Factor completely 5x2 − 50x + 120.
Select one:
a. 5(x − 3)(x − 8)
b. (5x − 15)(x − 8)
c. (x − 4)(5x − 30)
d. 5(x − 4)(x − 6)


Question 2
Factor completely 64x2 − 1
Select one:
a. (8x − 1)(8x − 1)
b. (8x − 1)(8x + 1)
c. (1 − 8x)(1 − 8x)
d. (1 − 8x)(1 + 8x)

Answer:

90°, 75°, and 15°

Step-by-step explanation:

In a right triangle, one of the angles is 90°.

           Let x = the smallest angle

Then 60 + x = the third angle

The sum of the three angles is 180°.

90 + 60 + x + x = 180

          150 + 2x = 180

                    2x =  30

                      x =   15

      Measure of right angle              = 90°

Measure of smallest angle = x         =  15°

     Measure of third angle = 60 + x = 75°  

The measures of the angles are 90°, 75°, and 15°.

Answer:

C. X= -2.01 and x= 1.67

Step-by-step explanation:

[tex]3x {}^{2} + x + 10 = 0 \\ 3x {}^{2} + 6x - 5x + 10 = 0 \\ 3x(x + 2) - 5(x + 2) \\ (x + 2)(3x - 5 )\\ x + 2 = 0 \: \: or \: \: 3x - 5 = 0 \\ x = - 2 \: \: or \: \: x = \frac{5}{3} [/tex]

ANSWER

B. No real solutions

EXPLANATION

The given equation is

[tex]3 {x}^{2} + x + 10 = 0[/tex]

By comparing to

[tex]a {x}^{2} + bx + c= 0[/tex]

We have a=3,b=1 and c=10.

We substitute these values into the formula

[tex]D = {b}^{2} - 4ac[/tex]

to determine the nature of the roots.

[tex]D = {1}^{2} - 4(3)(10)[/tex]

[tex]D = 1 - 120[/tex]

[tex]D = - 119[/tex]

The discriminant is negative.

This means that the given quadratic equation has no real roots.

Answer:

0.36

Step-by-step explanation:

z is inversely proportional to x:

z = k / x

When x is 16, z has the value 0.5625.

0.5625 = k / 16

k = 9

What is the value of z when x= 25?

z = 9 / 25

z = 0.36

Answer:

The answer is 9/25 or .36 if you prefer it in decimal form.

Step-by-step explanation:

inversely proportional means there is a constant that we are going to divide by.

So z is inversely proportional to x means z=k/x where k is a constant.

We are given when x=16, z=0.5625.  This information will be used to find our constant value k.

0.5625=k/16

Multiply both sides by 16:

16(0.5625)=k

Simplify:

9=k.

This means no matter what (x,z) pair we have the constant k in z=k/x will always be 9.

The equation we have is z=9/x.

Now we want to find z when x=25.

z=9/25

z=.36

Answer:

336.7 yards away from the cabin....

Step-by-step explanation:

The angle 30.7° is also the angle of the upper interior angle of the triangle (near the cabin)

Use the tan function:

opposite = 200 yards

adjacent = x

tan(30.7°) = (opposite / adjacent)

tan(30.7°) = 200 yards/x

x * tan(30.7°) = 200 yards

x = 200 yards/ tan(30.7°)

x= 200/ 0.594

x = 336.7 yards.

336.7 yards away from the cabin....

Answer: 337

Step-by-step explanation: you have to round up

Answer:

8

Step-by-step explanation:

one sixth of 48 is 8 therefore you have eight tomato plants

Answer:  The length and width of the rectangle are 19 cm and 5 cm respectively.

Step-by-step explanation:  Given hat the length of a rectangle is four centimeters more than three times its width and the area of the rectangle is 95 square centimeters.

We are to find the length and width of the rectangle.

Let W and L denote the width and the length respectively of the given rectangle.

