Answer:

Step-by-step explanation:
First of all, let's draw the two curves. First one (red) is a classic parabola, second (blue) is a similar curve with a tigher form. Imagine is made with paint so it's not high quality. The intersection between the two curves are easily found by solving a system of equations and are (0;0) and (1;1). At this point, the volume comes from the rotation of the shaded area, and can be obtained as difference from the rotation of the blue curve minus the red curve.
Remembering that the volume of the solid of revolution bound between
is given by
, in our case the volume is given by the expression
![\pi [\int_0^1 (\sqrt[4]{x})^2-(x^2)^2 dx] = \pi[\int_0^1 \sqrt{x}-x^4 dx] = \pi[\frac23x^\frac32 -\frac15 x^5 ] _0^1 = \pi (\frac23 -\frac15) = \frac7{15}\pi](https://tex.z-dn.net/?f=%5Cpi%20%5B%5Cint_0%5E1%20%28%5Csqrt%5B4%5D%7Bx%7D%29%5E2-%28x%5E2%29%5E2%20dx%5D%20%3D%20%5Cpi%5B%5Cint_0%5E1%20%5Csqrt%7Bx%7D-x%5E4%20dx%5D%20%20%3D%20%5Cpi%5B%5Cfrac23x%5E%5Cfrac32%20-%5Cfrac15%20x%5E5%20%5D%20_0%5E1%20%3D%20%5Cpi%20%28%5Cfrac23%20-%5Cfrac15%29%20%3D%20%5Cfrac7%7B15%7D%5Cpi)
Answer:
The Pythagorean theorem states that a2 + b2 = c2 in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two. The figure shows two right triangles that are each missing one side's measure.
Step-by-step explanation:
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Slop: second one (2/1)
Y-intercept: first one
Explanation
Slop is rise over run so how much it goes up or down on the top and how much it goes our right on the bottom
Y-intercept is where the point intersects with the y line so what point is on the y line
Answer:
CD= 15.03
Step-by-step explanation:
x1=7, x2= -8
y1=-4, y2=-5
distance CD= √(x2- x1) 2+ (y2-y1)2
= √( -8-7)2 + [-5-(-4)]2
= √(15)2+ (-5+4)2
= √225+ (1)2
= √225+1
= √226
= 15.03