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TiliK225 [7]
3 years ago
6

Ethan correctly answers 80% of the total questions on his history test. Enter the number of questions on Ethan’s history test.

Mathematics
2 answers:
jasenka [17]3 years ago
8 0
It might be about 20 questions
Citrus2011 [14]3 years ago
5 0
Since you didn't give me a total # of questions on the test, I can't give you a direct answer.... 


But I can walk you through.

In math, "of", means you have to multiply. 

80%= .8  This is bc 100% is = 1.00. 
() mean times or multiplied by
====================================================================
So you would do .8(how ever many total questions were on the test)
Whatever # you get is the answer. 


Hope I could help!!!
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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})

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What is the value of ▲ in the equation shown? [▲x4]+[6x3]=6[4+3
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Answer: 6

Step-by-step explanation:   [▲x4]+[6x3]=6[4+3

6[4+3=42 so if [6x3]=18 then [▲x4] needs to be 24 (24+18=42) ▲=6 as 6x4=24+18=42 (6[4+3)!

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