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3 years ago

Find the point on the plane 2x+5y+z=8 that is nearest to (2,0,1).

Mathematics

1 answer:

Svetach [21]3 years ago

5 0

Answer:

(2.2, 0.5, 1.1)

Step-by-step explanation:

The parametric equation of the line normal to the plane and through point (2, 0, 1) can be written ...

... L = (2, 0, 1) + t(2, 5, 1)

We want to find the value of t (and the corresponding point) that makes L satisfy the equation of the plane.

... 2(2+2t) +5(0 +5t) +1(1+t) = 8 . . . . . put values from L in for x, y, z in plane

... 5 + 30t = 8 . . . . . simplify

... t = (8 -5)/30 = 0.1 . . . . solve for t (subtract 5, divide by 30)

For this value of t, L is ...

... (2, 0, 1) + 0.1(2, 5, 1) = (2.2, 0.5, 1.1)

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there are 27 red or blue marbles in the bag the number of red marbles is five less than three times the number of the blue marbl

alexdok [17]

So assuming that the total =27
r+b=27
r=-5+3b
r=3b-5
subsitute 3b-5 for r in first equation
3b-5+b=27
4b-5=27
add 5
4b=32
divide by 4
b=8
subsitute
b+r=27
8+r=27
subtracct 8
r=19

red=19
blue=8

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3 years ago

Kerry has a bag containing white and yellow marbles. Kerry randomly selects one marble, records the result, and returns the marb

dexar [7]

Answer:

The probability that next selection is yellow marble = 63% .

Step-by-step explanation:

Given the selection of yellow marbles = 41 times.

The selection of white marble = 24 times.

Total number of selections made = 65

Now calculate the probability that the next selection will be the yellow marble. Therefore, the probability of getting yellow marble can be determined by dividing the yellow selection by total number of selections.

$\text{P(yellow)} = \frac{ \text{The selection of yellow marbles} }{ \text{ Total number of slections }} \\\text{P(yellow)} = \frac{41}{65} = 0.63 \ or \ 63 \ percent$

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3 years ago

Evaluate 2(4-1)^2 A. 60 B. 30 C. 18 D. 36

iogann1982 [59]

Remember the rules of PEMDAS

1. First you want to evaluate the parentheses. (4-1) = 3

2. Square:
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3. Multiply: 9*2 = 18

Your answer is C

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3 years ago

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Deffense [45]

Answer:

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You need the other 10 of those numbers to radicals, or numbers similar to pi (THESE ARE IRRATIONAL)

Step-by-step explanation:

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3 years ago

4. Julie saw 3 eagles each day she went bird-watching. How many eagles did Julie see in 6 days?

Umnica [9.8K]

9514 1404 393

Answer:

18 eagles

Step-by-step explanation:

Assuming Julie went bird-watching on each of those 6 days, she saw a total of ...

(3 eagles/day)(6 day) = 3·6 eagles = 18 eagles

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3 years ago

Find the point on the plane 2x+5y+z=8 that is nearest to​ (2,0,1).

Find the point on the plane 2x+5y+z=8 that is nearest to (2,0,1).