Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x)/g(x) and state its domain.

Consider the sequence 10, 2..

romanna [79]

Answer: see below

<u>Step-by-step explanation:</u>

1) 10, 2, 1.2, 1.12, 1.112, 1.1112

$t_n=\dfrac{t_{n-1}}{10}+1$

t₁ = 10

t₂ = 10/10 + 1 = 2

t₃ = 2/10 + 1 = 1.2

t₄ = 1.2/10 + 1 = 1.12

t₅ = 1.12/10 + 1 = 1.112

t₆ = 1.112/10 + 1 = 1.1112

2) 10, 2, -2, -4, -5, -5.5, ...

$t_n=\dfrac{t_{n-1}}{2}-3$

t₁ = 10

t₂ = 10/2 - 3 = 2

t₃ = 2/2 - 3 = -2

t₄ = -2/2 - 3 = -4

t₅ = -4/2 - 3 = -5

t₆ = -5/2 - 3 = -5.5

8 0

3 years ago

How many 2 1/2 hour movie can be shown consecutively in a 20 hour period?

Cloud [144]

20/2.5 = 8
So 8 movies can be shown in 20 hours.

5 0

3 years ago

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A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D (x) = 943 - 17 x, where q is the q

Alex73 [517]

Answer:

See expla below

Step-by-step explanation:

Given the demand function:

q = D (x) = 943 - 17 x

a) Find the elasticity:

Find the derivative of the demand function.

D'(x)= -17

Thus, elasticity expression is:

$\frac{x D'(x)}{D'(x)}$

$= \frac{x (-17)}{943 - 17x}$

$= \frac{17x}{943 - 17x}$

Elasticity expression = $E(x) = \frac{17x}{943 - 17x}$

b) At what price is the elasticity of demand equal to 1?

This means E(x) = 1

Substitute 1 for E(x) in the elasticity equation:

$E(x) = \frac{17x}{943 - 17x}$

$1 = \frac{17x}{943 - 17x}$

Cross multiply:

$943 - 17x = 17x$

Collect like terms

$17x + 17x = 943$

$34x = 943$

$x = \frac{943}{34}$

x = 27.74

Elasticity at the price of demand = 1 is 27.74

c) At what prices is the elasticity of demand elastic?

This means E(x) > 1

Therefore,

$\frac{17x}{943 - 17x} > 1$

Cross multiply:

$17x > 943 - 17x$

Collect like terms

$17x + 17x > 943$

$34x > 943$

$x > \frac{943}{34}$

x > 27.74

The elasticity of demand is elastic at x > 27.74

d) At what prices is the elasticity of demand inelastic?

This means E(x) < 1

Therefore,

$\frac{17x}{943 - 17x} < 1$

Cross multiply:

$17x < 943 - 17x$

Collect like terms

$17x + 17x < 943$

$34x < 943$

$x < \frac{943}{34}$

x < 27.74

The elasticity of demand is inelastic at x < 27.74

e) At what price is the revenue a maximum:

Total revenue will be:

R(x) = x D(x)

= x (943 - 17x)

= 943x - 17x²

R(x) = 934 - 17x(price that maximizes total revenue)

Take R(x) = 0

Thus,

0 = 943 - 17x

17x = 943x

$x = \frac{943}{17}$

$x = 27.74$

Total revenue is maximun at x= 27.74 per cookie

f) At x = 21 per cookie, find the price:

Thus,

R (21) = (943 * 21) - (17 * 21²)

= 19803 - 7497

= 12306

At x = 27.74, find the price:

R(27.74) = (943 * 27.74) - (17 - 27.74²)

= 26158.82 - 13081.63

= 13077.19

We can see the new price of cookie causes the total revenue to decrease.

Therefore, with a small increase in price the total revenue will decrease.

5 0

3 years ago

The house has a form of a rectangle with one side two and a half times as long as the other side. a Construct the expression for

Nookie1986 [14]

Answer: $A=2.5x^{2}$

Step-by-step explanation:

1. Let's write the following formula for calculate the area of a rectangle:

$A=yx$

Where $y$ is the lenght (the longer side) and $x$ is the width (the shorter side).

2. You know that the length is 2.5 times as long as the other side, which indicates a multiplication. Then:

$y=2.5x$

3. So, you must substitute $y$ into the equation for calculate the area of the rectangle and then you must simplify.

4. Then, you obtain the following expression:

$A=(2.5x)(x)\\A=2.5x^{2}$

4 0

3 years ago

What is the absolute magnitude of a star that has a period of 62 days?

mylen [45]

your 62 days shirt

3 0

3 years ago

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