Then, according to the given information, we have

[tex]L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since the area of a rectangle is the product of its length and width, so we must have

[tex]A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.[/tex]

Since the width of the rectangle cannot be negative, so we get

[tex]W=5~\textup{cm}.[/tex]

From equation (i), we get

[tex]L=3\times5+4=15+4=19~\textup{cm}.[/tex]

Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.

The length of the rectangle is 19 and the width is 5 and it can be determined by using the formula of area of the rectangle.

The length of a certain rectangle is four centimeters more than three times its width.

If the area of the rectangle is 95 square centimeters,

The length and width of the rectangle.

Let the length of the rectangle be L,

And the width of the rectangle is W.

The length of a certain rectangle is four centimeters more than three times its width.

The perimeter formulas of different two-dimensional shapes:

Then,

[tex]\rm L = 3W+4[/tex]

And If the area of the rectangle is 95 square centimeters,

It is the number of square units inside the polygon.

The area is a two-dimensional property, which means it contains both length and width

[tex]\rm Area \ of \ the \ rectangle = length \times width\\\\L\times W = 95[/tex]

Substitute the value of L from equation 1,

[tex]\rm L\times W = 95\\\\(3W+4) \times W = 95\\\\3W^2+4W=95\\\\3W^2+4W-95=0\\\\3W^2+19W-15W-95=0\\\\W(3W+19) -5(3W+19) =0\\\\(3W+19) (W-5) =0\\\\W-5=0, \ W=5\\\\3W+19=0, \ W = \dfrac{-19}{3}[/tex]

The width of the rectangle can not be negative than W = 5.

Therefore,

The length of the rectangle is,

[tex]\rm L = 3W+4\\\\L = 3(5)+4\\\\L=15+4\\\\L=19[/tex]

Hence, The length of the rectangle is 19 and the width is 5.

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Answer:

84.4 gallons to the nearest tenth.

Step-by-step explanation:

Average usage = miles travelled  / gallons used  so:

6.3 = 532 / gallons used

Gallons used  =   532 / 6.3

= 84.44.

Final answer:

To find the gallons of gasoline used, divide the total miles (532) by the average miles per gallon (6.3). This calculation results in approximately 84.4444 gallons, which can be rounded to 84.4 gallons of gasoline used.

Explanation:

To calculate the amount of gasoline used by the boater who traveled 532 miles averaging 6.3 miles per gallon, you need to divide the total miles traveled by the average miles per gallon. The formula to use is:

Gallons used = Total miles traveled ÷ Average miles per gallon
Plugging in the values given:

Gallons used = 532 miles ÷ 6.3 miles/gallon
This gives us:

Gallons used = 84.4444... gallons
To round to the nearest tenth of a gallon, we would round 84.4444... to 84.4 gallons. Thus, the boater used approximately 84.4 gallons of gasoline.

Answer: 2.85

Step-by-step explanation:

Given : A​ 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is ​(1.4​, 4.3​) .

We know that the the confidence interval for population mean [tex]\mu[/tex] is given by :-

[tex]\mu\pm E[/tex], where E is the margin of error.

Lower limit of confidence interval = [tex]\mu-E=1.4[/tex]          (1)

Upper limit of confidence interval =  [tex]\mu+E=4.3[/tex]        (2)

Adding (1) and (2), we get

[tex]2\mu=5.7\\\\\Rightarrow\ \mu=2.85[/tex]

Hence, the point estimator of the mean percentage of reservations that are canceled on the day of the​ flight = 2.85

The point estimator for the mean percentage of airline reservations being canceled on the day of the flight is 2.85%, found by averaging the lower and upper bounds of the given 90 percent confidence interval.

The point estimator of the mean percentage of reservations that are canceled on the day of the flight can be determined from the confidence interval given as (1.4, 4.3).

The point estimator is simply the mean of the lower and upper bounds of the confidence interval. To find this, we add the lower and upper limits together and divide by two.

The calculation is as follows:

[tex]\frac{1.4 + 4.3}{2} = 2.85[/tex]

Therefore, the point estimator for the mean percentage of airline reservations being canceled on the day of the flight is 2.85%.

