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

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

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

1/8 × 4

Rewrite it as

1/8 × 4/1

= (1×4)/(8×1)

= 4/8

= 1/2 teaspoon

Given root of polynomial function x=∛28

g(2)=x^{3} -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)

f(x) = 3x - 1

g(x) = 4x - 2

h(x) = 2f(x) + g(x)

h(x) = 2(3x - 1) + 4x - 2

= 6x -2 + 4x - 2

= 10x - 4

Use the chain rule with Fundamental Theorem of calculus

g′(x)=f(h(x)) h′(x) − f(ϕ(x)) ϕ′(x)

=f(x²) × d/dx (x²) − f(5x+1) × d/dx (5x+1)

= (sin x²)/(x²) × (2x) - (sin (5x+1))/(5x+1) × 5

= (2x sin x²)/(x²) - (-5 sin (5x+1))/(5x+1)

https://answers.yahoo.com/question/index?qid=20090424031100AAXjbJ0

I hope it'll help you.

What are you cutting your coke with?

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

⇒ (x² − 1) × 1 + 2x(x − 2) = 0

⇒ x²− 1 + 2x² − 4x = 0

⇒ 3x^{2} − 4x−1 = 0

It's a quadratic equation so, solve it using quadratic formula

⇒ [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]

x … Read more

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

Geometric … Read more

Let advance Tickets = A

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)

⁸C₂ × ⁴C₁ + ⁸C₂ × ⁴C₂

= 28 × 4 + 28 × 6

= 280

cos A = -4/5

A = cos^-1 (-4/5)

A = 143°

tan (143/2) = 2.98

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

Similarly, apply addition and subtraction

= 30 - 0.6 - 8

= 21.4

Rewrite it

= 7 × 100 + 8 × 1 + 9 × 0.1 + 8 × 0.001

= 700 + 8 + 0.9 + 0.008

= 708.908