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chubhunter [2.5K]
3 years ago
14

How to find a point on a line in 3d given the distance from one of the points?

Mathematics
1 answer:
balu736 [363]3 years ago
7 0

Let a line in three dimensions be specified by two points  and  lying on it, so a vector along the line is given by

(1)The squared distance between a point on the line with parameter  and a point  is therefore(2)

To minimize the distance, set  and solve for  to obtain

(3)

where  denotes the dot product. The minimum distance can then be found by plugging  back into (2) to obtain

<span>(4)(5)</span>
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Who EVER ANSWERS FIRST GETS 5 STARS AND BRAINLIEST 
stiks02 [169]
Part A. Riley and Louie each have $5,000 to invest. They both invest at a 2.5% simple interest rate.

Part B. Riley keeps her money invested for 7 years. How much interest will she earn?

Part C.After those 7 years how much will her investment be worth?

8 0
3 years ago
Find the value of x and y and please show all work.
elena55 [62]

Answer:

x=66

y=48

Step-by-step explanation:

because the two length is same, so the angle x= 66 will be same; y= 180-66-66=48

6 0
3 years ago
Read 2 more answers
A lottery consists of one $2000 winner, three $500 winners, and ten $100 winners. a total of 1000 tickets are sold for $10 each.
Semenov [28]

Answer: -5.5

 

WOKINGS

Given that the lottery has the following number of winners:

One $2000 winner

Three $500 winners

Ten $100 winners

 

Also Given,

A total of 1000 tickets are sold

Each ticket costs $10

 

The expected winning for a person purchasing one ticket is the sum of the products of the gain/loss and their corresponding probability.

 

There is one $2000 winner

There are 1000 tickets

The probability of winning $2000

= 1/1000

= .001

There are three $500 winners

There are 1000 tickets

The probability of winning $500

= 3/1000

= .003

 


There are ten $100 winners

There are 1000 tickets

The probability of winning $100

= 10/1000

= .01

 

Since each ticket costs $10

Everyone who buys a ticket automatically loses $10.

Therefore, the probability of losing $10 is 1

 

Now to calculate the expected winning for a person purchasing one ticket

= 2000(.001) + 500(.003) + 100(.01) – 10(1)

= 2 + 1.5 + 1 – 10

= -5.5

 

The expected winning is -5.5. This implies that a person playing this lottery can expect to lose $5.50 for every one ticket that they purchase. 

7 0
3 years ago
Polly stacked the tins from five boxes of cat food onto an empty shelf in a supermarket. There were 15 tins of cat food in each
Alexandra [31]

Answer:

(a) 3\frac{2}{3} boxes of cat food had been sold.

(b) \frac{11}{3} boxes of cat food had been sold.

Step-by-step explanation:

From the question,

Polly stacked the tins from five boxes of cat food onto an empty shelf and there were 15 tins of cat food in each box. That is,

5 × 15 tins of cat food were stacked onto the empty shelf.

5 × 15 = 75

Hence, 75 tins of cat food were stacked onto the empty shelf.

Also, from the question,

At the end of the week there were 20 tins left on the shelf and the rest of the tins had been sold, that is

75 - 20 tins had been sold

75 - 20 = 55

Hence, 55 tins of cat food had been sold.

To determine the number of boxes of cat food that had been sold,

Since there are 15 tins of cat food per box, then

we will divide 55 tins of cat food that had been sold by 15 tins of cat food per box

55 ÷ 15 = \frac{55}{15}

Hence, \frac{55}{15} boxes of cat food had been sold

(a) As a mixed number

\frac{55}{15}  = 3\frac{2}{3}

Hence, 3\frac{2}{3} boxes of cat food had been sold.

(b) As an improper fraction

\frac{55}{15}  = \frac{11}{3}

Hence, \frac{11}{3} boxes of cat food had been sold.

7 0
3 years ago
Name 5 that are near, but not equivalent to, 4/12
ICE Princess25 [194]
4/12ths is 1/3 when simplified. 1/3 in decimal form is .33

1/5; 1/5 is .2

¼; ¼ is .25

5/25: 5/25 is .2

6/24; 6/24 is .25

all of these fractions are near .33 but aren't equivalent to it.
7 0
3 years ago
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