Answer:

(6^⅕) (cos(-24°) + i sin(-24°))

Step-by-step explanation:

First, we convert from Cartesian to polar:

r = √((-3)² + (-3√3)²)

r = √(9 + 27)

r = 6

θ = atan( (-3√3) / (-3) ), θ in the third quadrant

θ = atan(√3)

θ = 240° + 360° k

Notice that θ can be 240°, 600°, 960°, etc.

Therefore:

-3 − 3√3 i = 6 (cos(240° + 360° k) + i sin(240° + 360° k))

Now we take the fifth root:

[ 6 (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕

(6^⅕) [ (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕

Applying de Moivre's Theorem:

(6^⅕) (cos(⅕ × 240° + ⅕ × 360° k) + i sin(⅕ × 240° + ⅕ × 360° k))

(6^⅕) (cos(48° + 72° k) + i sin(48° + 72° k))

If we choose k = -1:

(6^⅕) (cos(-24°) + i sin(-24°))

Answer:

A real Even integers

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

It's all down the the double parentheses. They mean 'round down to the nearest integer'. Also because of the 2 the integer will be even.

Answer:

$173.45

Step-by-step explanation:

the beginning value is $400. if it loses 13%, that means it keeps 87% of its value. so you multiply by 0.87 6 times for each year

Answer:

The image is (0 , -6)

Step-by-step explanation:

* Lets explain some important facts

- When a point reflected across a line the perpendicular

 distance from the point to the line equal the perpendicular  

 distance from its image to the same line

- If the line of the reflection is horizontal then the perpendicular

 distance between the point and the line is y - y1 , and the

 perpendicular distance between the image and the line is y2 - y

- If point (x , y) reflected across the x- axis, then its image is (x , -y)

* Lets solve the problem

∵ Point (0 , 0) reflected across the line y = 3

∴ y = 3 and y1 = 0

∴ The distance between the point and the line is 3 - 0 = 3

∴ The distance between the image and the line also = 3

∴ y2 - 3 = 3 ⇒ add 3 to both sides

∴ y2 = 6

∴ The y-coordinate of the image is  6

∴ The image of point (0 , 0) after reflection across the line y = 3 is (0 , 6)

- The image of the point reflected across the x-axis, then change the

  sign of the y-coordinate

∴ The final image of point (0 , 0) is (0 , -6)

* The image is (0 , -6)

Answer: The following statements is not applicable to typologies, "They may be used effectively as independent or dependent variables."

Typology is a complex measurement that affect the categorization of observations in terms of their property on multiple variables.They are typically nominal composite measures.They involve a set of categories or types. They are often used when researchers wish to summarize the intersection of two or more variables.

Answer:

a)  N = 1.06S +2000

b)  the old salary is scaled by a factor of 1.06 and translated upward by 2000.

Step-by-step explanation:

a) a 6% raise means the new salary is 100% + 6% = 106% of the old one. A raise of an additional dollar amount simply adds to the scaled salary.

__

b) The translations are "math speak" for the English description of "increased by 6% and then raised by 2000". "Increased by 6%" means that .06 of the amount is added to the amount, effectively multiplying it by 1.06. "Raised by 2000" means 2000 is added.

Answer:

The answer is A(3.5,7)

Point of partition refers that a point intersect a particular line or curve at a fixed ratio. The coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).

The coordinates of the A is (5,8).

The coordinates of the B is (-1,4).

P partitions the segment AB in the ratio 1:3.

Point of partition refers that a point intersect a particular line or curve at a fixed ratio.

When a point [tex]p(x,y)[/tex] intersect a line which has the coordinates [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] at a ratio l and m then this point can be represent as,

[tex]p(x,y)=\left ( \dfrac{lx_2+mx_1}{l+m} , \dfrac{ly_2+my_1}{l+m} \right )[/tex]

Put the values,

[tex]p(x,y)=\left ( \dfrac{1\times(-1)+3\times 5}{1+3} , \dfrac{1\times 4+3\times8}{1+3} \right )[/tex]

[tex]p(x,y)=\left ( \dfrac{-1+15}{4} , \dfrac{4+24}{4} \right )[/tex]

[tex]p(x,y)=\left ( \dfrac{14}{4} , \dfrac{28}{4} \right )[/tex]

[tex]p(x,y)=(3.5,7)[/tex]

Hence the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).

