Answer: The correct answer is 44.60
Step-by-step explanation:
Let's find the area of the rectangle first, and then add it with the area of the Circle to find the total area of the whole shape.
We know that the area of a Rectangle is L(Length) x W(Width)
So using the given information, 8 x 4 = 32
So the Area of the Rectangle = 32
Now let's find the area of the given circle,
<em>Area of a Circle: πr2 Remember ^ = stands for power</em>
The radius is half of the diameter
The diameter of the circle is 4
4/2 = 2 which is our radius, and now let's replace it in the equation.
= 3.14(r)^2
= 3.14(2)^2
= 3.14(4)
= 12.56 or some may have got 12.57
So now we add all areas together to get the total area,
32+12.57 = 44.57
Now rounding off to the nearest tenths, would give us 44.60
So the area of the figure rounded to the nearest tenth is 44.60
![\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)