An exotic-animal rancher needs to purchase feed for his unicorns. Unfortunately, commercial unicorn feed is not available. The unicornsrequireat least12 milligrams of zinc, 36 grams of protein, and 24 ounces of carbohydrates per day. A small bagof pegasus feed contains 2 milligrams of zinc, 2 grams of protein, and 2 ounces of carbohydrates, and it costs $25. A small bagof hippogriff feed contains 1milligram of zinc, 9 grams of protein, and 3 ounces of carbohydrates, and it costs $20. How many bags of each should the farmer purchase in order to supply the unicorns with the required nutrients for the lowest cost, and what is the minimum cost?

Constraints:

Objective Formula:

Answer:

58586

Step-by-step explanation:

gckhgcklghckhgchkc

Without using any calculus:

If x + y² = 5, then y² = 5 - x, so that

b = x y² = x (5 - x) = 5 x - x²

Complete the square to get

b = 25/4 - (x - 5/2)²

Then b gets a maximum value of 25/4 when x = 5/2.

Simple calculus method:

With b = 5 x - x², differentiate b with respect to x and set the derivative equal to 0 to solve for critical points:

db/dx = 5 - 2 x = 0   ==>   x = 5/2

Take the second derivative to determine whether b is concave or convex:

d²b/dx² = -2

The second derivative is negative, which means b is concave with respect to x, and this indicates x = 5/2 is the site of a local maximum, which is b (5/2) = 25/4.

More complicated calculus method:

Lagrange multipliers. The Lagrangian is

L (x, y, λ) = x y² - λ (x + y² - 5)

where we assume λ ≠ 0.

Take its derivatives:

dL/dx = y² - λ

dL/dy = 2 x y - 2 λ y

dL/dλ = x + y² - 5

Set each derivative equal to 0 to find the critical points. The first equation tells us y² = λ, and the second equation tells us x = λ, so

x + y² - 5 = 2 λ - 5 = 0

Solving this gives λ = x = y² = 5/2, so that b has an extreme value of

b = (5/2) (5/2) = 25/4

Deciding whether this is a maximum or minimum comes down to computing the Hessian determinant at the critical value. The Hessian is

[tex]H(x,y)=\begin{bmatrix}\dfrac{\partial^2b}{\partial x^2}&\dfrac{\partial^2b}{\partial x\partial y}\\\\\dfrac{\partial^2b}{\partial y\partial x}&\dfrac{\partial^2b}{\partial y^2}\end{bmatrix}=\begin{bmatrix}0&2y\\2y&2x\end{bmatrix}[/tex]

with determinant |H (x, y)| = -4 y². At the critical point, the determinant is -10 < 0, which indicates a maximum value of 25/4.

Answer:

0.25 or b is the correct answer

Answer:

2.10 is greater than 2.09

Step-by-step explanation:

because 2.10 has more equation than 2.09

Answer:

2.10 is GREATER than 2.09 so **TRUE**

Step-by-step explanation:

hope this helps </3

Answer:

∠EBF = 51°

∠DBE = 17°

∠ABF = 141°

∠EBA = 90°

∠DBC = 107°

∠DBF = 68°

Step-by-step explanation:

Hope this helps

Answer:

1.

a. m<EBF = 90 - 39 = 51

b. m<EBA = 90

c. m<DBE = 90 - 73 = 17

d. m<DBC = 90 + 17 = 107

e. m<ABF = 90 + 51 = 141

f. m<DBF = 17 + 51 = 68

2.

<ABD, <DBE, <EBF, <FBC, <DBF

3.

<ABF, <DBC

4.

<ABE, <EBC

Answer:

a. 61.92 in²

b. 21.396 ≈ 21.4%

c. $4.71

Step-by-step explanation:

a. Amount of waste = area of rectangular piece of stock - area of two identical circles cut out

Area of rectangular piece of stock = 24 in × 12 in = 288 in²

Area of the two circles = 2(πr²)

Use 3.14 as π

radius = ½*12 = 6

Area of two circles = 2(3.14*6²) = 226.08 in²

Amount of waste = 288 - 226.08 = 61.92 in²

b. % of the original stock wasted = amount of waste ÷ original stock × 100

= 61.92/288 × 100 = 6,162/288 = 21.396 ≈ 21.4%

c. 288 in² of the piece of stock costs $12.00,

Each cut-out circle of 113.04 in² (226.08/2) will cost = (12*113.04)/288

= 1,356.48/288 = $4.71.

Answer:

13,000 ft.

Step-by-step explanation:

X -------10960----------C---------------D---------------Y

The entire race (from X to Y) is 7 miles.  There are 5,280 ft. in one mile, so 7 miles is 36960 ft.

If we subtract 10,960 from 36,960, then we get the distance from C to Y.

36960-10960 = 26000

They tell you D is at the midpoint between C and Y

So if we divide 26,000 by 2, then we know the distance from C to D and from D to Y.

26000/2 = 13000

The checkpoints are C and D, so the distance between them is 13,000 ft.

Answer:

The bottom left option

Step-by-step explanation:

The answer is equal to 44.

