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3 years ago

6

What are two pair fractions with common denominators for 3/5 and 3/4

1 answer:

diamong [38]3 years ago

6 0

The cheap answer is, you simply "grab the denominator of one and multiply it times the other's top and bottom", so let's do so,

$\bf \cfrac{3}{5}\cdot \cfrac{4}{4}\implies \cfrac{12}{20}\qquad \qquad \qquad \qquad \qquad \cfrac{3}{4}\cdot \cfrac{5}{5}\implies \cfrac{15}{20}$

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Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).

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The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted $C$ , which we can parameterize by the vector-valued function,

$\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)$

for $0\le t\le1$ , which has differential

$\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

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$\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)$

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$\implies f(1,1,1)=2-e$

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<u>Accordi</u><u>ng</u><u> </u><u>to</u><u> </u><u>the</u><u> </u><u>qu</u><u>estion</u><u>,</u>

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