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let his speed upstream=S
Let the speed of the current=C
Let the distance he covered paddling upstream=D

D / [S  - C] = 15/60,
[D + 2] / [S + C]==[D+2] /C,
[2 - D] / C ==15/60, solve for C, D, S

C==4 mph - speed of the current
S ==8 mph - his speed in still water
D==1 mile - upstream from the Ridge when he realized he had lost his donuts.

First, we can square both sides of the equation to get rid of the square root. This gives us:

(a - 3)^2 = -a

We can then expand the left-hand side to get:

a^2 - 6a + 9 = -a

Combining like terms, we get:

a^2 - 5a + 9 = 0

We can then factor this equation to get:

(a - 1)(a - 9) = 0

This means that a = 1 or a = 9.

However, we need to check both solutions to make sure they are valid. If we substitute a = 1 into the original equation, we get:

(1 - 3)/sqrt(1) = -sqrt(1)

This is not a valid equation, since the square root of 1 is 1 and 1 - 3 is not equal to -1.

If we substitute a = 9 into the original equation, we get:

(9 - 3)/sqrt(9) = -sqrt(9)

This is a valid equation, since the square root of 9 is 3 and 9 - 3 is equal to 6.

Therefore, the only solution to the equation is a = 9.

(p,q,r) = (-4,1,7)

There are 6! = 720 ways to arrange the numbers 1, 2, 3, 4, 5, 6 in a row. However, not all of these arrangements will have the product of any two adjacent numbers being even.

In order for the product of two adjacent numbers to be even, at least one of the numbers must be even. Therefore, we can group the numbers into two sets: even numbers and odd numbers. There are 3 even numbers (2, 4, 6) and 3 odd numbers (1, 3, 5).

We can arrange the even numbers in 3! = 6 ways. We can arrange the odd numbers in 3! = 6 ways. Now, we need to consider the placement of the odd numbers. Since the product of two adjacent numbers must be even, the odd numbers can only be placed in the spaces between the even numbers. There are 4 spaces between the 3 even numbers. We need to choose 3 of these spaces to place the 3 odd numbers. We can do this in 4C3 = 4 ways.

Therefore, the total number of ways of arranging the numbers 1, 2, 3, 4, 5, 6 in a row so that the product of any two adjacent numbers is even is 3! * 3! * 4 = 72.

which is ~51.4 degrees

I think the answer is 280.

280/7 = 40

so its 40*12-40*5 = 280.

https://web2.0calc.com/questions/system_26201

Link to similar question:

https://web2.0calc.com/questions/probability_40373

14 nCr 5 + 14 nCr 4==3,003 solutions

There are 488 solutions.

The sum of the interior angles of a regular 20-gon is (20-2)*180 = 3600 degrees. Each angle of a regular 20-gon is 3600/20 = 180 degrees.

The sum of the interior angles of a regular heptagon is (7-2)*180 = 900 degrees. Each angle of a regular heptagon is 900/7 degrees.

Angle BCD is the angle between two consecutive sides of a regular 20-gon, so it is 180 degrees. Angle ACB is an interior angle of a regular heptagon, so it is 900/7 degrees. Therefore, angle BCD is 180 - 900/7 = 360/7 degrees.

To find the measure of angle BCD in degrees, we can use the properties of regular polygons and apply geometric reasoning.

Given: Three consecutive vertices of a regular n-gon: B, A, and D. A regular heptagon is constructed on AB, with vertex C next to A.

Let's consider a regular heptagon ABCDEFG with vertex C next to A. Since a heptagon is a 7-sided polygon, each interior angle of a regular heptagon measures:

Interior angle of a regular heptagon = (7 - 2) × 180° / 7 = 900° / 7

Now, let's focus on triangle BCD. Angle BCD is an interior angle of the regular heptagon.

Open your Trig Textbook and read on it, if you know how to read! Lazy.

What is the surface area formula for a sphere? Look it up in your Math Textbook. But calculating the radius, you have to add the radius of the Earth + 19,800 km. Then you have to convert that number into meters.

Once you determine the SA, then you divide 30 Watts by that SA and that would your answer would be  in Watts /m^2.

V = (4 π a^3)/3

Since you have the formula for the volume, you have the radius (a^3)==[8 x 10^8 m]^3, why can't you just substitute in the formula and find the volume? Or are you too busy playing video games or whatever? Don't  expect people to do your homework for you, lazy! Come on get on with it.

