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3 years ago

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Mrs. Vargas owns (4/5)of an acre in Tupelo Township. she wants to sell (2)/(3)of her land to her neighbor.What fraction of an ac

re does Mrs. Vargas want to sell.

1 answer:

Nataliya [291]3 years ago

4 0

<span>Convert your fractions to a decimal (1) One 5th = .20% 4/5th = .80 0r 80 % of an acre. She wants to sell 2/3rd, one third is 33.3, two third is 66.6, 2/3rd of 80 is 53.38 of an acre.80 x.666=53.38.

(2) One 5th = .20%,2 5th= 40% you need 40% of the 7/10, or 70% of the brownies. 70 times .40 =28 If the whole pan had 100 brownies Greg would buy 28 brownies.</span>

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1. By the chain rule,

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

I'm going to switch up the notation to save space, so for example, $z_x$ is shorthand for $\frac{\partial z}{\partial x}$ .

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We have

$x=e^{-t}\implies x_t=-e^{-t}$

$y=e^t\implies y_t=e^t$

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$\implies z_t=e^t\sec^2(1)(-e^{-t})+e^{-t}\sec^2(1)e^t=0$

Similarly,

$w_t=w_xx_t+w_yy_t+w_zz_t$

where

$x=\cosh^2t\implies x_t=2\cosh t\sinh t$

$y=\sinh^2t\implies y_t=2\cosh t\sinh t$

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To capture all the partial derivatives of $w$ , compute its gradient:

$\nabla w=\langle w_x,w_y,w_z\rangle=\dfrac{\langle1,-1,1\rangle}{\sqrt{1-(x-y+z)^2}}}=\dfrac{\langle1,-1,1\rangle}{\sqrt{-2t-t^2}}$

$\implies w_t=\dfrac1{\sqrt{-2t-t^2}}$

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If that's the case, then

$z_s=z_xx_s+z_yy_s$

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Putting everything together, we get

$z_s=\cos(s+t)\cos(s^2t)-2st\sin(s+t)\sin(s^2t)$

$z_t=\cos(s+t)\cos(s^2t)-s^2\sin(s+t)\sin(s^2t)$

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