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Fantom [35]
3 years ago
11

Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. What is the distance between the origin and

the plane?
Mathematics
1 answer:
Elenna [48]3 years ago
3 0

Answer:

The equation is:

(1/a)x + (1/b)y + (1/c)z = 1

Step-by-step explanation:

The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:

<0 - a, b - 0, 0 - 0>

<-a, b, 0> .....................(1)

The direction vector between (0, 0, c) and (0, b, 0) is given as:

<0 - 0, b - 0, 0 - c>

= <0, b, -c> .....................(2)

To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).

Doing this, we have:

<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>

To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:

(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0

(bc)x + (ac)y + (ab)z = (ac)b

Dividing both sides by abc, we have:

(1/a)x + (1/b)y + (1/c)z = 1

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10x+9=4x -9 solve <br><br> please help
Neporo4naja [7]

Answer:

x = -3

Step-by-step explanation:

To solve this, you need to isolate the variable x, this means only one side of the equation should have the variable x. To do this, you need to do the opposite operation from what's given (if it's addition, use subraction; if it's multiplication, use division; these work vise versa)

  • Subtract 9 from both sides of the equation. This gives you 10x = 4x - 18.
  • Subtract 4x from both sides of the equation. This gives you 6x = -18.
  • Divide both sides by 6. This gives you x = -3

The final answer is x = -3

7 0
2 years ago
A detergent company periodically tests its products for variations in the fill weight. To do this, the company uses x-bar and R
maw [93]

Answer:

10.9361

Step-by-step explanation:

The lower control limit for xbar chart is

xdoublebar-A2(Rbar)

We are given that A2=0.308.

xdoublebar=sumxbar/k

Rbar=sumR/k

xbar      R

5.8        0.42

6.1         0.38

16.02    0.08

15.95    0.15

16.12     0.42

6.18      0.23

5.87     0.36

16.2      0.4

Xdoublebar=(5.8+6.1+16.02+15.95+16.12+6.18+5.87+16.2)/8

Xdoublebar=88.24/8

Xdoublebar=11.03

Rbar=(0.42+0.38+0.08+0.15+0.42+0.23+0.36+0.4)/8

Rbar=2.44/8

Rbar=0.305

The lower control limit for the x-bar chart is

LCL=xdoublebar-A2(Rbar)

LCL=11.03-0.308*0.305

LCL=11.03-0.0939

LCL=10.9361

8 0
3 years ago
B. If instead you divide first to solve the equation, what<br> operation would you need to use last?
Sedbober [7]

Answer:

use  PEDMAS

P: PARENTHESIS

E: EXPONENTS

D: DIVISON

M: MULTIPLICATION

A: ADDITION

S: SUBTRACTION

Step-by-step explanation:

CAN YOU PLS MARK ME BRAINLIEST THANK YOU !

8 0
2 years ago
3. A woman deposits Php 23,200 into her account. How much would
nikklg [1K]

Answer:

(assuming simple interest)

I'll setup the problem and you can do the computation

Step-by-step explanation:

The formula for simple interest:

I = P*r*t

P = deposits

r = interest rate per period (a year)

t = number of periods

P = Php 23,200

r = 0.06

t = 1

If you have questions, send me a comment 

3 0
2 years ago
Solve the proportion
sergeinik [125]

y =  \frac{28}{5}

4 0
2 years ago
Read 2 more answers
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