6w-y=2z
6w=2z+y
w=(2z+y):6
w=(z:3)+(y:6)
Equation of a straight line is normally in the form: y = mx + c.
Where, m and c are constants in which;
m = gradient
c = y-intercept.
Comparing this standard way way of writing the equation of a straight line with the current scenario, this equation can be rewritten as;
y = b1x + b0.
This way, b1 = gradient of the line while b0 = y-intercept.
First, find the area of the circle using the formula A=pi r^2.
A=pi (2x+3)^2 = pi(4x^2 + 12x + 9)
Second, find the area of the rectangle inside by multiplying the polynomials.
(X+1)*(3x+2) = 3x^2 + 5x +2
Third, subtract the area of the rectangle from the area of the circle to find the area of the shaded region.
pi(4x^2 + 12x + 9) - 3x^2 + 5x +2 =area of shaded region
Or
(pi (2x+3)^2) - ((X+1)(3x+2)) = area of shaded region
Let us draw a triangle ABC with A=15° ,B=113° and b=7.
Please see the attached image.
We know that the sum of interior angles of a triangle is 180 degrees. Thus, we have
![A+B+C=180\\ \\ 15+113+C= 180\\ \\ C=62^{\circ}](https://tex.z-dn.net/?f=A%2BB%2BC%3D180%5C%5C%0A%5C%5C%0A15%2B113%2BC%3D%20180%5C%5C%0A%5C%5C%0AC%3D62%5E%7B%5Ccirc%7D)
Apply Sine rule in the triangle ABC, we get
![\frac{a}{\sin 15}= \frac{7}{\sin 113}\\ \\ a=\frac{7 \sin 15}{\sin 113}\\ \\ a=1.97\\ \\ \text{Again apply sine rule, we get}\\ \\ \frac{c}{\sin 62}= \frac{7}{\sin 113}\\ \\ c=\frac{7 \sin 62}{\sin 113}\\ \\ c=6.71](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%2015%7D%3D%20%5Cfrac%7B7%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Aa%3D%5Cfrac%7B7%20%5Csin%2015%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Aa%3D1.97%5C%5C%0A%5C%5C%0A%5Ctext%7BAgain%20apply%20sine%20rule%2C%20we%20get%7D%5C%5C%0A%5C%5C%0A%5Cfrac%7Bc%7D%7B%5Csin%2062%7D%3D%20%5Cfrac%7B7%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Ac%3D%5Cfrac%7B7%20%5Csin%2062%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Ac%3D6.71)
Therefore, we have
![a=1.97\\ c=6.71\\ C=62^{\circ}](https://tex.z-dn.net/?f=a%3D1.97%5C%5C%0Ac%3D6.71%5C%5C%0AC%3D62%5E%7B%5Ccirc%7D)
Answer:
Y intercept is (0, 5)
**Working on the others** will edit this answer when i get them