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)=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)
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
⇒ 3x2 − 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
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
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)
seriously... 8)
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
