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3 years ago

What’s the difference quotient simplified

Mathematics

1 answer:

mihalych1998 [28]3 years ago

7 0

$\text{Use}\ (a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\f(x+h)\to\text{exchange x to x + h}\\\\f(x)=x^3+3x\\\\f(x+h)=(x+h)^3+3(x+h)\\\\f(x+h)=x^3+3x^2h+3xh^2+h^3+3x+3h\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-(x^3-3x)}{h}\\\\=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-x^3-3x}{h}\\\\=\dfrac{(x^3-x^3)+3x^2h+3xh^2+h^3+(3x-3x)+3h}{h}\\\\=\dfrac{3x^2h+3xh^2+h^3+3h}{h}\\\\=\dfrac{h(3x^2+3xh+h^2+3)}{h}\\\\=\boxed{3x^2+3xh+h^2+3}$

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Answer:

She is doing a mistake of calculating interest after 9 months in place of after 12 months.

Step-by-step explanation:

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She is doing a mistake of calculating interest after 9 months in place of after 12 months.

The calculation of interest should be on a yearly basis (i.e. 12 months) as the interest rate is 2.5% per year. (Answer)

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4 years ago

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3 years ago

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Step-by-step explanation:

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Answer:

In case (a) car makes 105° turn.

In case (b) car makes 75° turn.

In case (c) car makes 105° turn.

Step-by-step explanation:

Figure is redrawn To explain properly (in attachment)

Given : streets are parallel means $\overline{AB}$ ║ $\overline{CD}$ ,

AB - 4th street , CD - 3rd street and XY - King Ave.

∠XLA = 75°

To find : (a) ∠XLB

(b) ∠LMD (left onto 3rd streat means left of car)

∠XLB + ∠XLA = 180° (Linear Pair = 2 adjacent angles are

supplementary)

∠XLB + 75° = 180°

∠XLB = 180 - 75

∠XLB = 105°

∴ In case (a) car makes 105° turn.

∠LMD = ∠XLA = 75° (Corresponding angles of parallel lines are equal)

∠LMD = 75°

∴ In case (b) car makes 75° turn.

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∠YMD + 75° = 180°

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∴In case (c) car makes 105° turn.

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3 years ago