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Identify the polynomial equivalent to (6x + 1)^2

blsea [12.9K]

Answer:

The answer you are looking for is the part d

3 0

3 years ago

What is 6+3(-8x-2)=12

stepladder [879]

Answer:

=12

Step-by-step explanation:

6+3(-8x-2)=12

6 0

3 years ago

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Simplify the expression 5 √(2 + √(18))

valentinak56 [21]

$5\sqrt{2+3\sqrt{2}}$

3 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:

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

3 0

3 years ago

The first tap can fill the pool in 10 hours. When the second tap was opened, the empty pool was filled in 6 hours. How long will

NARA [144]

Answer: $15\ hours$

Step-by-step explanation:

We can use the following formula to solve this exercise:

$\frac{T}{A}+\frac{T}{B}=1$

In this case "T" is the time in hours it takes to both taps fill the pool working together, "A" is the time in hours for the first tap filling the pool alone an "B" is the time in hours for the second tap filling the pool alone.

We can identify that:

$T=6\\\\A=10$

Then, we must subsitute the known values into the formula:

$\frac{6}{10}+\frac{6}{B}=1$

And finally we must solve for "B".

Then we get:

$\frac{6}{10}+\frac{6}{B}=1\\\\\frac{6}{B}=1-\frac{6}{10}\\\\\frac{6}{B}=0.4\\\\6=0.4B\\\\\frac{6}{0.4}=B\\\\B=15$

3 0

3 years ago

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