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crimeas [40]
3 years ago
9

The total revenue for Fred's Estates LLC is given as the function R(x) = 200x -0.25x2, where x is the number of villas booked. W

hat number of villas booked
produces the maximum revenue?
Mathematics
1 answer:
Tresset [83]3 years ago
5 0

Answer:

400 villas

Step-by-step explanation:

Since R(x)=200x−0.25x2 is a quadratic function with a negative leading coefficient, it represents a parabola opening downward. So its vertex will be the maximum of the function. If the coefficients are labeled, we have a=−0.25, b=200, and c=0. Then the vertex is found as follows.

x=−b/2a=−200/2(−0.25)=400

Therefore, maximum revenue will be attained when 400 villas are booked.

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The formula A=6V exponent 2/3 relates the surface area A, in square units, of a cube to the volume V, in cubic units. What is th
Sidana [21]

Answer:

729 in³

Step-by-step explanation:

Fill in the given numbers in the formula and solve for V.

... A = 6V^(2/3) . . . . . . the given formula

... 486 = 6V^(2/3) . . . . with the given area filled in

... 81 = V^(2/3) . . . . . . . divide by 6

... 81^(3/2) = V . . . . . . . raise to the 3/2 power. (2/3)·(3/2) = 1, so we have V on the right

... 729 = V . . . . in³

_____

You may have noticed that (81 in²)^(3/2) becomes 729 in³. The exponent operations work on the units, too.

7 0
3 years ago
Write the equation of each ellipse in standard form with the given characteristics.
Eddi Din [679]

Answer:

Step-by-step explanation:

The foci are horizontally aligned.

horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

center (h,k)

vertices (h±a,k)

length of minor axis = 2b

foci (h±c,k), c² = a²-b²

Apply your data and solve for h, k, a, and b.

foci (±3√19, 6)

h = 0

k = 6

Length of minor axis = 2b = 10

b = 5

foci (h±3√19, 6)

c = 3√19

c³ = a² - b²

171 = a² - 25

a²  = 196

x²/196 + (y-6)²/25 = 1

6 0
3 years ago
Meghan walked 1/3 mile in 3 minutes, 5 seconds. If she walk at the same rate, what portion of a mile will she walk in one second
ELEN [110]
1/555 of a mile. I did this by figuring out how many seconds it would take her to walk a full mile and then got the answer for 1 second
6 0
4 years ago
Consider the surface defined by the equation x3 + y3 + z3 = 3xyz. Use implicit differ- ∂z entiation to find ∂x. (Note z is not a
Aloiza [94]

Answer:    

   \frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}

Step-by-step explanation:

Given equation is x^{3}+y^{3}+z^{3}=3xyz ………………(1)

we use derivative formula \frac{d}{dx}(x^{n})  = n x^{n-1}

\frac{d}{dx}(x^{3)}  = 3 x^{2}

\frac{d}{dx}(z^{3)}  = 3 z^{2}

And also apply 'u v' formula

\frac{d}{dx}(uv})  = u\frac{d}{dx}(v)+v\frac{d}{dx}(u)

Differentiating  equation (1) partially with respective to 'x' , we treated 'y' as constant.

(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =3y(x\frac{∂z}{∂x}+z(1))   ( here y treated as constant so the derivative of constant function is zero in addition but in multiplication the constant is keep as like 'y').

on simplification , we get

(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =(3yx\frac{∂z}{∂x}+3yz)

again simplification, we get

3z^{2}\frac{∂z}{∂x}- 3yx\frac{∂z}{∂x}=3yz-3x^{2}

taking common '\frac{∂z}{∂x} on left on side , we get

(3z^{2}- 3yx)\frac{∂z}{∂x}=3yz-3x^{2}

dividing '(3z^{2}- 3yx) on both sides, we get

\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}

<u>Final answer</u>:-

\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}

6 0
3 years ago
3 – 4х = — 60 + 3x What is it?​
belka [17]

Answer:

9

Step-by-step explanation:

3−4x=−60+3x

Step 1: Simplify both sides of the equation.

3−4x=−60+3x

3+−4x=−60+3x

−4x+3=3x−60

Step 2: Subtract 3x from both sides.

−4x+3−3x=3x−60−3x

−7x+3=−60

Step 3: Subtract 3 from both sides.

−7x+3−3=−60−3

−7x=−63

divide by -7

9

5 0
3 years ago
Read 2 more answers
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