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4 years ago

Given that weekly demand curve of a local wine producer is p = 50 − 0.1q, and that

Mathematics

1 answer:

rusak2 [61]4 years ago

3 0

Answer:

Z(p) = -10p² + 600p - 6500

Step-by-step explanation:

Demand curve p = 50 - 0.1 q

Total cost function C(q) = 1500 + 10q

where q is the number of bottles produced each day and p is the selling prices per bottle.

Now, p = 50 - 0.1 q

o.1 q = 50 - p

q = 500 - 10p

Revenue = price × quantity = p × q

= p ( 500 - 10p)

= 500 p - 10p²

Profit = total revenue - total cost

Let Profit be Z since profit is function of price, therefore

Z(p) = pq - C(q)

Z (p)= 500 p - 10p² - (1500 + 10q)

Substituting the value of q in above expression,

Z(p) = 500 p - 10p² - ( 1500 + 10 (500 - 10p))

Z(p) = 500p -10p² - 1500 -5000 + 100p

Z(p) = -10p² + 600p - 6500

So, the weekly profit as a function of price p is Z(p) = -10p² + 600p - 6500.

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Solve the following equation. Then place the correct number in the box provided. x/6=3

Aliun [14]

Answer:

x=18

Step-by-step explanation:

if x/6=3, the you can use the mulitplication property of equations to solve. so multiply each side by 6. it will eliminate the fraction on the left side of the equal side, leaving you with x and then 6x3=18, therefore

x=18

5 0

3 years ago

Read 2 more answers

In the diagram, AB:BC is 3:4 and AC:42 Find BC

Afina-wow [57]

From the diagram:
AB + BC = AC
we know that AC = 42, therefore:
AB + BC = 42 ..............> equation I

We know that the ratio AB:BC is 3:4. This means that:
AB/BC = 3/4
4AB = 3BC
AB = (3/4) BC ...............> equation II

Substitute by equation II in equation I to get BC as follows:
(3/4) BC + BC = 42
1.75 BC = 42
BC = 24

Substitute with the value of BC in equation II to get AB as follows:
AB = (3/4) * 24 = 18

6 0

4 years ago

I need help with this question ( see image). Please show workings.

wel

Answer:

(a) AC = 12.565 m

(b) bearing of C from A is 90°

Step-by-step explanation:

(a) extend North line down & perpendicular to AC.

Call that perpendicular intersection "P".

∠BAC = 90° - 53° = 37°

cos 37° = AP/15

0.7986 = AP/15

AP = 11.979 m

∠PNC = 180° - 161° = 19°

∠BCP = 90° - 19° = 71°

18 cm = 0.18 m (red flag note: 18 cm looks very out of scale for the picture)

cos 71° = CP/0.18

0.3256 = CP/0.18

CP = 0.586 m

AC = 11.979 + 0.586 = 12.565 m

(b) The bearing to C from A is 90°

1.6003 = 15/x

x = 9.373 m

5 0

3 years ago

Ten percent of the reds are added to twenty percent of the blues, and the total is 24. Yet the product of the number of reds and

salantis [7]

0.10r + 0.20b = 24
3r = b + 20....b = 3r - 20

0.10r + 0.20(3r - 20) = 24
0.10r + 0.60r - 4 = 24
0.70r = 24 + 4
0.70r = 28
r = 28/0.70
r = 40 <=== there are 40 reds

0.10r + 0.20b = 24
0.10(40) + 0.20b = 24
4 + 0.20b = 24
0.20b = 24 - 4
0.20b = 20
b = 20/0.20
b = 100 <=== there are 100 blues

5 0

4 years ago

Find the volume of a smaller wedge cut from a sphere of radius 66 by two planes that intersect along a diameter at an angle of π

djverab [1.8K]

Answer:

The answer is " $\frac{\pi a^3}{9}$ ".

Step-by-step explanation:

please find the complete question in the attached file.

Let the sphere center be (0,0,0) and then let the intersection diameter lie all along the z-axis.

So one of the collision plans is the xz-plane the other is the path via an xz-plane angle.

$\theta = \frac{\pi}{6}$

All appropriate region could then be indicated in spherical coordinates

$E= {(\rho, \theta, \phi) : 0 \geq \rho \geq a, 0 \geq \theta \geq \frac{\pi}{6}, 0 \geq \phi \geq \pi }$

Calculating the volume:

$\to v(E)=\int \int_{E} \int dV\\$

$=\int_{0}^{\frac{\pi}{6}} \int_{0}^{\pi} \int_{0}^{a} \rho^2 \sin \phi d \rho d \phi d \theta\\\\ =\int_{0}^{\frac{\pi}{6}} d \theta \int_{0}^{\pi} \sin \phi d \int_{0}^{a} \rho^2 d \rho\\\\= [\theta]^{\frac{\pi}{6}}_{0} [-\cos \phi]^{\pi}_{0} [\frac{\rho^3}{3}]^{a}_{0}\\\\= \frac{\pi}{6} [1+1] \frac{a^3}{3}\\\\=\frac{\pi a^3}{9}$

4 0

3 years ago