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3 years ago

5/x - 3/4 = Simplify

Mathematics

1 answer:

Verdich [7]3 years ago

7 0

Answer:

$\frac{20-3x}{4x}$

Step-by-step explanation:

-This is an LCM problem.

-To simplify, we introduce a least common multiplier which is equivalent the product of the denominators:

$LCM=x\times 4\\\\=4x$

#We introduce the LCM and adjust the fractions based on it :

$=\frac{5}{x}+\frac{3}{4}\\\\\\=\frac{20}{4x}+\frac{3x}{4x}\\\\\\=\frac{20-3x}{4x}$

Hence, the simplified form of the fraction is: $\frac{20-3x}{4x}$

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katen-ka-za [31]

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3 years ago

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Sophie [7]

Answer:

Distributive property

Step-by-step explanation:

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3 years ago

Round 26 to its greatest place value

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6 0

3 years ago

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(a) Show that y Superscript 8 Baseline plus x minus 3 equals 0 is an implicit solution to StartFraction dy Over dx EndFraction

Nitella [24]

Answer:

Step-by-step explanation:

8 0

3 years ago

Find the directional derivative of the function at the given point in the direction of the vector v. h(r, s, t) = ln(3r + 6s + 9

vodka [1.7K]

Answer:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=(\frac{2}{7}\overrightarrow{\rm i})*(\frac{1}{r+2s+3t})+(\frac{6}{7}\overrightarrow{\rm j})*(\frac{2}{r+2s+3t})+(\frac{3}{7}\overrightarrow{\rm k})*(\frac{3}{r+2s+3t})$

Step-by-step explanation:

First, let’s check to see if the direction vector is a unit vector:

$||v||=\sqrt{(14)^{2} +(42)^{2} +(21)^{2} } =\sqrt{2401} =49$

It’s not a unit vector. therefore let's divide the vector by its magnitude in order to convert it into a unit vector:

$\overrightarrow{\rm v}=(\frac{14}{49}\overrightarrow{\rm i})+(\frac{42}{49}\overrightarrow{\rm j})+(\frac{21}{49}\overrightarrow{\rm k})= (\frac{2}{7}\overrightarrow{\rm i})+(\frac{6}{7}\overrightarrow{\rm j})+(\frac{3}{7}\overrightarrow{\rm k})$

Now, the directional derivative is given by:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=\frac{\partial h(r,s,t)}{\partial r}\overrightarrow{\rm i} + \frac{\partial h(r,s,t)}{\partial s}\overrightarrow{\rm j} + \frac{\partial h(r,s,t)}{\partial t}\overrightarrow{\rm k}$

So let's calculate the partial derivates:

$\frac{\partial }{\partial r} ln(3r+6s+9t)=\frac{3}{3r+6s+9t}=\frac{1}{r+2s+3t}$

$\frac{\partial }{\partial s} ln(3r+6s+9t)=\frac{6}{3r+6s+9t}=\frac{2}{r+2s+3t}$

$\frac{\partial }{\partial t} ln(3r+6s+9t)=\frac{9}{3r+6s+9t}=\frac{3}{r+2s+3t}$

Therefore:

3 0

3 years ago