Answer:

bottom left

Step-by-step explanation:

Answer:

Given that m∠DEF = 142, m∠GEF = (9x - 8)°, and m∠DEG = (3x + 6),

GEF + DEG = DEF

[tex]9x - 8 + 3x + 6 = 142\\\\12x - 2 = 142\\\\12x = 144\\\\x = 12[/tex]

Answer:

Yes

Step-by-step explanation

6:3 multiply by 3 is equal to 18:3

Answer:

Yes

Step-by-step explanation:

This is because 6x3 is 18 for the 18:3 and 1x3 is 3 in the 18:3. You can also think it this way, 18/3 and 6/1 if you divide both you get an answer of 6 so they both are the same meaning making them equivalent

Answer:

im not sure but I think its 40

Step-by-step explanation:

bc 3/4 is $30 so 4/4 is an hour then she each would be $10 so 1/4 is 10 then 2/4 is 20 then 3/4 is 30 then 4/4 is 40

Answer:

$40 per hour

Step-by-step explanation:

I hope this helps!

Answer:

b

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

∡BEN=122

x=17

Step-by-step explanation:

Since you know that when two sides are congruent like this then the to angles are congruent then you know that angle BNE equals 29.

Once you know that since we know that 180 is the sum of all three angles set an equation like this:

180=29+29+(11x-65)

Take off parentheses since you can't simplify in them.

180=29+29+11x-65

Combine like terms.

180=11x-7

Solve for x.

187=11x

x=17

Plug that in to (11x-65) to find angle BEN

angle BEN = 11(17)-65

angle BEN=122

Answer:

s=-1.5

Step-by-step explanation:

We need to isolate the variable.

1. Subtract 4.5s from both sides

2. We now have the equation -4s+1=7

3. Subtract 1 from both sides

4. -4s=6

5. Divide both sides by -4

6. The answer would be s=-1.5

Answer:

the top empty box is 5 the second down box is 4 the box under 6 is 8

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Answer:

50 mph

Step-by-step explanation:

300 / 6 = 50

you can check this by setting up the equation,

6 x 50 = 300

So with this being said, you can conclude that your parents are driving a 50 miles per hour.

Answer:

1.66666666667

Step-by-step explanation:

Answer:

(1,7)

Step-by-step explanation:

SImply replace x by (1) in the expression to find the value of h:

h(1) = 4 (1) + 3 = 4 + 3 = 7

so for x = 1, h is 7 , which is written as: (1, 7)

Answer:

473 tickets

Step-by-step explanation:

8,500/18=472.2222222 but, since you can’t sell only part of a ticket, you’ll round up to get 473 tickets.

Answer:

Well, we need a definition or length/width of the figure of it first, let me see what I can find, I'll leave it in my replies.

Step-by-step explanation:

so basically the writing says to draw the lines indicated by arrows and include the markings on the last one because they indicate that all the sides are equal in length  

;P hope this helps!

Answer:

8x^6-27y^6

Step-by-step explanation:

simplify the expression

Answer:

t is not proportional because the price of of 1 chicken wing is not the same for each quantity ordered.

Step-by-step explanation:

Answer:

It is not proportional because the price of 1 chicken wing is not the same for each quantity ordered

Step-by-step explanation: i just got it right on the iready quiz

Answer:

Constant of proportionality [tex] = \frac{1}{400} [/tex]

Step-by-step explanation:

A. The constant of proportionality can be calculated as the ratio of y to x. In this case, y = amount of paint, while x = the area of the wall

The area of the wall determines the amount of paint needed to cover the wall.

Constant of proportionality, k = y/x.

Any given pair cam be used as y and x to find k.

Thus, using (100, ¼),

[tex] k = \frac{\frac{1}{4}}{100} = \frac{1}{4}*\frac{1}{100} [/tex]

Constant of proportionality [tex] = \frac{1}{400} [/tex]

This means that as area of the wall increases, amount of paint increases and the ratio between them would always be [tex] \frac{1}{400} [/tex].

Answer:

y=[tex]\frac{1}{4}[/tex]x+3

Explanation:

you have to use the formula y₂-y₁/x₁-x₂ in order to find your slope and what ever you get from that is your slope

Answer: 5[tex]y[/tex] − 1 + [tex]y^{2}[/tex]

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below. Thank you!

Step 1: Collect like terms.

(3[tex]y[/tex] + 2[tex]y[/tex]) + (6 − 3 − 4) + (-6[tex]y^{2}[/tex] + 7[tex]y^{2}[/tex])

Step 2: Simplify.

5[tex]y[/tex] − 1 + [tex]y^{2}[/tex]

~I hope I helped you! :) Good luck!~

Answer:

Step-by-step explanation:

Here you go mate

step 1

3y +6+ 2y - 3 - 6y^2+ 7y^2-4  equation

step 2

3y +6+ 2y - 3 - 6y^2+ 7y^2-4  simplify

3y+6+2y+(-3)+(-6y^2+)7y^2+(-4)

step 3

3y+6+2y+(-3)+-6y^2+7y^2+(-4)  combine the terms that are alike

step 4

(-6y^2+7y^2)+(3y+2y)+(6+(-3)+(−4))

answer

y^2+5y+−1