Two times a number less one hundred and twenty-five is equal to four hundred
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 ![\pi \int_a^b [f(x)]^2dx](https://tex.z-dn.net/?f=%5Cpi%20%5Cint_a%5Eb%20%5Bf%28x%29%5D%5E2dx)
, 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)
If He began at 4:15 and ended at 5:50 then that would be 95 minutes
Answer: Diego, 4a + 9b is equivalent
Step-by-step explanation:
7a + 5b - 3a + 4b
= (7a - 3a) + (5b + 4b) We rerange the variables, and put them together with (), which make it more clear to solve.
= 4a + 9b
There's many properties you can use to find an unknown angle.
There are too many to lists but one core example would be an isosceles triangle that has two adjacent sides and angles.
Let's say that the sides of an isosceles triangle are any number "x"
now since two sides of the triangle are the same we can add these two x's together.
x+x = 2x
now the other side of the triangle can be anything you like. We can call it 4x for this example.
now if we add them all together we'll get 4x+2x=6x
Now since the angles of a triangle add up to 180 degrees
we can equate 6x=180 leaving x to be 30.
Now since x belongs to both sides of the triangle we can say that both angles are congruent as well because the two sides of the triangle are congruent. This is a known triangle law.
Since both angles are now 30 degrees this will leave us with 2(30) = 60
now if we subtract 180 - 60 we'll get 120 which is the remainder of the 3rd angle of the side that corresponds with 4x.
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