Find the sum of -3a and 5a -3

A beverage company works out a demand function for its sale of soda and finds it to be x = D(p) = 3100 - 20p where x = the quant

Shtirlitz [24]

Answer with Step-by-step explanation:

We are given that a demand function

$x=D(p)=3100-20p$

Where x=The quantity of sodas sold

p=Per can price (in cents)

We have to find the price p for which the demand inelastic.

Differentiate the demand function w.r.t p

$D'(P)=-20$

Price elasticity of demand= $E(p)=\frac{-pD'(p)}{D(p)}$

Price elasticity of demand= $E(p)=\frac{-p(-20)}{3100-20p}$

When demand is inelastic then

E(p)<1

$\frac{20p}{3100-20p}$ <1

Multiply by (3100-20p) on both sides

$20p$

Adding 20p on both side of inequality

$40p$

Divide by 40 on both sides

$p$

When the value of price is less than 77.5 then the demand of elasticity is inelastic.

3 0

3 years ago

Use ratio language to describe the relationship of any two things you can think of.

miss Akunina [59]

Answer:

Step-by-step explanation:

the recipe called for 3 cups of flour and 4 cups of sugar. That means there is 3/4 cups of flour for each cup of sugar.

She drove 60 miles in 3hrs. This means she drove 60/3 = 20 miles per hr.

hope this helps?

3 0

3 years ago

Triangle QRS is transformed as shown on the graph. Which rule describes the transformation?

hjlf

Answer: Ro, 270 degrees

Step-by-step explanation:

When doing rotational transformation, you always rotate counter-clockwise. In this case, the triangle on the top right is the original figure, and the triangle on the bottom left is the image. You can pick any point on the original triangle and compare it to its corresponding point on the image to figure out how it has been transformed.

6 0

3 years ago

Read 2 more answers

Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (2 comma 0

SVETLANKA909090 [29]

Answer:

The volume of the tetrahedron is:

$\frac{50}{3}=16.667$

Step-by-step explanation:

The volume of the tetrahedron is given by the intersection of the planes x = 0, y = 0, z = 0 and the plane formed by the three points given.

The equation of the plane formed by the three points is:

Points: (2,0,0);(0,5,0);(0,0,4)

$\pi :\frac{x}{2} +\frac{y}{5} +\frac{z}{4} =1$

It can also be expressed as:

$10x + 4y+5z=20$

We have to calculate the triple integral, therefore we must define the domain:

The values of x are given by:

0≤x≤2

We will integrate the values of y between the y = 0 axis and the line formed when z = 0:

z=0 ⇒ 10x + 4y=2 ⇒ $y=\frac{20-10x}{4} =$

$0\leq y \leq 5-\frac{5}{2}x$

We will integrate the values of z between the plane z = 0 and the plane 10x + 4y+5z=20

10x + 4y+5z=20 ⇒ $z=\frac{20-10x-4y}{5} =4-2x-\frac{4}{5}y$

$0\leq z \leq 4-2x-\frac{4}{5}y$

The volume of the tetrahedron is:

$\int\limits^{2}_{0} \ \ \ \int\limits^{5-\frac{5}{2} x}_{0} \ \ \ \int\limits^{4-2x-\frac{4}{5}y }_{0} {z} \, dz\, dy \,dx$

$\int\limits^{2}_{0} \ \ \ \int\limits^{5-\frac{5}{2} x}_{0} \frac{z^2}{2}|^{4-2x-\frac{4}{5}y}_0\, dy \,dx$

$\frac{z^2}{2}|^{z=4-2x-\frac{4}{5}y}_{z=0}=\frac{5}{25}(5x+2(y-5))^2$

$\int\limits^{2}_{0} \ \ \ \int\limits^{5-\frac{5}{2} x}_{0} {\frac{5}{25}(5x+2(y-5))^2}\, dy \,dx$

$\int\limits^{2}_{0} {-\frac{25}{6}(x-2)^3} dx=-\frac{25}{24} (x-2)^4|^{2}_{0}=\frac{50}{3}$

6 0

4 years ago

The Leukemia and Lymphoma Society sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in donations, bu

loris [4]

Donations = $10,000
Revenue = $55 per race enry
Expense = $15 per race entry
Budget ≥ $55,000

Let x = the number of race entries.
Total revenue = Donations + Race entries - Expenses
Therefore
10000 + 55x - 15x ≥ 55000
40x ≥ 45000
x ≥ 1125

Answer: Race entries ≥ 1125

6 0

4 years ago