plug them in and you get that answer.

Hope it helps!

The distance from the center to where the foci is located is 8 units

The formula associated with the focus of an ellipse is given as;

c² = a² − b²

where;

Let's use the Pythagorean theorem

Hypotenuse square = opposite square + adjacent square

Substitute the values into the formula

c² = 10² - 6²

Find the square

c² = 100 - 36

c² = 64

Find the square root

c = √64

c = 8

Thus, the distance from the center to where the foci is located is 8 units

Learn more about Pythagorean theorem here:

https://brainly.com/question/654982

#SPJ1

The equation can be used to model the number of subscribers, y, in the city t years after 2000 is  y = 200,000(1+60)t.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

The first step is to calculate the percentage increase for each year.

If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year.

(100+60)% = (100/100 + 60/100)

                 =  (1 + 0.6)

After 2,000, the subscribers will be 200,000×(1+0.6).

For the following years the 200,000×(1+0.6)t

So, the value of y will be given by,

Y=200,000(1+0.6)t

Hence,The equation Y=200,000(1+0.6)t .

To learn more about equation from the given link:

https://brainly.com/question/10270435

#SPJ4

1. False

2. True

3. True

4.  A register is not part of RAM.

1. False. The largest unsigned value is 2ⁿ⁻¹.

2ⁿ⁻¹ is the maximum value an unsigned value can take where n is the number of bits allocated for it.

2. In terms of 2's complement a signed number is equal to the value of the number but with the opposite sign. True.

For a signed number in 2's complement, we first convert the number to binary. Then we invert all the bits and add 1 to the result.

This gives us the 2's complement representation of the number. The result will have the same magnitude as the original number, but the opposite sign.

3. True. If the sum of two digits exceeds the radix, then we need to carry over to the next place value.

For example, if we are using base 10 (decimal), then we can only add two digits together if the sum is less than or equal to 9. If the sum is greater than 9, we need to carry over to the next place value.

Similarly, if we are using base 2 (binary), then we can only add two digits together if the sum is less than or equal to 1.

If the sum is greater than 1, we need to carry over to the next place value.

4. A register is not part of RAM. Registers are small, high-speed storage locations that are located within the processor itself.

RAM, on the other hand, is external to the processor and is used for temporary storage of data and instructions.

To know more about register, visit:

https://brainly.com/question/31481906

#SPJ11

Answer:

She should buy the coat and pay for shipping

Step-by-step explanation:

Set up a proportion to express the the 80 pounds to yen.

\(\frac{2}{292.82}\) = \(\frac{80}{x}\)

2 x 40 = 80

292.82 x 40 = 11,712.80

230.50 + 25.30 = 255.8

255.80 < 11,712.80

Helping in the name of Jesus.

Answer:

70

Step-by-step explanation:

\(\boxed{21}\)

When you multiply a negative and a negative, it is going to be a positive number. In this case, we're multiplying -3 and -7, which is equal to 21. If you're not sure of the answer for multiplication problems like this, just use a calculator to check your work.

Hi there! Hopefully this helps!

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

When you multiply two negatives (-, -,), you are gonna get a positive(+)

[Like making a cross out of two lines].

\(-3(-7) = +3(+7)\)

Answer:

41

Step-by-step explanation:

pay attention to the order of operation

4*7 - 63/ 9 +20, first multiplication and division from left to right

28  - 7  + 20 , second addition and subtraction from left to right

    21 +20

       41

Answer:

Step-by-step explanation:

Use PEDMAS

First perform division, then multiplication and then addition & subtraction.

4 * 7  - 63÷9 + 20 = 4*7 - 7 + 20    {Division}

                             = 28 - 7 + 20     {Multiplication}

                             =  41

The polynomial which is not equivalent to (5x – 2)(-2x + 4) is -10x + 20x + 4x – 8 and is therefore denoted as option A.

This is referred to as a type of algebraic expression in which the exponents of all variables should be a whole number.

