A Millipede has how many legs

Write the slope intercept form of the equation of the line through the given point

ozzi

Answer:

y = $-\frac{3}{4}$ x

Step-by-step explanation:

slope-intercept form: y = mx + b

Given: slope(m) = $-\frac{3}{4}$ , point (4, -3)

We already have the value of m, but we need to find the value of b. To do this, input the given values of the slope and the point into the equation:

-3 = $-\frac{3}{4}$ (4) + b

Solve for b:

-3 = $-\frac{3}{4}$ (4) + b

-3 = -3 + b

0 = b

The value of b is zero. We can now write the equation:

y = $-\frac{3}{4}$ x + 0

y = $-\frac{3}{4}$ x

The equation written in slope-intercept form is: y = $-\frac{3}{4}$ x

8 0

3 years ago

. Use Lagrange multipliers to find the maximum and minimum values of the function, f, subject to the given constraint, g. (Place

zzz [600]

Answer:

Minimum value of f(x, y, z) = (1/3)

Step-by-step explanation:

f(x, y, z) = x⁴ + y⁴ + z⁴

We're to maximize and minimize this function subject to the constraint that

g(x, y, z) = x² + y² + z² = 1

The constraint can be rewritten as

x² + y² + z² - 1 = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = x⁴ + y⁴ + z⁴ - λ(x² + y² + z² - 1)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points, each of the partial derivatives is equal to 0.

(∂L/∂x) = 4x³ - λx = 0

λ = 4x² (eqn 1)

(∂L/∂y) = 4y³ - λy = 0

λ = 4y² (eqn 2)

(∂L/∂z) = 4z³ - λz = 0

λ = 4z² (eqn 3)

(∂L/∂λ) = x² + y² + z² - 1 = 0 (eqn 4)

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

4x² = 4y²

4x² - 4y² = 0

(2x - 2y)(2x + 2y) = 0

x = y or x = -y

Also,

4x² = 4z²

4x² - 4z² = 0

(2x - 2z) (2x + 2z) = 0

x = z or x = -z

when x = y, x = z

when x = -y, x = -z

Hence, at the point where the box has maximum and minimal area,

x = y = z

And

x = -y = -z

Putting these into the constraint equation or the solution of the fourth partial derivative,

x² + y² + z² = 1

x = y = z

x² + x² + x² = 1

3x² = 1

x = √(1/3)

x = y = z = √(1/3)

when x = -y = -z

x² + y² + z² = 1

x² + x² + x² = 1

3x² = 1

x = √(1/3)

y = z = -√(1/3)

Inserting these into the function f(x,y,z)

f(x, y, z) = x⁴ + y⁴ + z⁴

We know that the two types of answers for x, y and z both resulting the same quantity

√(1/3)

f(x, y, z) = x⁴ + y⁴ + z⁴

f(x, y, z) = (√(1/3)⁴ + (√(1/3)⁴ + (√(1/3)⁴

f(x, y, z) = 3 × (1/9) = (1/3).

We know this point is a minimum point because when the values of x, y and z at turning points are inserted into the second derivatives, all the answers are positive! Indicating that this points obtained are

S = (1/3)

Hope this Helps!!!

6 0

2 years ago

If f(x)= 2x-2 and g(x) =x^2 -8x+19, then f(x)=g(x) for what values of x?

frozen [14]

Answer:

24.

Step-by-step explanation:

With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.

7 0

3 years ago

Read 2 more answers

F(4) = ______<br> If g(x) = 2, x = _____

disa [49]

Answer:

Step-by-step explanation:

From the graph attached,

For x = 4,

Value of the function will be,

f(4) = y value at x = 4

f(4) = -10

Similarly, for y = g(x) = 2,

x value of the function will be,

x = 0

For which g(0) = 2

Therefore, for x = 0 value of the function will be 2.

g(0) = 2

5 0

2 years ago

A seagull was flying about sea level looking to catch a fish below sea level. The elevation above sea level was 125 1/2 feet. He

frez [133]

Answer:

The seagull's position halfway is 85.5 feet.

Step-by-step explanation:

The seagull is at 125 1/2 feet above the sea level.

The fish is at 45 1/2 feet below the sea level.

The distance between the seagull and fish = seagull's distance above the sea level + fish's distance below the sea level

= 125 1/2 + 45 1/2

= $\frac{251}{2}$ + $\frac{91}{2}$

= $\frac{342}{2}$

= 171

The distance between the seagull and fish is 171 feet.

Since the seagull stops halfway, then;

seagull's position = $\frac{171}{2}$

= 85.5

The seagull's position halfway is 85.5 feet.

8 0

2 years ago