Use Pythagorean theorem:
9i-j = sqrt (9^2 - 1^2) = sqrt(81-1) = sqrt80
now divide both terms in V by that:
u = 9/sqrt(80)i - 1/sqrt(80)j
see attached picture:
Answer:
Step-by-step explanation:
Vertical Asymptote: x=2Horizontal Asymptote: NoneEquation of the Slant/Oblique Asymptote: y=x 3+23 Explanation:Given:y=f(x)=x2−93x−6Step.1:To find the Vertical Asymptote:a. Factor where possibleb. Cancel common factors, if anyc. Set Denominator = 0We will start following the steps:Consider:y=f(x)=x2−93x−6We will factor where possible:y=f(x)=(x+3)(x−3)3x−6If there are any common factors in the numerator and the denominator, we can cancel them.But, we do not have any.Hence, we will move on.Next, we set the denominator to zero.(3x−6)=0Add 6 to both sides.(3x−6+6)=0+6(3x−6+6)=0+6⇒3x=6⇒x=63=2Hence, our Vertical Asymptote is at x=2Refer to the graph below:enter image source hereStep.2:To find the Horizontal Asymptote:Consider:y=f(x)=x2−93x−6Since the highest degree of the numerator is greater than the highest degree of the denominator,Horizontal Asymptote DOES NOT EXISTStep.3:To find the Slant/Oblique Asymptote:Consider:y=f(x)=x2−93x−6Since, the highest degree of the numerator is one more than the highest degree of the denominator, we do have a Slant/Oblique AsymptoteWe will now perform the Polynomial Long Division usingy=f(x)=x2−93x−6enter image source hereHence, the Result of our Long Polynomial Division isx3+23+(−53x−6)
Answer:
Jane's situation is the one which represents a porportional relationship.
Step-by-step explanation:
To verify the proportionality betwen a ratio you have to divide all the ratios and all them have to get the same constant factor.
So, if you divide the matt's ratios you aren't gonna find the same constant factor
12/1=12
20/2=10
31/2=15,5
But if you try with Jane's ones:
12/1=12
24/2=12
36/3=12
This 12 is the known constant factor, which show us that these ratios are proportional.
Answer:
<h2>The fourth graph, from left to right, is the correct answer.</h2>
Step-by-step explanation:
The given piecewise function is
Notice that the domain of the function specifies that, from zero to three, the function represents a decreasing (because the variable is negative) straight line. When the function is defined from 3 to infinite, the function is a constant of 5.
<em>So, the right graph must shows first a decreasing line, where the initial point is solid and the final point is empty, as the fourth fraph (from left to right), then it must show a horizontal line with an initial point solid.</em>
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Therefore, the fourth graph, from left to right, is the correct answer.
