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4 years ago

How can you change linear equation in form ax+by=c to y=mx+b form and vice versa

1 answer:

3 0

You simply have to take the linear equation form (ax + by = c) and solve for y. So you get:
by = c - ax
y = c/b - ax/b

Since c/b will be a constant, you can replace it with any variable (i.e. b), and so that represents the y-intercept and a/b will also be a constant, so that can also be replaced by any variable (i.e. m), and it represents the slope.

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

velikii [3]

Answer:

The maximum value= 36

Minimum value = - 36

Step-by-step explanation:

Given that

f(x, y, z) = 8 x + 8 y + 4 z

h(x,y,z)=4 x² + 4 y² + 4 z² - 36

From Lagrange multipliers

Δf = λ Δh

Δf = < 8 ,8 , 4>

Δh = < 8 x ,8 y , 8 z>

Δf = λ Δh

< 8 ,8 , 4> = < 8 λ x ,8 λ y , 8 λ z>

8 = 8 λ x -------------1

8 = 8 λ y ---- ------2

4 = 8 λ z ----------------3

From equation 1 ,2 and 3

Now by putting the value of x,y and z in the following equation

4 x² + 4 y² + 4 z² = 36

$4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{(2\lambda)^2 }=36$

$\dfrac{4}{\lambda^2 }+ \dfrac{4}{\lambda^2 }+ \dfrac{1}{\lambda^2 }=36$

So the value of λ is

$\lambda =\pm \dfrac{1}{2}$

When λ = 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= 2 , y = 2 , z=1

f(x, y, z) = 8 x + 8 y + 4 z

f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1

f(2, 2, 1) =36

When λ = - 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= - 2 , y = - 2 , z= - 1

f(x, y, z) = 8 x + 8 y + 4 z

f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)

f(-2, -2, -1) = - 36

The maximum value= 36

Minimum value = - 36

7 0

3 years ago

Read 2 more answers

I need help 1.09 divided by 3.08 show your solution Thank you so much if u helpt me

gayaneshka [121]

Answer:

<h2 /><h2>answer will be 0.3538</h2>

Step-by-step explanation:

$\frac{1.09}{3.08} = 0.3538$

6 0

4 years ago

Find a so that the point (-1, 2) is on the graph of f(x)=ax^2+5.

Gnesinka [82]

We are asked to determine the value of a such that the function f(x) = ax^2 + 5 is fit for the point given (-1,2). In this case, we substitute 2 to y and -1 to x. The result is then 2 = a*(-1)^2 + 5 ; 2 = a + 5; a is then equal to -3

4 0

4 years ago

When shopping for a personal loan, why is it important to limit the amount of loan applications you submit?

Korvikt [17]

Answer:

The best answer is actually, When shopping for a loan, do not submit too many applications. Each time you submit an application, the lender will do a hard inquiry on your credit score. Having too many hard inquiries at one time will negatively affect your credit and raise your interest rate.

this is 100% correct

4 0

3 years ago

The store allowed 85 people in 5 hours .. how many people were allowed to enter per hour?

ale4655 [162]

Answer:

17 people per hour

Step-by-step explanation:

85/5

3 0

3 years ago