y = ( 3 + 2x - x² )³

Using power and chain rule we get:

dy/dx = 3(3 + 2x - x²)² × d/dx (3 + 2x - x²)

= 3(2 - 2x)( 3 + 2x - x² )²

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It's a quadratic equation so factor out it. Break the 7x in two terms 4x+3x and rewrite.

2x² + 7x + 6 = 0 ⇒ 2x² + 4x + 3x + 6 = 0

Now, take 2x common from first two terms and 3 from last two terms

⇒ 2x(x + 2) + 3(x + 2) = … Read more

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Ones = 0

Tens = 00

Hundreds = 000

Thousands = 0,000

Ten Thousands = 00,000

Hundred Thousands = 000,000

Millions = 0,000,000

Ten Millions = 00,000,000

Hundred Millions = 000,000,000

Billions = 0,000,000,000

Ten Billions = 00,000,000,000

Hundred Billions = 000,000,000,000

Trillions = 0,000,000,000,000

14.3 trillions = 14,300,000,000,000

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1/8 × 4

Rewrite it as

1/8 × 4/1

= (1×4)/(8×1)

= 4/8

= 1/2 teaspoon

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Given root of polynomial function x=∛28

g(2)=x3 -28=0

Applying Newton's method

x_(n+1) = x_n - (g(x_n)) / (g'(x_n))

For c₁ ⇒ c₁ = c₀ - (g(c₀)) / (g'(c₀))

Thus, c₀ =3

So, g'(3)=27

g(3)=27-28=-1

c₁ = (3-(-1)) / (27) = (81+1) / (27)

c₁ = (82)/(27)

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To find 'c', solve f'(x)=0

⇒ (x² − 1) × 1 + 2x(x − 2) = 0

⇒ x²− 1 + 2x² − 4x = 0

⇒ 3x2 − 4x−1 = 0

⇒ [4±√16-(4)(3)(-1)] / (2(3))

⇒x = (2±√7)/(3)

⇒x = (2+√7)/(3) and x = (2-√7)/(3)

x = (2+ √7)/(3) = 1.55 ∈(1,2]

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geometric return = ⁿ√{(1+r₁) × (1+r₂) × ...} - 1

Where, r = rate of return

n = number of periods

For 1st yr, rate of return = r₁ = 5% = 0.05

For 2nd yr, rate of return = r₂ = -30% = -0.3

Number of years = 2

geometric return = √{(1 + 0.05)(1 - 0.3)}-1= √{(1.05) (0.7)}-1

= -0.143

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door tickets = D

Make equations according to the problem

A + D = 120.....(1)

10A + 15D = \$1390....(2)

Multiplying eq(1) by 10 and subtracting from eq(2) we get

D = 38(number of tichets at door)

Put value of D in eq(1) we get-

A + 38 = 120

A = 82(number of tichets were purchased in advance)

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16 + (28/2) - (6 /10) - 4 × 2

Use order of operation, i.e., PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction)

First, simplify parenthesis

= 16 + 14 - 0.6 - 4 × 2

Now, multiplication

= 16 + 14 - 0.6 - 8