(5x – 2)(-2x + 4) when expanded will give:

-10x² + 20x + 4x – 8 which can be rewritten as the following below:

This is therefore the reason why -10x + 20x + 4x – 8 was chosen as the correct choice.

Read more about Polynomial here https://brainly.com/question/1600696

#SPJ1

The options are:

A) -10x + 20x + 4x – 8

B) 4x + 20x – 10x2 – 8

C) -8 + 24x – 10x2

D) -10x2 + 24x – 8

The rent of the apartment during the 11th year would be $2,253.59 per month. To calculate the rent of the apartment during the 11th year, we can use the formula for compound interest:

Future Value = Present Value * (1 + Rate)^Time

In this case, the initial rent is $1300 per month, and the rate of increase is 9.5% per year. We need to find the future value after 10 years (since we're calculating for the 11th year).

First, let's calculate the future value after 10 years:

Future Value = $1300 * (1 + 0.095)^10

            = $1300 * (1.095)^10

            = $1300 * 2.531046

            ≈ $3293.36

So, the rent after 10 years would be approximately $3293.36 per month.

To find the rent during the 11th year, we need to increase this value by 9.5%:

Rent during 11th year = $3293.36 * (1 + 0.095)

                    = $3293.36 * 1.095

                    ≈ $3606.26

Therefore, the rent of the apartment during the 11th year would be approximately $3606.26 per month.

To know more about compound interest, refer here:

https://brainly.com/question/13155407#

#SPJ11

Answer:

53

Step-by-step explanation:

x - the age of the person who entered the room.

(12 + 19 + 24 + 21 + 21 + x)/6 = 25

12 + 19 + 24 + 21 + 21 + x = 150

97 + x = 150

x = 53

Answer:

53

Step-by-step explanation:

Answer:

Step-by-step explanation:

Refer to your previous question:

Radius of the inscribed circle is the apothem of the hexagon.

Apothem (a) and half of the side (s) make a 30-60-90 right triangle.

The ratio of the legs, as per property of 30-60-90 triangle:

Half the side is s = 10 units, then side of the hexagon is 20 units.

The area of the hexagon:

Correct choice is D

As per the given equation, the stone was dropped from a height of approximately 1.08 feet or about 13 inches.

The velocity of a free-falling object is an important concept in physics, and it is defined by the equation:

v = 2gh

In this equation, v represents the velocity of the object in feet per second, g represents the acceleration due to gravity in feet per second per second, and h represents the distance that the object has fallen in feet.

Suppose a stone is dropped from a certain height and strikes the water with a velocity of 138 feet per second. Our task is to estimate the height from which the stone was dropped.

To solve this problem, we need to rearrange the equation to solve for h. We start by dividing both sides of the equation by 2g:

h = v/2g

Substituting the given values, we get:

h = 138/2(32) = 1.078125

To know more about equation here

https://brainly.com/question/10413253

#SPJ1

Umm maybe u forgot to attach the picture we got similar question here hope it helps

Formula for inverse of matrix:

matrix              →           inverse matrix

\(A = \bold{ \sf { \begin{pmatrix}a&b\\ c&d\end{pmatrix} \ \ \ \rightarrow \ \ A^{-1} = \dfrac{1}{(ad-bc)} \begin{pmatrix}d&-b\\ -c&a\end{pmatrix} }}\)

The return value of the function call round(3.14159, 3) is c. 3.14. The round function rounds the first argument (3.14159) to the number of decimal places specified in the second argument (3). In this case, it rounds to 3.14.

The function call in your question is round(3.14159, 3). The "round" function takes two arguments: the number to be rounded and the number of decimal places to round to. In this case, the number to be rounded is 3.14159 and the desired decimal places are 3.

The return value is the result of the rounding operation. In this case, rounding 3.14159 to 3 decimal places gives us 3.142.

