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3 years ago

Pls help working this out step by step: Simplify fully (4+√12)(5-√3)

Mathematics

1 answer:

Airida [17]3 years ago

4 0

Answer:

14 + 6 $\sqrt{3}$

Step-by-step explanation:

(4 + $\sqrt{12}$ )(5 - $\sqrt{3}$ )

Each term in the second factor is multiplied by each term in the first factor

4(5 - $\sqrt{3}$ ) + $\sqrt{12}$ (5 - $\sqrt{3}$ ) ← distribute parenthesis

= 20 - 4 $\sqrt{3}$ + 5 $\sqrt{12}$ - $\sqrt{36}$

= 20 - 4 $\sqrt{3}$ + 5(2 $\sqrt{3}$ ) - 6

= 20 - 4 $\sqrt{3}$ + 10 $\sqrt{3}$ - 6 ← collect like terms

= 14 + 6 $\sqrt{3}$

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4 years ago

Read 2 more answers

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belka [17]

$v=\dfrac h{3x}\implies\dfrac{\mathrm dv}{\mathrm dt}=\dfrac{3x\frac{\mathrm dh}{\mathrm dt}-3h\frac{\mathrm dx}{\mathrm dt}}{3x^2}$

By the chain rule,

$\dfrac{\mathrm dh}{\mathrm dt}=\dfrac{\mathrm dh}{\mathrm dx}\dfrac{\mathrm dx}{\mathrm dt}$

We have

$h(x)=4e^{2x-6}-x^2+5\implies\dfrac{\mathrm dh}{\mathrm dx}=8e^{2x-6}-2x$

and we're given that $x$ changes at a constant rate of $\frac{\mathrm dx}{\mathrm dt}=0.2$ thousand people per minute, which means

$\dfrac{\mathrm dv}{\mathrm dt}=\dfrac{3x\left(8e^{2x-6}-2x\right)\left(0.2\frac{\text{thousand people}}{\rm min}\right)-3h\left(0.2\frac{\text{thousand people}}{\rm min}\right)}{3x^2}$

At the moment $x=4$ thousand people are in the park, we have $h(4)=4e^2-11$ , so we find

$\dfrac{\mathrm dv}{\mathrm dt}=\dfrac{12\left(8e^2-8\right)-3(4e^2-11)}{240}\dfrac{\text{thousand people}}{\rm min}=\dfrac{7(4e^2-3)}{80}\dfrac{\text{thousand people}}{\rm min}$

or approximately 2.324 thousand people per minute.

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4 years ago

What is the answer to 7/9+(-5/12)

galina1969 [7]

13 / 36 :)

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3 years ago

A bank requires a four- digit access code for each account. The access code is generated using the digits 0-9, and the digits ca

zheka24 [161]

Answer:

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Step-by-step explanation:

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4 years ago