The statements that are true are A, C, D, and E.

Let x be the speed of Joseph's kayak and y be the speed of the current.

We know that Joseph was kayaking for 15 minutes and that the bag was 2 miles away from the Breakneck Ridge trail-head when he found it.

This means that Joseph traveled 15x miles and the bag traveled 15y miles.

We also know that the bag was carried downstream by the current, so the distance it traveled is equal to the distance it would have traveled if Joseph had been kayaking in the opposite direction for 15 minutes.

This means that 15y = 15x - 2

Solving for y, we get y = x - 2/3

Therefore, the speed of the current in the Hudson River is x - 2/3 = 2 - 2/3 = 4/3 miles per hour.

So the answer is 4/3

12.8

H = 1/2 (1/CF + 5/36), 

   
1/1100=4 * sqrt[H * (H-1/12)*(H-1/18)*(H-1/CF)], solve for H, CF

H=0.0837303
CF ==35 - largest possible altitude

When you have a question like this, you have to specify something like" what are the SMALLEST 4 positive integers.....etc.", because the LARGEST can go to infinity.

So, the smallest 4 positive integes are stated in your question! They are: 2, 4, 6, 8 because:

2 mod 11 ==2

4 mod 11 ==4

6 mod 11 ==6

8 mod 11 ==8

Their sum{2 + 4 + 6 + 8} ==20 mod 11 ==9 - the remainder.

P.S. If you had specified that the 4 numbers were all 2-digit numbers and you wanted the SMALLEST 2-digit numbers, then you could have:13, 15, 17, 19. If you divide these 4 by 11, you will have the same remainders of: 2, 4, 6, 8......and so on.

That was wrong, but okay.

Let the four integers be a,b,c,d. We know that a≡2(mod11), b≡4(mod11), c≡6(mod11), and d≡8(mod11). Adding all of these congruences, we get [a+b+c+d\equiv 2+4+6+8\equiv 20\pmod{11}.]Therefore, the remainder when a+b+c+d is divided by 11 is 0​.

To find the maximum possible distance from point A to point P in the given diagram, we need to determine the position of point P relative to the square ABCD.

Let's analyze the diagram step by step:

The large square ABCD has a side length of 6 units.

Four smaller squares are placed in the corners of ABCD, with side length 2 units each.

The vertices of these smaller squares are labeled as W, X, Y, and Z.

We want to find the maximum distance from point A to point P.

To maximize the distance from A to P, we should consider the scenario where P is located at the opposite corner of the large square ABCD relative to A. In this case, P would be at point D, which is the farthest possible point from A.

Therefore, the maximum possible distance from A to P is equal to the diagonal of the large square ABCD. Using the Pythagorean theorem, we can calculate this diagonal length:

Diagonal = √(Side^2 + Side^2) = √(6^2 + 6^2) = √(36 + 36) = sqrt(72) = 6*sqrt(2).

To find the lengths BC and BZ in triangle AB, we can use the angle bisector theorem.

The angle bisector theorem states that in a triangle, if an angle bisector divides the opposite side into two segments, the ratio of the lengths of those segments is equal to the ratio of the lengths of the other two sides.

Let's use the angle bisector theorem to find BC and BZ.

First, let's consider the angle bisector BY. According to the angle bisector theorem, we have:

AY / CY = AB / BC

Substituting the given values, we get:

16 / 16 = 16 / BC

Simplifying the equation, we have:

1 = 16 / BC

Cross-multiplying, we get:

BC = 16

So, BC has a length of 16.

Next, let's consider the angle bisector CZ. According to the angle bisector theorem, we have:

AY / BY = AC / BC

Substituting the given values, we get:

16 / BY = (16 + BC) / BC

Since we already found that BC = 16, we can substitute that value:

16 / BY = (16 + 16) / 16

Simplifying the equation, we have:

16 / BY = 2

Cross-multiplying, we get:

BY = 8

Now, we have the length of BY, but we want to find BZ. Since BY is an angle bisector, it divides the angle at B into two equal angles. This means that triangle BYZ is isosceles, and BZ has the same length as BY.

Therefore, BZ = BY = 8.

In summary, in triangle AB, the length of BC is 16, and the length of BZ is 8.

Incorrect, pls retry.