The distance from London to Manchester is 199.9 what is this to the nearest 10 miles?

Answers

Answer 1

Answer: 200 miles (199.9 is only 0.1 away from 200 but 9.9 away from 190)
SO it is 200

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. Let A = (−2, 4) and B = (7, 6). Find the point P on the line y = 2 that makes the total distance AP + BP as small as possible.

Answers

Answer:

P(1,2)

Step-by-step explanation:

There are 2 points.

A(-2,4) and B(7,6)

the point P on the y=2 can also represented as P(x,2)

We can use the distance formula to find the distances AP and BP

$\text{dist} = √((x_1 - x_2)^2 + (y_1 - y_2)^2)$

for AP: A(-2,4) and P(x,2)

$AP = √((-2 - x)^2 + (4 - 2)^2)$

$AP = √((-2 - x)^2 + 4)$

$AP = √((-1)^2(2 + x)^2 + 4)$

$AP = √((2 + x)^2 + 4)$

for BP: B(7,6) and P(x,2)

$BP = √((7 - x)^2 + (6 - 2)^2)$

$BP = √((7 - x)^2 + 16)$

the total distance AP + BP will be

$√((2 + x)^2 + 4)+√((7 - x)^2 + 16)$ (plot is given below)

Our task is to find the value of x such that the above expression is small as possible. (we can find this either through plotting or differentiating)

If you plot the above equation, the minimum point of the curve will be clearly visible, and it will be at x = 1. Hence, the point P(1,2) is such that the total distance AP + BP is as small as possible.

Final answer:

The point P that makes the total distance AP + BP smallest on the line y=2 is given by the x-coordinate of the midpoint of A and B because the shortest distance is in a straight line. Therefore, the point P is (2.5, 2).

Explanation:

To find the point P on the line y = 2 that makes the total distance AP + BP the smallest, you need to recall that the shortest distance between two points is a straight line. So, ideally, we want to find a point P (x,2) that is on the same vertical line (or x-coordinate) that intersects the line AB at the midpoint.

Step 1: Find the midpoint of A and B. The midpoint M is obtained by averaging the x and y coordinates of A and B: M = ((-2+7)/2 , (4+6)/2) = (2.5, 5).

Step 2: Since line y = 2 is horizontal, the x-coordinate of our point P will stay the same with the midpoint x-coordinate. Therefore, P has coordinates (2.5, 2).

So, the point on the line y = 2 that makes the total distance AP + BP as small as possible is P (2.5, 2).

Learn more about Point here:

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(9* 1010) - (4 * 1010) =
How to answer

Answers

For this you will utilize PEMDAS. So work what’s in the parenthesis first.

(9090) - (4040)

Then subtract both of them.

5050

Answer: 5050

How does kinetic energy affect the stopping distance of a small vehicle compared to a large vehicle

Answers

Kinetic energy is the energy of a moving body. Body with greater kinetic energy stops slower than a body with less kinetic energy.

Help me solve the other half of my question !!!!!!!!!click here !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

thanks

Answers

Using 1st equation:
15 = 16/3 + b
(45-16)/3 = b
29/3 = b

Using last equation:
47 = 16*7/3 + b
(141-112)/3 = b
29/3 = b

The slope of the line below is -5 which of the following is the point slope form of the line

Answers

Answer:

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (2, - 7), thus

y - (- 7) = - 5(x - 2) , that is

y + 7 = - 5(x - 2) → B

Is the sequence geometric? If so, identify the common ratio. 6, 12, 24, 48,

Answers

Answer: Yes, the given sequence is geometric with common ration 2.

Step-by-step explanation: The given sequence is:

6, 12, 24, 48, . . ..

We are to check whether the above sequence is geometric or not. If it is geometric, we are to find the common ratio.

Geometric sequence - a sequence of numbers where each term is found by multiplying by a constant to the preceding term. This constant is called the common ratio, r.

The consecutive terms of the given sequence can be written as:

$a_1=6,\n\na_2=12,\n\na_3=24,\n\na_4=48,\n\netc.$

We can see that

$(12)/(6)=(24)/(12)=(48)/(24)=~.~.~.~=2,\n\n\Rightarrow (a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)=~.~.~.~=2,\n\n\Rightarrow a_2=2* a_1,~~a_3=2* a_2,~~a_4=2* a_3,~.~.~.etc.$

Therefore, each term is formed by multiplying 2 to the preceding term.

Thus, the given sequence is a geometric sequence with common ratio 2.

Yes
common ratio= r2/r1 or r3/r2 or r4/r3 if it is all the same then it is a geometric sequence, so the common ratio is 2 because 12/6=2, 24/12=2 and 48/24=2

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