Once you have completed the above problems and checked your solutions, complete

Problem 1.

My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.

Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.

Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.

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Problem 2.

For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.

If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.

Answer:

A. 30 degrees

Step-by-step explanation:

Set the two angles equal to each other:

3x-15 = 45-x

Solve for x:

4x -15 = 45

4x = 60

x = 15

Finally, plug in the x to one of the equations (preferably 45 - x since it's easier to solve) and solve for x.

45 - 15 = 30

Answer:

A 30 degrees

Step-by-step explanation:

Answer:

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

Step-by-step explanation:

Given that:

y = 6x - x² , y = 8  about  x = 2

To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8

6x - x² - 8

6x - x² - 8 = 0

-x² + 6x - 8 = 0

x² - 6x + 8 = 0

(x -4) (x - 2  ) = 0

So;

x = 2 , x = 4

Thus, the region bound of the integral  are from a = 2 and b = 4

Therefore , the volume of the solid can be computed as :

[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]

[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]

[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]

[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

Answer: please find the answer in the explanation.

Step-by-step explanation:

1.) The distance is not proportional to time. Because the distance was constant from time = 3 seconds to 10 seconds.

2.) A person running down a field to score a touchdown. Not enough information.

3. A dog jogging at a constant speed for 20 minute. The distance is proportional to time because of the constant speed.

4.) The distance is proportional to time because their is increase in distance covered and increase in time taken.

5.) A truck passing through the 4 cities at a constant speed. The distance is proportional to time because the speed is constant.

6.) A horse running around a race track. Distance is not proportional to time because this is not a linear motion.

Answer:

6cot 50

Step-by-step explanation:

Tan 50=6/x

x= 6/(tan 50)

x= 6cot 50°

Answer:

? = 6 cot 50

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 50 = 6 /?

? tan 50 = 6

? = 6 / tan 50

We know that 1 / tan 50 = cot 50

? = 6 cot 50

The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.

Answer :

The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.

Answer:The minimum of function A occurs 1 unit higher than the minimum of function B.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Trust

Answer:

its 28 dude, because it says that adults and children are played more on saturday.(adults on Saturday=$8 and children under 12 are $4

Answer:

The area can be expressed as: [tex]\pi r^2+lw[/tex].

We have l=10, because 18-2(4)

We have w=8, as given.

Thus, the rectangle area is 80.

There are two semicircles, but they add to form a full circle, which makes things a lot easier. We have the circle area formula, and substituting the values gives us 50.24 as the circle volume

80+50.24=130.24.

Rounded to 1 decimal place that is 130.2

Hope this helps :)

Answer:

can you send a picture please? i have no clue how to answer this. it seems confusing with the numbers

Answer:

7 units

Step-by-step explanation:

(number line:)

<- -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ->

         there are 7 units from 1 to -6 (you don't count the 0)

(I'm not sure if you understood my explanation, but I do am sure about the answer, so if there is something you didn't understand let me know, and which part are you confused about so I can help you out!)

Answer:

[tex]\huge\boxed{\sf 7\ units}[/tex]

Step-by-step explanation:

To find that how much far they are from each other, we can subtract both of them.

=> 1 - (-6)

=> 1 + 6

=> 7 units

So, they are 7 units apart from each other.

Answer:

[tex]\boxed{ \sf 1350 \ cm^2}[/tex]

Step-by-step explanation:

Surface area of a cube = 6a²

a = side length

The side length is given 15 cm.

[tex]6(15)^2[/tex]

[tex]6(225)[/tex]

[tex]1350[/tex]

The surface area of the cube is 1350 cm².

Answer:

In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B. Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

23-(12+6)+8

23-18+8

31-18

13

answer is 13

Step-by-step explanation:

Using the BODMAS rule,bracket of division or multiplication, addition or subtraction.

This applies the rule:

therefore,

23- (12+6)+8 ,calculate within bracket first

=23-(18)+8

now remove the bracket,by multiply by the -1

=23-18+8

the start calculate from the left to right

=23-10

=13

therefore the answer is 13

Answer:

20 and 1/4.

