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myrzilka [38]
3 years ago
6

A tetherball is swinging in a horizontal circle around a pole attached with a 1.2m long massless rope. it makes an angle of 40 d

egrees with the pole. with what velocity is the ball moving?
Mathematics
1 answer:
max2010maxim [7]3 years ago
8 0
<span>If you are given a tetherball swinging in a horizontal circle around a pole attached with a 1.2m long massless rope and it makes an angle of 40 degrees with the pole, you will have a velocity of the ball moving at 0.84m/s.</span>
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Help. <br>Please its urgent show workings.<br>​
laiz [17]

Answer:

see explanation

Step-by-step explanation:

There are 2 possible approaches to differentiating these.

Expand the factors and differentiate term by term, or

Use the product rule for differentiation.

I feel they are looking for use of product rule.

Given

y = f(x). g(x) , then

\frac{dy}{dx} = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

y = (2x - 1)(x + 4)²

f(x) = 2x - 1 ⇒ f'(x) = 2

g(x) = (x + 4)²

g'(x) = 2(x + 4) × \frac{d}{dx} (x + 4) ← chain rule

       = 2(x + 4) × 1

        = 2(x + 4)

Then

\frac{dy}{dx} = (2x - 1). 2(x + 4) + (x + 4)². 2

    = 2(2x - 1)(x + 4) + 2(x + 4)² ← factor out 2(x + 4) from each term

    = 2(x + 4) (2x - 1 + x + 4)

    = 2(x + 4)(3x + 3) ← factor out 3

    = 6(x + 4)(x + 1)

--------------------------------------------------------------------------

(b)

y =  x(x² - 1)³

f(x) = x ⇒ f'(x) = 1

g(x) = (x² - 1)³

g'(x) = 3(x² - 1)² × \frac{d}{dx} (x² - 1) ← chain rule

        = 3(x² - 1)² × 2x

        = 6x(x² - 1)²

Then

\frac{dy}{dx} = x. 6x(x² - 1)² + (x² - 1)³. 1

    = 6x²(x² - 1)² + (x² - 1)³ ← factor out (x² - 1)²

    = (x² - 1)² (6x² + x² - 1)

     = (x² - 1)²(7x² - 1)

----------------------------------------------------------------------

(c)

y = (x² - 1)(x³ + 1)

f(x) = x² - 1 ⇒ f'(x) = 2x

g(x) = (x³ + 1) ⇒ g'(x) = 3x²

Then

\frac{dy}{dx} = (x² - 1). 3x² + (x³ + 1), 2x

   = 3x²(x² - 1) + 2x(x³ + 1) ← factor out x

   = x[3x(x² - 1) + 2(x³ + 1) ]

   = x(3x³ - 3x + 2x³ + 2)

   = x(5x³ - 3x + 2) ← distribute

    = 5x^{4} - 3x² + 2x

--------------------------------------------------------------------

(d)

y = 3x³(x² + 4)²

f(x) = 3x³ ⇒ f'(x) = 9x²

g(x) = (x² + 4)²

g'(x) = 2(x² + 4) × \frac{d}{dx}(x² + 4) ← chain rule

       = 2(x² + 4) × 2x

       = 4x(x² + 4)

Then

\frac{dy}{dx} = 3x³. 4x(x² + 4) + (x² + 4)². 9x²

    = 12x^{4}(x² + 4) + 9x²(x² + 4)² ← factor out 3x²(x² + 4)

    = 3x²(x² + 4) [ 4x² + 3(x² + 4) ]

    = 3x²(x² + 4)(4x² + 3x² + 12)

    = 3x²(x² + 4)(7x² + 12)

5 0
2 years ago
How many cubes would you use to make the structure above/below
loris [4]
The answer is 17 cubes.
I drew lines to make cubes so I could see it better 
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3 years ago
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Need to solve this problem in steps 5(2x+6)=-4(-5-2x)+3x
Dovator [93]

Answer:

Simplifying

5(2x + 6) = -4(-5 + -2x) + 3x

Reorder the terms:

5(6 + 2x) = -4(-5 + -2x) + 3x

(6 * 5 + 2x * 5) = -4(-5 + -2x) + 3x

(30 + 10x) = -4(-5 + -2x) + 3x

30 + 10x = (-5 * -4 + -2x * -4) + 3x

30 + 10x = (20 + 8x) + 3x

Combine like terms: 8x + 3x = 11x

30 + 10x = 20 + 11x

Solving

30 + 10x = 20 + 11x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11x' to each side of the equation.

30 + 10x + -11x = 20 + 11x + -11x

Combine like terms: 10x + -11x = -1x

30 + -1x = 20 + 11x + -11x

Combine like terms: 11x + -11x = 0

30 + -1x = 20 + 0

30 + -1x = 20

Add '-30' to each side of the equation.

30 + -30 + -1x = 20 + -30

Combine like terms: 30 + -30 = 0

0 + -1x = 20 + -30

-1x = 20 + -30

Combine like terms: 20 + -30 = -10

-1x = -10

Divide each side by '-1'.

x = 10

Simplifying

x = 10

5 0
3 years ago
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mixas84 [53]

Step-by-step explanation:

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2 years ago
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The area of a rectangle is the product of its length and width. Both length and width are whole numbers. A rectangular poster ha
lesya [120]

Answer: a rectangular poster has an area of 260 square inches.the width of the poster is greater than 10 inches and is a prime number

Step-by-step explanation: a rectangular poster has an area of 260 square inches.the width of the poster is greater than 10 inches and is a prime number.what is the width

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3 years ago
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