Can some one help with this question?
1 answer:
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Answer:
I) f + g = 10/3
II) 4f + 2g = 20/3
III) f = 2 and g = 4/3
Step-by-step explanation:
From the chart,
P = 25
q = 40
The total number of one centimeter lines in the first n diagrams is given by the expression
2/3n^3 + fn^2 + gn.
When n = 1, the total number of line = 4. So,
2/3(1)^3 + f(1)^2 + g(1) = 4
2/3 + f + g = 4
Make f+g the subject of formula
f + g = 4 - 2/3
f + g = (12 - 2)/3
f + g = 10/3 ......(1)
When n = 2
Total number of line = 12
2/3(2)^3 + f(2)^2 + g(2) = 12
2/3×8 + 4f + 2g = 12
16/3 + 4f + 2g = 12
4f + 2g = 12 - 16/3
4f + 2g = (36 - 16)/3
4f + 2g = 20/3 ......(2)
(iii) To find the values of f and g, solve equation 1 and 2 simultaneously
f + g = 10/3 × 2
4f + 2g = 32/3
2f + 2g = 20/3
4f + 2g = 32/3
- 2f = - 12/3
f = 12/6
f = 2
Substitutes f in equation 1
f + g = 10/3
2 + g = 10/3
g = 10/3 - 2
g = (10 - 6)/3
g = 4/3
Answer:
see explanation
Step-by-step explanation:
Given
x² - 3x - 40 = 0
Consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term (- 3)
The factors are - 8 and + 5, since
- 8 × 5 = - 40 and - 8 + 5 = - 3, thus
(x - 8)(x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x + 5 = 0 ⇒ x = 5
------------------------------------------------------
Given
4x² - 81 = 0 ← this is a difference of squares and factors in general as
a² - b² = (a + b)(a - b), thus
4x² - 81
=(2x)² - 9²
= (2x + 9)(2x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 9 = 0 ⇒ 2x = - 9 ⇒ x = -
2x - 9 = 0 ⇒ 2x = 9 ⇒ x =