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Answer:

Ballistic motion is usually modeled by a quadratic function.

Step-by-step explanation:

The usual assumption is that the only force acting on the object is that due to gravity, and that it is constant and directed downward. With this assumption, along with the assumption of a flat Earth, the resulting model is a downward-opening quadratic function.

Answer:

quadratic function.

Step-by-step explanation: "

ballistic motion is modeled with a quadratic function"

Answer:

33.75

Step-by-step explanation:

You first need to determine the total distance of the round trip. This is twice the 45 mile trip in the morning, which is 90 miles. In order to determine the total amount of time spent on the round trip, convert the time travel to minutes.

1 hr + 10 mins = 70 mins

1hr + 30 = 90 mins

So his total travel time would equal to 90+70=160 minutes

his average speed is:

90mi/160min * 60min/1hr = 90*60/160

= 33.75

Elijah's average speed for the round trip is approximately 31.76 miles per hour.

To calculate the average speed for the round trip, we need to determine the total distance traveled and the total time taken.

In the morning, Elijah drove 45 miles in 1 hour and 10 minutes. To convert the minutes to hours, we divide 10 minutes by 60, which gives us 10/60 = 1/6 hours. Therefore, his morning travel time is 1 hour + 1/6 hour = 7/6 hours.

On the way home, the same trip took him 1 hour and 30 minutes. Converting the minutes to hours, we divide 30 minutes by 60, which gives us 30/60 = 1/2 hours. Therefore, his return travel time is 1 hour + 1/2 hour = 3/2 hours.

To calculate the total distance traveled, we sum the distance from the morning trip and the return trip: 45 miles + 45 miles = 90 miles.

The total time taken for the round trip is the sum of the morning travel time and the return travel time: 7/6 hours + 3/2 hours = 17/6 hours.

To calculate the average speed, we divide the total distance by the total time: 90 miles / (17/6 hours).

Dividing 90 miles by 17/6 hours is the same as multiplying 90 miles by 6/17, which gives us (90 * 6) / 17 = 540/17.

Therefore, Elijah's average speed for the round trip is approximately 31.76 miles per hour.

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 The maximum error on volume = 270cm³

The relative error on the volume =0.08

The percentage error on volume = 8%.

How to calculate the volume of a given cube?

To calculate the volume of a given cube, the following steps should be taken as follows:

Formula for volume of a cube = a³

where;

a = 15 cm

Volume(V) = 15³ = 3375cm³

The maximum error on volume(dV);

= 3×side²×dx

= 3×15²×0.4cm

= 270cm³

The relative error on the volume;

= dV/V

= 270/3375

= 0.08

The percentage error on volume;

=Relative error × 100

= 0.08× 100

= 8%

Answer:

  To make 18 oz of furniture​ polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed.

Step-by-step explanation:

The ratio of ingredients is ...

  oil : vinegar = 3 : 1

So vinegar is 1 of the 3+1 = 4 parts of the polish mix. The amount of vinegar required for 18 oz of polish is ...

  (1/4)×(18 oz) = 4.5 oz

The remaining quantity is olive oil:

  18 oz - 4.5 oz = 13.5 oz

To make 18oz of furniture polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed. These quantities are found by setting up an equation based on the problem's conditions and solving for x.

To begin solving the problem we need to understand that both the vinegar and the olive oil are together making up the 18oz of furniture polish. Since the amount of olive oil is three times the amount of vinegar, we can denote the quantity of vinegar as 'x'. Thus, the quantity of olive oil will be '3x'.

Adding these together gives us the total ounces, thus, we have our equation: x + 3x = 18. Solving this, we get 4x = 18. Dividing by 4 gives us x = 18/4 = 4.5.

