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rjkz [21]
3 years ago
8

Write an equation in point slope form for the line with a slope of 3 passes through (1,2)

Mathematics
1 answer:
alexgriva [62]3 years ago
4 0

Answer:

y-2=3(x-1)

Step-by-step explanation:

The point-slope form of a line is given as:

y-y_1=m(x-x_1)

Where

m is the slope

x_1 is the x-coordinate of the point given (passing through the line)

y_1 is the y-coordinate of the point given (passing through the line)

Now,

Given,

Slope = m = 3

x_1 = 1

y_1 = 2

Now, we simply plug these into the formula for point-slope form of a line:

y-y_1=m(x-x_1)\\y-2=3(x-1)

This is the point-slope form.

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Write 8.87 as a mixed number and as an improper fraction.<br> Do not try to simplify your answers.
kodGreya [7K]

Answer:

  8 87/100 = 887/100

Step-by-step explanation:

"Eight and eighty-seven hundredths" is ...

  8 87/100 = 887/100

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Convert to standard form.<br> y-5=-3(x+2)​
Paul [167]

Answer:

Step-by-step explanation:

y-5=3(x+2)

y-5=3x+6

y-5-6=3x+6-6

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Solve for x: -4x – 12 &gt; 36 A. x &gt; -12 B. x &gt; 12 C. x &lt; -12 D. x &lt; 12
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Step-by-step explanation:

-4x – 12 > 36

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Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat
tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

<u>Step 1</u>:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane.   Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

<u>Step( ii):</u>

By using  Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ  Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

                                  δ f / δ x +λ  δ Ф  / δ x =0

                           ⇒ y z + λ ( 1) = 0

                          ⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

                            δ f / δ x +λ  δ Ф  / δ x =0

                        ⇒ x z + λ ( 9) = 0

                        ⇒ \frac{xz}{9} = - λ .......(b)

Obtain the equations are δ F / δ z = 0

                                  δ f / δ x +λ  δ Ф  / δ z =0

                                   x y + λ ( 4) = 0

                                    ⇒ \frac{xy}{4} = - λ .......(c)

<u>Step (iii):-</u>

Equating (a) and (b) equations

we get         y z = \frac{xz}{9}

cancel 'z' value we get  x = 9y  .......(d)

Equating (b) and (c) equations

we get     \frac{xy}{4}  = \frac{xz}{9}

cancel 'x' value on both sides , we get

              4z =9y  ......(e)

substitute (d) (e) values in equation (1)  we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

<u> y = 1</u>

substitute y =1 in x = 9y

<u>x = 9</u>

substitute y =1 in 4z =9y

<u>z = 9 /4</u>

therefore the dimensions are x =9 , y=1 and z = 9 /4

<u>Conclusion</u>:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

              9 + 9 + 4(9/4) = 27

           27 =27

so satisfied equation

     

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3 years ago
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