Answer:
Option B. is the answer.
Step-by-step explanation:
The given question is incomplete without the attachment; here is the attachment enclosed with the answer.
Since coordinates of the point representing rock is (3, 2) and coordinates of the tree are (16, 21) and treasure divides the line joining rock and tree in the ratio of 5:9.
We know the formula to get the coordinates of point P(x, y) joining (a, b) and (c, d) in the ratio of m : n is
P(x, y) = ![[\frac{(mc+na)}{m+n}, \frac{(md+nb)}{m+n}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%28mc%2Bna%29%7D%7Bm%2Bn%7D%2C%20%5Cfrac%7B%28md%2Bnb%29%7D%7Bm%2Bn%7D%5D)
From the given formula,
Coordinates of treasure P = ![[\frac{((5\times 16)+(9\times 3)}{(5+9)}, \frac{(5\times 21)+(9\times 2)}{(5+9)}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%28%285%5Ctimes%2016%29%2B%289%5Ctimes%203%29%7D%7B%285%2B9%29%7D%2C%20%5Cfrac%7B%285%5Ctimes%2021%29%2B%289%5Ctimes%202%29%7D%7B%285%2B9%29%7D%5D)
= ![[\frac{(80)+(27)}{(14)}, \frac{(105)+(18)}{(14)}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%2880%29%2B%2827%29%7D%7B%2814%29%7D%2C%20%5Cfrac%7B%28105%29%2B%2818%29%7D%7B%2814%29%7D%5D)
= ![[7.64, 8.78]](https://tex.z-dn.net/?f=%5B7.64%2C%208.78%5D)
≈ (7.6, 8.8)
Therefore, Option B will be the answer.
Answer:
0
Step-by-step explanation:
37×0=0 just like 123x0=0
Answer:
The number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways
Step-by-step explanation:
We need to find the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E.
There are 9 letters in the word WONDERFUL
There is a condition that letter R is always next to E.
So, We have two letters fixed WONDFUL (ER)
We will apply Permutations to find ways of arrangements.
The 7 letters (WONDFUL) can be arranged in ways : ⁷P₇ = 7! = 5040 ways
The 2 letters (ER) can be arranged in ways: ²P₂ =2! = 2 ways
The number of ways 'WONDERFUL' can be arranged is: (5040*2) = 10,080 ways
So, the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways
In this item, we are asked to determine or calculate for the distance between the points A (1,4) and B(-3,-2)
The distance between the two points can be computed through the equation below.
d = sqrt ((x₂ - x₁)² + (y₂ - y₁)³)
We can choice whichever of the two points will have the first abscissa or the first ordinate. For the purpose of showing the solution here, it is assumed that A has the coordinates of (x₁,y₁) and B (x₂,y₂)
Substituting,
d = sqrt ((-3 - 1)² + (-2 -4)²)
d = 2√13
<em>ANSWER: 2√13 , ~7.21</em>
