No solutions jzksksalalaooaoaoaiaiaiakkskakakakakkaksoaoaoaokw
It would be B.
The 6 and 9 look the same up side down and so do the HOH
Answer:
Steps below, ask if you need further explanation.
Step-by-step explanation:
You've graphed the points, but it wants the lines and their equations.
Horizontal lines are of the form y=a, where a is the y value the line is at. Verticla lines are of the form x=b, where b is the x value the line is at. horizontal lines have a slope of 0 and vertical lines have an undefined slope, I will show you why.
Slope is found by (y2 - y1)/(x2 - x1) where (x1, y1) and (x2, y2) are the two points you are finding the slope between. A horizontal ine has no change in x s y2 - y1 = 0 so the fraction becomes 0/(x2-x1) = 0, so the slope is 0. No change in x makes the denominator 0, and dividing by 0 is undefined.
For the slanted line you will get a non zero or undefined slope, ets call it m. Then to find the line just plug into the formula y1 - y = m(x1 - x) where m is that slope and (x1, y1) is ONE of the poitns you are measuring the slope of. You just choose one, they will both get the same answer. Then just solve for y. Not y1, you want just y on one side of the equation.
Let me know if you need more explicit walking through.
Integrating with shells is the easier method.
<em>V</em> = 2<em>π</em> ∫₁³ <em>x</em> (√<em>x</em> + 3<em>x</em>) d<em>x</em>
That is, at various values of <em>x</em> in the interval [1, 3], we take <em>n</em> shells of radius <em>x</em>, height <em>y</em> = √<em>x</em> + 3<em>x</em>, and thickness ∆<em>x</em> so that each shell contributes a volume of 2<em>π</em> <em>x</em> (√<em>x</em> + 3<em>x</em>) ∆<em>x</em>. We then let <em>n</em> → ∞ so that ∆<em>x</em> → d<em>x</em> and sum all of the volumes by integrating.
To compute the integral, just expand the integrand:
<em>V</em> = 2<em>π</em> ∫₁³ (<em>x </em>³ʹ² + 3<em>x</em> ²) d<em>x</em>
<em>V</em> = 2<em>π</em> (2/5 <em>x </em>⁵ʹ² + <em>x</em> ³) |₁³
<em>V</em> = 2<em>π</em> ((2/5 ×<em> </em>3⁵ʹ² + 3³) - (2/5 × 1⁵ʹ² + 1³))
<em>V</em> = 4<em>π</em>/5 (9√3 + 64)
