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3 years ago

If 1/2x^2 - 1/4 x + 3 what is the value of x = 8 ?

Mathematics

1 answer:

Vitek1552 [10]3 years ago

7 0

Answer:

If x=8 then the equation is equal to 33

If 1/2(x)^2-1/4x=3=8 then x=-2.98 and x=3.35

Step-by-step explanation:

Given:

1/2x^2-1/4x+3

Two solutions possible:

If x=8 then 1/2(8)^2-1/4(8)+3=32-2=3=33

If 1/2(x)^2-1/4x+3=8 then .5x^2-.25x-5=0

factoring:

(.707x+2.11)(.707x-2.37)=0

.707x=-2.11 and .707x=2.37

x=-2.98 and x=3.35 rounded to 2 places

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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

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Answer:

See expla below

Step-by-step explanation:

Given the demand function:

q = D (x) = 943 - 17 x

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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

$17x + 17x = 943$

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

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)

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= 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.

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Answer:

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