Answer:
Angle T = 62°; Angle U = 43°; Angle V = 75°
Step-by-step explanation:
First, find x. We know that the interior angles of a triangle will always add up to 180°.
180° = (5x +2)° + (6x + 3)° + (2x + 19)° –––Combine like terms
180° = 13x + 24 –––Subtract 24 from both sides
156° = 13x ––– Divide both sides by 13 to get x alone
12° = x
Now that we know what x is, we can substitute it in the expressions for the angles.
Angle T:
5x +2
5(12) + 2
60 +2
62°
Angle U:
2x + 19
2(12) + 19
24 + 19
43°
Angle V:
6x + 3
6(12) + 3
72 + 3
75°
Check:
They must equal 180° when added together:
75° + 62° + 43° = 180°
75° + 105° = 180°
180° = 180°
![\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B343%7D%7B3%7D%20%7D%20%20%5Cint%5Climits%5E7_0%20%20%5Cint%5Climits%5E%7Bx%5E2%7D_0%20%7B4x%5Csin%28y%29%7D%20%5C%2C%20dydx%20%20%3D%20-%5Cfrac%7B3%7D%7B343%7D%20%20%5Cint%5Climits%5E7_0%20%7B4x%5Ccos%28x%5E2%29%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D-%5Cfrac%7B3%7D%7B343%7D%20%5Cint%5Climits%5E%7B49%7D_0%20%7B2%5Ccos%28t%29%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%20%5Cleft%5B%5Csin%28t%29%5Cright%5D_0%5E%7B49%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%5Csin49)