Therefore, to make 18oz of furniture polish, you will need 4.5 oz of vinegar and 13.5 oz (3 times 4.5) of olive oil.

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Answer:

Step-by-step explanation:

This is a right triangle with the 90 degree angle identified at D and the 60 degree angle identified at B. Because of the triangle angle sum theorem, the angles of a triangle all add up to equal 180 degrees, so angle C has to be a 30 degree angle.

There is a Pythagorean triple that goes along with a 30-60-90 triangle:

( x , x√3 , 2x )

where each value there is the side length across from the

30 , 60 , 90 degree angles.

We have the side across from the 90 degree angle, namely the hypotenuse. The value for the hypotenuse according to the Pythagorean triple is 2x. Therefore,

2x = 2√13

and we need to solve for x. Divide both sides by 2 to get that

x = √13

Now we can solve the triangle.

The side across from the 30 degree angle is x, so since we solved for x already, we know that side DB measures √13.

The side across from the 60 degree angle is x√3, so that is (√13)(√3) which is √39.

And we're done!

Answer:

  24,000(0.908)^t > 15,000; no

Step-by-step explanation:

The multiplier each year is 100% - 9.2% = 90.8% = 0.908. There is only one answer choice with this as the yearly multiplier.

_____

In order to answer the yes/no question, we chose to rewrite the inequality as ...

  24000·0.908^t -15000 > 0

The graph shows that is true for t < 4.87. In 5 years, the forest area will be below the minimum.

Answer:

[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{2\pi}{3},\frac{4\pi}{3}[/tex]

Step-by-step explanation:

If I'm interpreting that correctly, you are trying to solve this equation:

[tex]sin(\theta )+1=cos(2\theta)[/tex]

for theta.  To do this, you will need a trig identity sheet (I'm assuming you got one from class) and a unit circle (ditto on the class thing).

We need to solve for theta.  If I look to my trig identities, I will see a double angle one there that says:

[tex]cos(2\theta)=1-2sin^2(\theta)[/tex]

We will make that replacement, then we will have everything in terms of sin.

[tex]sin(\theta)+1=1-2sin^2(\theta)[/tex]

Now get everything on one side of the equals sign to solve for theta:

[tex]2sin^2(\theta)+sin(\theta)=0[/tex]

We can factor out the common sin(theta):

[tex]sin\theta(2sin\theta+1)=0[/tex]

By the Zero Product Property, either

[tex]sin\theta=0[/tex] or

[tex]2sin\theta+1=0[/tex]

Now look at your unit circle and find that the values of theta where the sin is 0 are located at:

[tex]\theta=\frac{\pi }{2},\frac{3\pi}{2}[/tex]

The next one we have to solve for theta:

[tex]2sin\theta+1=0[/tex] simplifies to

[tex]2sin\theta=-1[/tex] and

[tex]sin\theta=-\frac{1}{2}[/tex]

Look at the unit circle again to find the values of theta where the sin is -1/2:

[tex]\theta=\frac{2\pi}{3},\frac{4\pi}{3}[/tex]

Those ar your values of theta!

Answer:

The required expression is [tex]m=\frac{-15}{-3-4}[/tex].

Step-by-step explanation:

The general form of the equation is

[tex]gm=cm+rg[/tex]             .... (1)

We need to solve this equation for m.

Subtract cm from both the sides.

[tex]gm-cm=rg[/tex]

Taking out the common factor.

[tex]m(g-c)=rg[/tex]

Divide both sides by (g-c).

[tex]\frac{m(g-c)}{g-c}=\frac{rg}{g-c}[/tex]

[tex]m=\frac{rg}{g-c}[/tex]               ..... (2)

The given equation is

[tex]-3m=4m-15[/tex]            ..... (3)

From (1) and (3), we get

[tex]g=-3,c=4,rg=-15[/tex]

Substitute g=-3, c=4, rg=-15 in equation (2).

[tex]m=\frac{-15}{-3-4}[/tex]

Therefore the required expression is [tex]m=\frac{-15}{-3-4}[/tex].

