(-4a^3bc^2)(a^3b^2c)(3ab^4c^5)

Mathematics

1 answer:

3241004551 [841]3 years ago

4 0

Answer:( -22•3a7b7c8)

Step-by-step explanation:

STEP1

Equation at the end of step 1

((0-(((4•(a3))•b)•(c2)))•(((a3)•(b2))•c))•(3ab4•c5)

STEP 2

Equation at the end of step2

((0 - ((22a3 • b) • c2)) • a3b2c) • 3ab4c5

STEP 3

Multiplying exponential expressions :

3.1 a6 multiplied by a1 = a(6 + 1) = a7

Multiplying exponential expressions :

3.2 b3 multiplied by b4 = b(3 + 4) = b7

Multiplying exponential expressions :

3.3 c3 multiplied by c5 = c(3 + 5) = c8

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[Supply] $p = q^2+20$
[Demand] $p=-4q^2+10q+18600$

Equilibrium price is when
Supply = Demand
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The simplified equation is in quadratic form.
There are three main methods for solving a quadratic equation: factorizing, completing the square, or quadratic formula.

Using the formula, we need the value of a, b, and c which is the constant of the quadratic equation.
$q_1= \frac{-b+ \sqrt{(b)^2-4ac)} }{2a}$ , and $q_2= \frac{-b- \sqrt{(b)^2-4ac)} }{2a}$

We have a = 1, b = -2, and c = -3716
Substituting these values into the formula we have
$q_1= \frac{-(-2)+ \sqrt{(-2)^2-4(1*-3716)} }{2} =61.97$
$q_2= \frac{-(-2)- \sqrt{(-2)^2-4(1*-3716)} }{2} =-59.97$

Since 'q' represents a quantity, we can't have negative values, so we choose the value of 'q' to be 61.97 ≈ 62 (rounded to the nearest whole number)

Answer: Equilibrium quantity = 62

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