4.5 to the -11 power

What is the equation of the line in slope intercept form using these points?

deff fn [24]

Answer:

y = -x - 1

Step-by-step explanation:

1. The slope-intercept form of any linear equation is y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.

2. To find the slope given two points, we can use the formula $\frac{y_2-y_1}{x_2-x_1}$ and plug in the corresponding variable.

$\frac{5-(-2)}{-6-1}$
$\frac{5+2}{-7}$
$\frac{7}{-7}$
$-1$

3. Okay, so the slope is -1x or just -x. This means that the equation looks like this so far: y = -x + b

4. To find b, the y-intercept, we can take the equation of $b = y_1 - m * x_1$ and plug in the values!

$b = -2-(-1)*1$
$b = -2 + 1 * 1$
$b = -1 * 1$
$b = -1$

5. Now that we have our y-intercept and slope, let's plug in those values and find the equation!

$y = -x - 1$

Therefore, the equation of the line is y = -x - 1. I hope this helped you!

3 0

2 years ago

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:

Step 1:-

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)

Step( ii):

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)

Step (iii):-

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

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

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

Conclusion:-

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

3 0

2 years ago

This is due today i would appreciate it a lot if smn could help me with it :/

Vesnalui [34]

Answer:

Conclusion:

The rate of change of function 1 = 3

The rate of change of function 2 = 5/3

Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

Hence, function 2 has a greater initial value.

Step-by-step explanation:

Function 1)

Determining rate of change for function 1:

x 1 2 3 4

y 5 8 11 14

Finding the rate of change or slope using the formula

Rate of change = m = [y₂-y₁] / [x₂-x₁]

Taking any two points, let say (1, 5) and (2, 8)

Rate of change = m = [8-5] / [2-1]

= 3/1

= 3

Therefor, the rate of change of function 1 = m = 3

using point-slope form to determine the function equation

y-y₁ = m (x-x₁)

where m is the rate of change or slope

substititng m = 3 and the point (1, 5)

y - 5 = 3(x - 1)

y - 5 = 3x-3

y = 3x-3+5

y = 3x + 2

Thus, equation of function 1 will be:

y = 3x + 2

Determining Initial Value for Function 1:

substituting x = 0 in the equation to determine the initial value

y = 3(0)+2

y = 0+2

y = 2

Therefore, the initial Value of function 1 will be: y = 2

Function 2)

Determining the rate of change for function 2:

Given the function 2

$y\:=\:\frac{5}{3}x+3$

comparing with the slope-intercept form of a linear function

y = mx+b where m is the rate of change

so the rate of change of function 2 = m = 5/3

Determining Initial Value for Function 2:

substituting x = 0 in the equation to determine the initial value

$y\:=\:\frac{5}{3}x+3$

$y\:=\:\frac{5}{3}\left(0\right)+3$

$y = 0+3$

$y = 3$

Therefore, the initial Value of function 2 will be: y = 3

Conclusion:

The rate of change of function 1 = 3

The rate of change of function 2 = 5/3

Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

Hence, function 2 has a greater initial value.

8 0

2 years ago

In Colorado Springs, a local newspaper ran a full page of nearly 100 mug shots of people the police wanted to arrest for serious

wolverine [178]

Answer:

86% probability. hope this helps :)

Step-by-step explanation:

7 0

2 years ago

What’s the answer to this please, thanks!

Bumek [7]

Answer:

8 < x < 16

Step-by-step explanation:

Consider an angle slightly less than 180 between the 4 and 12 ft sides. The measure between the 2 end points is slightly less than the total of the two sides. So the greatest length is 16.

Consider an angle slightly more than 0 between the 4 and 12 ft sides. The measure between the 2 end points is slightly more than the difference between the two sides. So the lowest length is 8.

3 0

2 years ago