Answer:

the corect answer on edge is c

Step-by-step explanation:

Answer:

Step-by-step explanation:

The second equation tells you ...

  y = 8 -3x

Using this expression in the first equation gives you ...

  2x +3(8 -3x) = 3

  2x +24 -9x = 3 . . . . . eliminate parentheses

  21 = 7x . . . . . . . . . . .  add 7x -3

  3 = x . . . . . . . . . . . . . . divide by 7

  y = 8 -3×3 = -1 . . . . . . use the second equation to find y

The solution is (x, y) = (3, -1).

Answer:

the correct answers for edu are 2x+3(8-3x)=3 than 3 and last -1

Step-by-step explanation:

The midpoint can be defined using formula,

[tex]M(x_m=\dfrac{x_1+x_2}{2},y_m=\dfrac{y_1+y_2}{2})[/tex]

So by knowing [tex]x_m, x_1[/tex] and [tex]y_m, y_1[/tex] we can calculate [tex]x_2, y_2[/tex]

First we must derive two equations,

[tex]x_m=\dfrac{x_1+x_2}{2}\Longrightarrow x_2=2x_m-x_1[/tex]

and

[tex]y_m=\dfrac{y_1+y_2}{2}\Longrightarrow y_2=2y_m-y_1[/tex]

Then just put in the data,

[tex]x_2=2\cdot(-2)-3=-7[/tex]

[tex]y_2=2\cdot(-3)-0=-6[/tex]

So the other endpoint has coordinates [tex](x,y)\Longrightarrow(-7, -6)[/tex] therefore the answer is D.

Hope this helps.

r3t40

To work out the mid point of two points you, add the x coordinates and divide by 2, and you take the y coordinates and divide by two:

So:

[tex]midpoint = \frac{sum.of.x-coords}{2},  \frac{sum.of.y-coords}{2}[/tex]

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

So the x-coords of the midpoint is:

[tex]\frac{sum.of.x-coords}{2}[/tex]

and

y -coords of midpoint is:

[tex]\frac{sum.of.y-coords}{2}[/tex]

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

However, in this question we are trying to work out one of the endpoints.

First let's say that the coordinates of the missing endpoint is:

(x , y)

_____________________________________________

That means that the x-coords of the midpoint of (x, y) and the other endpoint (3, 0) is :

[tex]\frac{3 + x}{2}[/tex]

However, we already know the x-coord of the midpoint ( it's -2). So we can form an equation to workout x:

[tex]\frac{3 + x}{2} = -2[/tex]                (multiply both sides by 2)

[tex]3 + x = -4[/tex]                      (subtract 3 from both sides)

[tex]x = -7[/tex]

This is the x-coord of the other endpoint

_______________________________________________

Let's do the same for the y coordinates:

We know y coords for the midpoint of (x, y) and (3, 0) is:

[tex]\frac{0 + y}{2}[/tex]

But we also know the ycoord is -3. So we can form an equation and solve for y:

[tex]\frac{0+y}{2} = -3[/tex]

[tex]\frac{0 + y}{2} = -3[/tex]   (multiply both sides by 2)

[tex]0 + y = -6[/tex]                (simplify)

[tex]y = -6[/tex]

This is the y-coord of the other endpoint

___________________________________

Now we just put these coords together to get the coordinate of the other endpoint:

Endpoint is at:

(x, y)                           (substitute in values that we worked out)

=  (-7, -6)

_________________________________________________

D. (-7, -6)

________________________________________________

Note:

If there is anything you don't quite understand or was unclear

- please don't hesitate to ask below in the comments.

Answer:

3

Step-by-step explanation:

the missing no is 3

I have answered ur question

Answer:

3

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Given that Tristan records the number of customers who visit the store each hour on a Saturday.

His data representing the first seven hours are 15, 23, 12, 28, 20, 18, and 23.

There are 7 entries and if written in ascending order 12,15,18,20,23,23,28

Median = middle entry -20

If one more entry is added then we have two middle entries and median would be the average of the two.

