You buy a 24 pack of 591mL bottles of water. How many Liters is that?

1 answer:

3 0

24 bottles x 591 mL/bottle = 14,184 mL

Since 1L = 1000 mL,

14,184 mL x 1L/1000mL = 14,184/1000 = 14.184L (14 whole liters)

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Use the chain rule to find dw/dt. w = ln x2 + y2 + z2 , x = 7 sin(t), y = 9 cos(t), z = 6 tan(t)

DENIUS [597]

By the chain rule,

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

We have

$\dfrac{\partial w}{\partial x}=\dfrac{2x}{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial y}=\dfrac{2y}{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac{2z}{x^2+y^2+z^2}$

$\dfrac{\mathrm dx}{\mathrm dt}=7\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-9\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=6\sec^2t$

So we have

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac2{x^2+y^2+z^2}\left(7x\cos t-9y\sin t+6z\sec^2t\right)$
$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{2\left(49\sin t\cos t-81\cos t\sin t+36\tan t\sec^2t\right)}{49\sin^2t+81\cos^2t+36\tan^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{8\sin t(9-16\cos^4t)}{\cos t(36+13\cos^2t+32\cos^4t)}$

3 0

2 years ago

Find the sum of 2x2 3x - 4, 8 - 3x, and -5x2 2. -3x2 - 2 -7x2 - 2 -3x2 6 -7x2 - 6x - 2

Law Incorporation [45]

-3x to the second power - 2

I believe this is your answer.

4 0

2 years ago

Can you please help me with this

Vitek1552 [10]

Answer:

log9

Step-by-step explanation: