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scoundrel [369]

1 year ago

7

Laura, Maria, and Nathan had 2 1 4 cups of milk to share for breakfast. Laura poured some milk on her breakfast cereal. Then she

gave the remaining 2 3 of the milk to Maria. How many cups of milk did Laura give to Maria

1 answer:

ollegr [7]1 year ago

7 0

The cups of milk Laura gave to Maria is 19/12 cups is 19/12 cups

<h3>How to calculate fraction</h3>

Total cups of milk to share = 2 1/4 cups

Laura = x

Maria = 2/3 cups

Total = Laura + Maria

2 1/4 = x + 2/3

2 1/4 - 2/3 = x

9/4 - 2/3 = x

(27-8) / 12 = x

19/12 = x

= 1 7/12

Therefore, the cups of milk Laura gave to Maria is 19/12 cups

Learn more about fraction:

brainly.com/question/11562149

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3 years ago

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2 years ago

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustra

Rainbow [258]

Answer:

$x = t$

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Step-by-step explanation:

Given

$x=t$

$y=e^{-t}$

$z=2t-t^2$

(0, 1, 0)

The vector equation is given as:

$r(t) = (x,y,z)$

Substitute values for x, y and z

$r(t) = (t,\ e^{-t},\ 2t - t^2)$

Differentiate:

$r'(t) = (1,\ -e^{-t},\ 2 - 2t)$

The parametric value that corresponds to (0, 1, 0) is:

$t = 0$

Substitute 0 for t in r'(t)

$r'(t) = (1,\ -e^{-t},\ 2 - 2t)$

$r'(0) = (1,\ -e^{-0},\ 2 - 2*0)$

$r'(0) = (1,\ -1,\ 2 - 0)$

$r'(0) = (1,\ -1,\ 2)$

The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)

It should be noted that:

The equation of a line through position vector a and parallel to vector v is given as:

$r(t) = a + tv$

Such that:

$a = (0,1,0)$ and $v = r'(0) = (1,-1,2)$

The equation becomes:

$r(t) = (0,1,0) + t(1,-1,2)$

$r(t) = (0,1,0) + (t,-t,2t)$

$r(t) = (0+t,1-t,0+2t)$

$r(t) = (t,1-t,2t)$

By comparison:

$r(t) = (x,y,z)$ and $r(t) = (t,1-t,2t)$

The parametric equations for the tangent line are:

$x = t$

$y = 1 - t$

$z = 2t$

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