Hence if median is to remain the same, eighth hour no of customers visited should be 20

Answer is 20

Answer:

v = 1.45 × 10⁷ m/s

Step-by-step explanation:

Given:

Inner radius of the cylinder, r₁ = 20 mm = 0.2 m

outer  radius of the cylinder, r₂ = 80 mm = 0.8 m

Potential difference, ΔV = 600V

Now, the work done (W) in bringing the charge in to the inner conductor

W = [tex]\frac{1}{2}mv^2[/tex]

where, m is the mass of the electron = 9.1 × 10⁻³¹ kg

v is the velocity of the electron

also,

W = qΔV

where,

q is the charge of the electron = 1.6 × 10⁻¹⁹ C

equating the values of work done and substituting the respective values

we get,

qΔV =  [tex]\frac{1}{2}mv^2[/tex]

or

1.6 × 10⁻¹⁹ × 600 = [tex]\frac{1}{2}\times 9.1\times 10^{-31}v^2[/tex]

or

[tex]v = \sqrt\frac{2\times 600\times 1.6\times 10^{-19}}{9.1\times 10^{-31}}[/tex]

or

v = 14525460.78 m/s

or

v = 1.45 × 10⁷ m/s

Final answer:

The speed of the electron as it reaches the inner conductor is calculated using conservation of energy, giving a final speed of approximately 1.46 × 107 m/s.

Explanation:

Electron Velocity in Coaxial Conductors

An electron released from the outer conductor will be accelerated towards the higher potential inner conductor due to the electric field between them. To calculate the speed of the electron as it reaches the inner conductor, we use the concept of conservation of energy. The electrical potential energy lost by the electron as it moves from the outer to the inner conductor is converted into kinetic energy.

The initial potential energy (Ui) of the electron can be given by:

where q is the charge of the electron (q = -1.6 × 10-19 C) and V is the potential difference (V = 600 V).

The final kinetic energy (Kf) when the electron reaches the inner conductor is:

where m is the mass of the electron (m = 9.11 × 10-31 kg) and v is the final speed we want to find.

Using conservation of energy (Ui + Ki = Kf + Uf and noting that both the initial kinetic energy Ki and the final potential energy Uf are zero), we get:

Solving for v gives us the final speed of the electron:

This is the speed of the electron when it reaches the inner conductor.

Answer:

  2√5

Step-by-step explanation:

The Pythagorean theorem tells you how to find the distance from the origin.

  d = √((-2)² +4²) = √20 = 2√5

The vector's magnitude is 2√5 ≈ 4.47214.

Answer:

The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]

Step-by-step explanation:

Given : Vector whose terminal point is (-2, 4).

To find : What is the magnitude of the position vector?

Solution :

We have given, terminal point (-2,4)

The magnitude of the point x(a,b) is given by,

[tex]|x|=\sqrt{a^2+b^2}[/tex]

Let point x=(-2,4)

[tex]|x|=\sqrt{(-2)^2+(4)^2}[/tex]

[tex]|x|=\sqrt{4+16}[/tex]

[tex]|x|=\sqrt{20}[/tex]

Therefore, The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]

Final answer:

To find the vertices of the system of inequalities x ≤ 3, -x + 3y ≤ 12, and 4x + 3y ≥ 12, we can solve each pair of inequalities to find the intersection points. The vertices are the points where the lines intersect. The coordinates of the vertices are (3, 0), (0, 4), and (3, 5). For the function f(x, y) = x - 2y, the point where the maximum value is found in the system of inequalities is (5, 3).

Explanation:

To find the coordinates of the vertices formed by the system of inequalities x ≤ 3, -x + 3y ≤ 12, and 4x + 3y ≥ 12, we can solve each pair of inequalities to find the intersection points. The vertices are the points where the lines intersect.

The solution is (3, 0), (0, 4), and (3, 5), so the correct answer is B.

For the second question, to find the point where the maximum value is found for the function f(x, y) = x - 2y in the system of inequalities graphed below, we need to locate the highest point on the graph. From the given options, (5, 3) is the point where the maximum value is found, so the correct answer is D.