So, the correct answer is:

b. 3.142

Visit here to learn more about function call:

brainly.com/question/25762866

#SPJ11

Answer:

150

Step-by-step explanation:

The restaurant should expect to serve 180 customers in week 10.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. Therefore, the number of customers served in week 10 will be 180.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. This means that after 10 weeks, the number of customers served will be the same as it was in week 1. Since week 1 had 180 customers served, week 10 will also have 180 customers served.

As you can see, the number of customers served in week 10 is the same as the number of customers served in week 1. Therefore, the restaurant should expect to serve 180 customers in week 10.

Learn more about customer on

https://brainly.com/question/26313265

#SPJ1

Answer:

\(\overline{DE} \cong \overline{GF}\) and \(\overline{DG} \cong \overline{EF}\) by CPCTC

Step-by-step explanation:

The given information are;

The shape of the given polygon DEFG = Parallelogram with diagonal DF

Therefore, we have;

Response area

\(\overline{DE} \left | \right | \overline{GF}\) and  \(\overline{DG} \left | \right | \overline{EF}\) (Opposite sides of a parallelogram are parallel)

∠GFD ≅ ∠EFD (Alternate interior angles)

∠DFG ≅ ∠FDE (Alternate interior angles)

\(\overline{DF} \cong \overline{DF}\) (By the reflexive property of congruence)

Therefore

ΔDGF ≅ ΔFED (Angle-Side-Angle (ASA) condition of congruency)

Which gives;

\(\overline{DE} \cong \overline{GF}\) and \(\overline{DG} \cong \overline{EF}\) (Congruent Parts of Congruent Triangles are Congruent (CPCTC).

a. The continuous growth rate of the bacteria is 21%

b. The initial population of bacteria is 715

c. The culture will contain 2043 bacteria after 6 × 10⁻⁴ years

Since \(n(t) = 715e^{0.21t}\) represents the number of bacteria in the culture.

This function is similar to an exponential function of the form  \(y(t) = Ae^{\lambda t}\) where λ = growth rate

Comparing n(t) and y(t), we see that λ = 0.21

So, the continuous growth rate of the bacteria is 0.21 = 0.21 × 100 %

= 21%

So, the continuous growth rate of the bacteria is 21%

Since \(n(t) = 715e^{0.21t}\) represents the number of bacteria in the culture, the initial population of bacteria is obtained when t = 0.

So, \(n(t) = 715e^{0.21t}\)

\(n(0) = 715e^{0.21(0)} \\= 715e^{0} \\= 715 X 1\\= 715\)

So, the initial population of bacteria is 715

To find the time when the number of bacteria will be 2043, this means n(t) = 2043.

Since  \(n(t) = 715e^{0.21t}\)

Making t subject of the formula, we have

t = ㏑[n(t)/715]/0.21

So, substituting n(t) = 2043 into the equation, we have

t = ㏑[n(t)/715]/0.21

t = ㏑[2043/715]/0.21

t = ㏑[2.8573]/0.21

t = 1.05/0.21

t = 4.99

t ≅ 5 hours

Converting this to years, we have t = 5 h × 1 day/24h × 1 year/365 days

= 5/8760

= 5.7 × 10⁻⁴ years

≅ 6 × 10⁻⁴ years

So, the culture will contain 2043 bacteria after 6 × 10⁻⁴ years

Learn more about exponential bacteria growth here:

https://brainly.com/question/23654169

#SPJ1

The probability is approximately 0.000008155 or 0.0008155%.

To compute the probability of winning the million-dollar prize in the lottery, we need to determine the number of favorable outcomes (matching all six numbers) and the total number of possible outcomes.

The number of favorable outcomes is 1 because there is only one combination of six numbers that matches the numbers on your ticket.

The total number of possible outcomes can be calculated using the formula for combinations. Since there are 48 balls in the machine and 6 balls are drawn, the total number of possible outcomes is given by:

C(48, 6) = 48! / (6!(48-6)!) = 48! / (6!42!) = 12271512

Therefore, the probability of winning the million-dollar prize with a single lottery ticket is:

P(win) = favorable outcomes / total outcomes = 1 / 12271512 ≈ 0.00000008155

The complete question is:

In a certain lottery, 48 balls numbered 1 through 48 are placed in a machine and six of them are drawn at random. If the six numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. If in this lottery, the order the numbers are drawn in does matter, compute the probability that you win themillion-dollar prize if you purchase a single lottery ticket.

