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4 years ago

URGENT! FOR BRAINLY

Mathematics

1 answer:

Butoxors [25]4 years ago

3 0

B. set up like a proportion. 18/408.24 equals 42/ X. Cross multiply so that 17,146.08 is equal to 18 X, then divide both sides by 18

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Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

Feliz [49]

$f(x,y,z)=2z^2x+y^3$

$f$ has gradient

$\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k$

which at the point (-1, 4, 3) has a value of

$\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k$

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say $\vec u=15\,\vec\imath+25\,\vec\jmath$ , in which case we have

$\|\vec u\|=\sqrt{15^2+25^2}=5\sqrt{34}$

Then the derivative of $f$ at (-1, 4, 3) in the direction of $\vec u$ is

$D_{\vec u}f(-1,4,3)=\nabla f(-1,4,3)\cdot\dfrac{\vec u}{\|\vec u\|}=\boxed{\dfrac{294}{\sqrt{34}}}$

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3 years ago

What is the cube root of -1/512

Stella [2.4K]

Answer:

$-\frac{1}{8}$

Step-by-step explanation:

$\sqrt[3]{-\frac{1}{512}}=\frac{\sqrt[3]{-1}}{\sqrt[3]{512}}=\frac{-1}{8}=-\frac{1}{8}$

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3 years ago

Select the correct answer from each drop-down menu. Margie is practicing for an upcoming tennis tournament. Her first serve is g

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Answer:

Step-by-step explanation:

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3 years ago

While preparing for a party, Luis spent 25 minutes blowing up 10 balloons. Write an equation to express how many minutes it took

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3 years ago

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Suppose on a certain test, fifty students earn a perfect score and fifty students earn a zero. determine the mean grade and stan

kodGreya [7K]

Answer:

Mean=50.

standard deviation=50.

Step-by-step explanation:

Let the perfect score be 100.

The mean(average) of a data is given by: $Mean=\frac{sum of data points}{number of data points}$

Here the number of data points are 100. out of which 50 attains a value 100,and 50 attains value 0.

so, sum of data points=50×100+50×0=5000.

$Mean=\frac{5000}{100}$

Mean=50.

"Now the standard deviation of data points are calculated by firstly subtracting mean from every entry and then square the number and take it as new entry and calculate the mean of the new data entry and lastly taking the square root of this new mean".

Here if 50 is subtracted from each entry the new entry will have 50 entries as '50' and 50 entries as '-50'.

next on squaring we will have all the 100 entries as '2500'.

now the mean of these entries is: $\frac{2500\times100}{100}$

=2500

taking it's squareroot we have $\sqrt{2500}=50$

Hence, standard deviation=50.

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4 years ago

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