Step-by-step explanation:

9x^2 * y^(-2), for x = -3 and y = 2.

9(-3)^2 * 2^(-2)

= 9 * 9 * (1/4)

= 81 * 1/4

= 81 / 4

= 20.25

= 20 and 1/4.

Hope this helps!

Answer:

Step-by-step explanation:

Let's fill the values in.

9(-3)*2(2)*-2

Using PEMDAS, we would first multiply the two numbers where x and y used to be.

-27 * 4 * -2

Now we would finish multiplying this.

216.

Hope this helps!! <3

Answer:

x = 16

Step-by-step explanation:

3x - 10 = 2(x+3)

First step is solve this:

2(x+3) = 2*x + 2*3 = 2x + 6

then:

3x - 10 = 2x + 6

3x - 2x = 6 + 10

x = 16

Check:

3*16 - 10 = 2(16+3)

48 - 10 = 2*19 = 38

Answer:

x = 16

Step-by-step explanation:

you start off by isolating the variable

Answer:

Tablets.

Step-by-step explanation:

You didn't want an explanation so....here you go....no explanation.

Hope that helps and maybe earns a brainliest.

Have a great day!

This is assuming that p is not in the denominator. To make it more clear that p is not in the denominator, I recommend you write (1/3)p.

Taking 1/3 of a number is the same as dividing by 3.

Example:

27/3 = 9

27*(1/3) = 9

Answer:

25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

y=x-1

2=3-1

2=2

y=-3x+11

2=-3(3)+11

2=-9+11

2=2

Answer:

Step-by-step explanation:

If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.

Step-by-step explanation:

half life time-50%-8.4hr

so for 10%- 8.4/5=1.68 hr

now for 70%

1.68 × 7 = 11.76 hrs

to one decimal place - 11.8hrs

11.8 hours ago, there were 70% more of the substance if an isotope of lead has a half-life of 8.4 hours.

Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.

Half-life period - 50% -8.4hours

so for 10%- 8.4/5 = 1.68 hour

now for 70%

1.68 × 7 = 11.76 hours

To one decimal place - 11.8hours

Hence, 11.8hours is the answer.

To learn more about half-life here

https://brainly.com/question/17159063

#SPJ2

Answer:

[tex]\boxed{y = -2}[/tex]

Step-by-step explanation:

Hey there!

To find y when x is -5 we go to -5 on the x-axis.

When at -5 find where the blue line is vertical to -5,

which is -2.

Hope this helps :)

Answer:

infinite solutions

Step-by-step explanation:

4x = 2x + 2x + 5(x-x)

Simplify

4x = 2x + 2x + 5*0

4x = 2x + 2x

4x = 4x

Divide by x

4 =4

This is always true so this has infinite solutions

White figure Area = 128[tex]\pi[/tex]

White surface area = appro. 301

Yellow area = 320[tex]\pi[/tex]

Yellow Surface area = approx. 653

Area found with = 2πrh+2πr2

Surface Area found with = 2πrh+2πr2

You need to memorize them for tests

Hope that helped!!! k

Answer:

3(4)to the 3

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The area of triangle PQR which is an SAS triangle, to the nearest tenth, is: A. 24.1 m²

The area of an SAS triangle = ½ × bc × sin(A).

Given the following:

Area of triangle PQR = ½ × (14)(6) × sin(35)

Area of triangle PQR = 24.1 m²

Learn more about the area of an SAS triangle on:

https://brainly.com/question/22472034

#SPJ2

Answer:

  One-sixth d + one-eighth d = 1

Step-by-step explanation:

When they work together, their rates of completion add. They want to build one shed, so the number of sheds being built is ...

  (Kaitlyn's sheds per day)×(days Kaitlyn works) +(Mark's sheds per day)×(days Mark works) = 1 shed

  (1/6)d + (1/8)d = 1 . . . . matches the last choice