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tiny-mole [99]
3 years ago
6

What is 3 1/3 x 2 1/4 ?

Mathematics
2 answers:
vfiekz [6]3 years ago
8 0

3 \frac{1}{3}  \times 2 \frac{1}{4}  \\   = \frac{(3 \times 3) + 1}{3}  \times  \frac{(2 \times 4) + 1}{4}  \\  =  \frac{9 + 1}{3}  \times  \frac{8 + 1}{4}  \\  =  \frac{10}{3}  \times  \frac{9}{4}  \\  =  \frac{90}{12}  \\  =  \frac{15}{2}
The answer is 15/2 = 7.5
swat323 years ago
6 0

You need to change the mixed number into a improper fraction:

3\dfrac{1}{3}=\dfrac{3\cdot3+1}{3}=\dfrac{10}{3}\\\\2\dfrac{1}{4}=\dfrac{2\cdot4+1}{4}=\dfrac{9}{4}\\\\3\dfrac{1}{3}\cdot2\dfrac{1}{4}=\dfrac{10}{3}\cdot\dfrac{9}{4}\\\\=\dfrac{5}{3}\cdot\dfrac{9}{2}=\dfrac{5}{1}\cdot\dfrac{3}{2}=\dfrac{15}{3}=7\dfrac{1}{2}=7.5

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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

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(a)

y = (2x - 1)(x + 4)²

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g(x) = (x + 4)²

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Then

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    = 2(x + 4) (2x - 1 + x + 4)

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

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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)

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

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y = (x² - 1)(x³ + 1)

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g(x) = (x³ + 1) ⇒ g'(x) = 3x²

Then

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