The 2x and 76 are opposite angles so they are equal.
2x = 76
x = 38 degrees
y and 76 are adjacent angles so y = 180 - 76
= 104 degrees
Answer:
A) {x | -1 < x < 7}
Step-by-step explanation:
Given in the question two inequalities,
Inequality 1
(x - 2 < 5)
x < 5 + 2
x < 7
x is smaller than 7
Inequality 2
(x + 7 > 6)
x > 6 - 7
x > -1
x is greater then -1
When (x - 2 < 5) U (x + 7 > 6).
(x < 7) U (x > -1)
-1 < x < 7
When combined, x is greater than -1 but smaller than 7
Volume of sphere = 4/3 πr³
Volume of sphere = 4/3 π (5)³ = 500/3 π ft³
Answer:500/3 π ft³ (Answer B)
You know that
so
.
Area of a shaded region is:
![$A=\int\limits_0^k\dfrac{y^2}{4}\,dy=\frac{1}{4}\int\limits_0^ky^2\,dy=\frac{1}{4}\left[\frac{y^3}{3}\right]_0^k=\frac{1}{4}\left[\frac{k^3}{3}-\frac{0^3}{3}\right]=\frac{1}{4}\cdot\dfrac{k^3}{3}=\boxed{\frac{k^3}{12}}](https://tex.z-dn.net/?f=%24A%3D%5Cint%5Climits_0%5Ek%5Cdfrac%7By%5E2%7D%7B4%7D%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cint%5Climits_0%5Eky%5E2%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%5D_0%5Ek%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7Bk%5E3%7D%7B3%7D-%5Cfrac%7B0%5E3%7D%7B3%7D%5Cright%5D%3D%5Cfrac%7B1%7D%7B4%7D%5Ccdot%5Cdfrac%7Bk%5E3%7D%7B3%7D%3D%5Cboxed%7B%5Cfrac%7Bk%5E3%7D%7B12%7D%7D%20)
so k:
![\dfrac{k^3}{12}=\dfrac{9}{4}\\\\\\k^3=\dfrac{9\cdot12}{4}\\\\\\k^3=9\cdot3\\\\k^3=3^3\quad|\sqrt[3]{(\ldots)}\\\\\boxed{k=3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bk%5E3%7D%7B12%7D%3D%5Cdfrac%7B9%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D%5Cdfrac%7B9%5Ccdot12%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D9%5Ccdot3%5C%5C%5C%5Ck%5E3%3D3%5E3%5Cquad%7C%5Csqrt%5B3%5D%7B%28%5Cldots%29%7D%5C%5C%5C%5C%5Cboxed%7Bk%3D3%7D)
