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scoray [572]
3 years ago
11

Which expression represents the number of feet that are in x yards?

Mathematics
2 answers:
nignag [31]3 years ago
7 0
C

I think that this is the correct answer
AleksandrR [38]3 years ago
3 0

we know that

1\ yard=3\ feet

Let

y-------> the number of feet that are in x yards

by proportion

<u>Find the value of y</u>

\frac{3}{1} \frac{feet}{yard}=\frac{y}{x} \frac{feet}{yards} \\ \\y=3x\ feet

therefore

<u>the answer is the option C</u>

3x

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7 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
Which ratio is porportional to 18/21? A.2/3 B. 30/35 C. 36/48 D.1/3
defon
You can solve this problem by applying the proccedure below:
 
 You have:
 
 a) 18/21=2/3
 18x3/21x2
 36≠42 (2/3 is not proportinal to 18/21).
 
 b)18/21=30/35
 18x35/21x30
 630=630  (30/35 is proportional to 18/21)
 
 c)18/21=36/48
 18x48/21x36
 864≠756  (36/48<span> is</span><span> not proportinal to 18/21)
</span> 
 d)18/21=1/3
 18x3/21x1
 54≠21  (<span> 1/3 is</span><span> not proportinal to 18/21)
</span> 
 Therefore, you can conclude that the correct option is: B.30/35
8 0
2 years ago
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