ROUND 75.4614 TO THE NEAREST THOUSANDTH

A garden shop determines the demand function q = D(x) = 5x + 200 / 30x + 11 during early summer for tomato plants where q is the

cricket20 [7]

Answer: a) $E(x)=\dfrac{-5945}{(30x+11)(5x+200)}$ , b) 0.7975, demand is inelastic, c) increase.

Step-by-step explanation:

Since we have given that

$D(x)=\dfrac{5x+200}{30+11}$

So, derivative w.r.t x would be

$D'(x)=\dfrac{5(30x+11)-30(5x+200)}{(30x+11)^2}\\\\D'(x)=\dfrac{150x+55-150x-6000}{(30x+11)^2}\\\\D'(x)=\dfrac{5945}{(30x+11)^2}$

As we know that

$E(x)=\dfrac{-xD'(x)}{D(x)}\\\\\\E(x)=\dfrac{\dfrac{-(-)5945x}{(30x+11)^2}}{\dfrac{5x+200}{30x+11}}\\\\\\E(x)=\dfrac{5945x}{(30x+11)(5x+200)}$

(b) Find the elasticity when x = 2.

So, we put x = 2, we get that

$E(2)=\dfrac{5945\times 2}{(30(2)+11)((5(2)+200))}\\\\E(2)=\dfrac{11890}{(60+11)(10+200)}\\\\E(2)=\dfrac{11890}{71\times 210}\\\\E(2)=\dfrac{11890}{14910}\\\\E(2)=0.7975$

Since, 0.7975 < 1, so the demand is inelastic.

(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?

The total revenue will also increase with increase in price.

As total revenue = $price\times quantity$

Hence, a) $E(x)=\dfrac{-5945}{(30x+11)(5x+200)}$ , b) 0.7975, demand is inelastic, c) increase.

4 0

3 years ago

Use the remainder theorem to find the remainder for each of the following divisions. (x²+3x+1)/(x+2)

Jet001 [13]

Answer:

The remainder of this division is -1.

Step-by-step explanation:

Given data in the question:-

Dividend= $x^2+3x+1$

Divisor= $x+2$

Solution:-

To find the remainder using the remainder theorem. We have to substitute -2 in the dividend and on solving that we will get the remainder.

We got -2 from the divisor when we equate the divisor to 0.

x+2=0

x=-2

$p(a)=x^2+3x+1\\$

Substituting -2 in above written equation.

$p(-2)=(-2)^2+3(-2)+1\\p(-2)=4-6+1\\p(-2)=5-6\\p(-2)=-1$

3 0

3 years ago

15 Points

lakkis [162]

Answer:

y = 22⅘

Step-by-step explanation:

5x = 4

x = 0.8

y + 62(0.8) - 3y = 4

2y = 49.6 - 4

2y = 45.6

y = 22.8

4 0

3 years ago

Find a mathematical model for the below statement. (Use k for the constant of proportionality.) The gravitational attraction F b

zubka84 [21]

Answer:

$F = k\frac{m_1m_2}{r^2}$

Step-by-step explanation:

Direct proportional:

Multiplication

Inverse proportional:

Division

The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to the masses

This means that:

$F = k\frac{m_1m_2}{}$

Inversely proportional to the square of the distance r between the objects.

Denominator is $r^2$ . Thus:

$F = k\frac{m_1m_2}{r^2}$

4 0

3 years ago

Which undefined geometric term can be described as a one-dimensional set of points that has no beginning or end

Komok [63]

Answer:

A line

Step-by-step explanation:

A line is one dimensional

A line has a set of points

A line has no beginning or end, only length

5 0

3 years ago

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