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qwelly [4]
3 years ago
8

) The points (1, 0, 3), (1, 1, 1), and (−2, −1, 2) lie on a unique plane a1x1 + a2x2 + a3x3 = b. Using your previous answers, fi

nd an equation for this plane. (Hint: think about the relationship between the previous system and the one you would need to solve in this question.)

Mathematics
2 answers:
Rudik [331]3 years ago
6 0

Answer:

x1-2x2-x3= -2

Step-by-step explanation:

Substitute the three points to get three equations:

a1+0a2+ 3a3=d --------------eq i

a1+a2+a3=d----------------eq ii

-2a1-a2+2a3=d---------------eq iii

subtract eq i from eq ii

a2-2a3=0 ----------- eq iv

now add eq iv to eq iii

-2a1=d ------- eq v

put eq v in eq i

a1 + 3a3=-2a1

a3=  -a1 ----------- eq vi

put eq vi in eq iv

a2-2(-a1)=0

a2= -2a1 ------ eq vii

put eq v, eq vi and eq vii in the equation of plane

a1x1+ a2x2+a3x3=d

a1x1 -2a1x2-a1x3=-2a1

x1-2x2-x3= -2

Akimi4 [234]3 years ago
6 0

Answer:

2x₁ - x₂ + x₃ = 2

Question in full

(a) Find the general solution for the following system of linear equations:

z2 + 3z3 − z4 = 0

−z1 − z2 − z3 + z4 = 0

−2z1 − 4z2 + 4z3 − 2z4 = 0

(b) Give an example of a solution to the previous system of linear equations.

(c) The points (0, 1, 3), (1, 1, 1), and (−1, −2, 2) lie on a unique plane in R 3 , defined by an equation of the form a1x1 + a2x2 + a3x3 = b. Using your previous answers, find an equation for this plane. (Hint: think about the relationship between the previous system and the one you would need to solve in this question.)

Step-by-step explanation:

The augmented matrix is \left[\begin{array}{ccc}1&2&3&0\\4&5&6&0\\7&8&9&0\end{array}\right]

The echelon form

The general solution and the sample solution

as well as the equation of the plane

are given in the attached solution below

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Of 100 students,65 are members of a mathematics club and 40 are members of a physics club. if 10 are members of neither club the
alexandr1967 [171]

a. 15 students are members of both clubs

b. 50 students only are members of the mathematics club

c. 25 students only are members of the physics club

Step-by-step explanation:

The given is:

  • There are 100 students
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  • 40 are members of a physics club
  • 10 are members of neither club

We need to find how many students are members of

a. both clubs?

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c. only physics club

∵ The total number of students = 100

∵ 10 are members of neither club

- Subtract 10 from 100 to find the members of the mathematics

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∵ 100 - 10 = 90

∴ There are 90 members of the mathematics club or physics club

∴ n(mathematics or physics) = 90

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∵ n(mathematics) = 65

∵ 40 students are members of a physics club

∴ n(physics) = 40

∵ n(mathematics or physics) = n(mathematics) + n(physics) - n(both)

∴ 90 = 65 + 40 - n(both)

∴ 90 = 105 - n(both)

- Add n(both) to each side

∴ n(both) + 90 = 105

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∴ n(both) = 15

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a. 15 students are members of both clubs

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∴ n(mathematics only) = 65 - 15 = 50

∴ 50 students only are members of the mathematics club

b. 50 students only are members of the mathematics club

∵ 40 students are members of the physics club

∵ 15 of them are members of the mathematics club

∴ n(physics only) = 40 - 15 = 25

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Learn more:

You can learn more about word problems in brainly.com/question/8907574

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5 0
3 years ago
PLEASE HELPPP!!!! Will give brainiest!!!!
Lady_Fox [76]

Answer:

  • 0.008 °C

Explanation:

<u>1) Write the changes in the temperature of the city over the 4 days in an easy way to read.</u>

<u />

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  • - 0.75 °C
  • 4/9 ° C

<u />

<u>2) Write the expression to show the average daily change in temperature.</u>

The average of a set of data is calculated with the expression:

  • Average = (sum of the data) / amount of data

Hence, you need to add the four change of temperature data and divide by 4.

The expression is:

  • Average =  [ 1.34 °C + (- 5 / 7 °C) + ( - 0.75 °C) + 4/9 ° C ] / 4

<u>3) Write the steps to solve the expression:</u>

You can choose between adding  fractions or adding the decimal forms of the numbers.

If you choose adding decimals, keep the complete decimals in your calculator, to avoid the accumulation of errors due to rounding. Round only the final result.

These are the steps.

<u>a. Find the decimal forms of the fractions:</u>

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<u>b. Add the four data:</u>

  • 1.34°C + (- 0.71428 °C) + (-0.75 °C) + 0.44444 °C ≈ 0.32019 °C

<u />

<u>c. Divide the sum by the number of data (4)</u>

  • 0.32019 °C / 4 ≈ 0.080004 °C

<u>4. Round to the nearest hundredth</u>

The place of the hundreth is the second after the decimal point, which is 8 in this case:

  • 0.080004 °C ≈ 0.08 °C

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An answer can be 1357
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X=2

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leonid [27]

Answer: 7

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