slope = y2-y1 / x2-x1=
-1 -5 / 2 - -1 = -6/3 = -2
slope = -2
y intercept = y =mx +b
y = -2x +b
y=-2*-1 +b
5 = -2 +b
b = 5-2
b =3
y intercept = 3
Answer:
-3/19
Step-by-step explanation:
slope = rise/run = (y1 - y2) / (x1 - x2)
s = (19 - 16) / (-9 -10)
s = 3/-19 = -3/19
Is 26 included in the division if not the answer is 0.05
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<u>Solution-</u>
The two parabolas are,
By solving the above two equations we calculate where the two parabolas meet,
Given the symmetry, the area bounded by the two parabolas is twice the area bounded by either parabola with the x-axis.
![\therefore Area=2\int_{-c}^{c}y.dx= 2\int_{-c}^{c}(16x^2-c^2).dx\\=2[\frac{16}{3}x^3-c^2x]_{-c}^{ \ c}=2[(\frac{16}{3}c^3-c^3)-(-\frac{16}{3}c^3+c^3)]=2[\frac{32}{3}c^3-2c^3]=2(\frac{26c^3}{3})\\=\frac{52c^3}{3}](https://tex.z-dn.net/?f=%5Ctherefore%20Area%3D2%5Cint_%7B-c%7D%5E%7Bc%7Dy.dx%3D%202%5Cint_%7B-c%7D%5E%7Bc%7D%2816x%5E2-c%5E2%29.dx%5C%5C%3D2%5B%5Cfrac%7B16%7D%7B3%7Dx%5E3-c%5E2x%5D_%7B-c%7D%5E%7B%20%5C%20c%7D%3D2%5B%28%5Cfrac%7B16%7D%7B3%7Dc%5E3-c%5E3%29-%28-%5Cfrac%7B16%7D%7B3%7Dc%5E3%2Bc%5E3%29%5D%3D2%5B%5Cfrac%7B32%7D%7B3%7Dc%5E3-2c%5E3%5D%3D2%28%5Cfrac%7B26c%5E3%7D%7B3%7D%29%5C%5C%3D%5Cfrac%7B52c%5E3%7D%7B3%7D)
![So \frac{52c^3}{3}=\frac{250}{3}\Rightarrow c=\sqrt[3]{\frac{250}{52}}=1.68](https://tex.z-dn.net/?f=So%20%5Cfrac%7B52c%5E3%7D%7B3%7D%3D%5Cfrac%7B250%7D%7B3%7D%5CRightarrow%20c%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B250%7D%7B52%7D%7D%3D1.68)
Answer:
Cos(θ) = 8 / 17
Step-by-step explanation:
<em>Cos = Adjacent / Hypotenuse</em>
Side that is adjacent to θ = 8
hypotenuse of the triangle = 17
<u>Cos(θ) = 8 / 17</u>
Hope this helps!