To know more about probability:

https://brainly.com/question/31828911

#SPJ4

Answer:

They are supplementary.

Step-by-step explanation:

A linear pair consists of two opposite angles whose non-common sides create a straight line. If a linear pair consists of two angles, then they are supplementary

Answer:

1 = 128°

2= 52°

3= 47°

4= 133°

5= 81°

Step-by-step explanation:

Since both the lines are parallel, we can write

angle 2 = 52° and angle 3 = 47° (Being alternate angles)

angle 5 + 52° + 47° = 180° (Sum of angles in a straight line), which gives angle 5 = 81°

angle 1 + 52° = 180° (Sum of co-interior angles), which gives angle 1 = 128°

angle 4 + 47° = 180° (Sum of co-interior angles), which gives angle 4 = 133°

y = (-1/8)x^2 is a downward opening parabola with vertex = the origin (0,0) relatively flat.

Parabola points horizontally  left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.  

what is parabola?

Focus and directrix are equidistant from the vertex.

Focus has an x coordinate = 0 and y coordinate <0 axis of symmetry is the y axis or x=0.

Find one more point on the parabola, go horizontally from the focus to the parabola, that distance equals the distance from the parabola at that point to the directrix. its x coordinate = -2 times its y coordinate. it helps to graph a rough sketch of the parabola.

y = (-1/8)x^2

y = (-1/8)(-2y)^2

y = -4y^2/8 = -y^2/2

2y = -y^2

2 =- y

x=-2y = -2(-2) = 4

plug that point (4,-2) into y =(-1/8)x^2

-2 = (-1/8)(4)^2 = -16/8 = -2 = the y coordinate of the vertex,

x coordinate = 0

the focus = (0,-2)

distance from the focus to the vertex = 2

distance from the directrix to the vertex = 2

the latus rectum = distance from the parabola points horizontally  left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.   "Latus rectum" is the math term for that distance.

To learn more about parabola refer to

https://brainly.com/question/64712

#SPJ1

y = (-1/8)x² is a downward opening parabola with vertex = the origin (0,0) relatively flat. Parabola points horizontally  left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.  

What is a parabola?

A parabola is a U-shaped plane curve. Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line.

The topic of conic sections includes a parabola, and all of its principles are discussed here.

Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms.

Several examples of parabolas in real life The wheel stance in yoga resembles a parabola.

The Banana's shape is beginning to resemble a parabola. A parabola is emerging from the Rainbow.

A series of points in a plane that are evenly spaced off from a straight line is referred to as a parabola.

Focus and directrix are equidistant from the vertex.

Focus has an x coordinate = 0 and y coordinate <0 axis of symmetry is the y axis or x=0.

Find one more point on the parabola, and go horizontally from the focus to the parabola, that distance equals the distance from the parabola at that point to the directrix. its x coordinate = -2 times its y coordinate. it helps to graph a rough sketch of the parabola.

y = (-1/8)x²

y = (-1/8)(-2y)²

y = -4y²/8 = -y²/2

2y = -y²

2 =- y

x=-2y = -2(-2) = 4

plug that point (4,-2) into y =(-1/8)x²

-2 = (-1/8)(4)² = -16/8 = -2 = the y coordinate of the vertex,

x coordinate = 0

the focus = (0,-2)

distance from the focus to the vertex = 2

distance from the directrix to the vertex = 2

the latus rectum = distance from the parabola points horizontally left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.   "Latus rectum" is the math term for that distance.

Hence, the distance from the focus to the vertex is 2 and the distance from the directrix to the vertex is 2 of the parabola y=-1/8x².

To learn more about parabolas visit,

brainly.com/question/64712

#SPJ1