What is the midpoint between (-4,4),(-2,2)

The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its la

cluponka [151]

Answer:

x = 31 hundred dolars and

y = 91/2 = 45.5 hundred dolars

Step-by-step explanation:

Given

R(x) = (40−8x+5y)*x + (50+9x−7y)*y

C(x) = (40−8x+5y)*10 + (50+9x−7y)*29

We can use the equation

P(x) = R(x) - C(x)

where

P(x) is the profit

R(x) is the revenue

and C(x) is the costs

In order to maximize the telephone company's profit, we apply

P'(x) = R(x)' - C(x)' = 0

⇒ R(x)' = ((40−8x+5y)*x + (50+9x−7y)*y)' = (40x-8x²+14xy+50y-7y²)'

⇒ C(x)' = ((40−8x+5y)*10 + (50+9x−7y)*29)' = (1850+181x-153y)'

⇒ P'(x) = -8x²-7y²-141x+203y+14xy-1850

The first-order partial derivatives of these functions are

Px(x,y) = -16x-141+14y

Py(x,y) = -14y+203+14x

Setting these equal to zero and solving we obtain:

-16x+14y-141 = 0

14x-14y+203=0

we get the solution

x = 31 and y = 91/2 = 45.5

Finally, the company should produce 3100 units of the first system, and 4550 units of the second system.

8 0

2 years ago

Charlie bought a pair of shorts at the store when they were having a 45% off sale. If the regular price of the pair of shorts wa

spayn [35]

Answer:

$13.20

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of the cylinder B, but it is the right in

yaroslaw [1]

Answer:

tha answer is d .

Step-by-step explanation:

i did this test

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Find the area of a regular polygon

Dimas [21]

Answer:

(N-2)x180=sum of interior angles

So (5-2)x180=540

Divided by number of sides=540/4=108... then each angle is 108 divide to triangles ..so they will have 2 angles =54 2 sides =4 the last angle =72 ."of the triangle " area of triangle =1/2xsxsxsin(side in

between)

So 1/2x4x4xsin(72)= then multiply it by 5 as u will have 5 triangles .. so it will be 190.2(probably i tried)

Step-by-step explanation:

4 0

1 year ago

Find the eccentricity, b. identify the conic, c. give an equation of the directrix, and d. sketch the conic.

densk [106]

Answer:

a) 10/3

b) hyperbola

c) x = ± 6/5

Step-by-step explanation:

a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:

$r=\frac{ep}{1\pm e*cos\theta}$

Given the conic equation: $r=\frac{12}{3-10cos\theta}$

We have to make it to be in the form $r=\frac{ep}{1\pm e*cos\theta}$ :

$r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }$

Comparing with $r=\frac{ep}{1\pm e*cos\theta}$

e = 10/3 = 3.3333, p = 6/5

b) since the eccentricity = 3.33 > 1, it is a hyperbola

c) The equation of the directrix is x = ±p = ± 6/5

6 0

1 year ago