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Free_Kalibri [48]
3 years ago
15

The function f(x) = 1.25x^2 models the packaging costs, in cents, for a box shaped like a rectangular prism. The side lengths ar

e 2x in., 2x in., and 0.5x in. What are reasonable domain and range values for this function, if the longest side length of the box can be no greater than 20 in.? Write the answers in interval notation.
Mathematics
1 answer:
stira [4]3 years ago
5 0

Answer:

I need this tooo, did u find it??

Step-by-step explanation:

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The formula for volume of a prism is v=(1/2bh)h so it would be
​(1/2​​ ×7.8×4)×9= 140.4
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3 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:

<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

     

3 0
3 years ago
Consider the quadratic equation 3x^2-6=2x. (a) What is the value of the discriminant? (b) What does the discriminant of the quad
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Answer:

(a) discriminant is positive, 76

(b) the above tells you there are two real roots

Step-by-step explanation:

the discriminant is 'b² - 4ac'

3x² - 2x - 6 = 0  ∴ a = 3, b = -2, c = -6

(-2)² - 4(3)(-6) = 4 + 72

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204, because each day 6 goes up, so 34 x 6 = 204. Hope this helps :)
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3 years ago
What does 2 + 1+ 1 x 10 =
sammy [17]
The answer is 13!

Follow PEMDAS (:
4 0
3 years ago
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