PQ peependicular to PS
Thus angle QPS = 90⁰
![\angle QPR + \angle RPS = \angle QPS](https://tex.z-dn.net/?f=%5Cangle%20QPR%20%2B%20%5Cangle%20RPS%20%3D%20%5Cangle%20QPS)
7x - 9 + 4x + 22 = 90⁰
11x = 77
x = 7
Thus angle QPR = 7(7) - 9 = 40⁰
<u>Answer-</u>
<em>$2000</em><em> were invested at 5%</em>
<u>Solution-</u>
Let x amount of money was invested at 5% and (6000-x) amount was invested as 3%
We know that,
![i=\dfrac{P\cdot r\cdot t}{100}](https://tex.z-dn.net/?f=i%3D%5Cdfrac%7BP%5Ccdot%20r%5Ccdot%20t%7D%7B100%7D)
Putting the values,
![i_1=\dfrac{P_1\cdot r_1\cdot t}{100}](https://tex.z-dn.net/?f=i_1%3D%5Cdfrac%7BP_1%5Ccdot%20r_1%5Ccdot%20t%7D%7B100%7D)
![i_1=\dfrac{x\cdot 5\cdot 1}{100}=\dfrac{5x}{100}](https://tex.z-dn.net/?f=i_1%3D%5Cdfrac%7Bx%5Ccdot%205%5Ccdot%201%7D%7B100%7D%3D%5Cdfrac%7B5x%7D%7B100%7D)
And
![i_2=\dfrac{P_2\cdot r_2\cdot t}{100}](https://tex.z-dn.net/?f=i_2%3D%5Cdfrac%7BP_2%5Ccdot%20r_2%5Ccdot%20t%7D%7B100%7D)
![i_2=\dfrac{(6000-x)\cdot 3\cdot 1}{100}=\dfrac{3(6000-x)}{100}](https://tex.z-dn.net/?f=i_2%3D%5Cdfrac%7B%286000-x%29%5Ccdot%203%5Ccdot%201%7D%7B100%7D%3D%5Cdfrac%7B3%286000-x%29%7D%7B100%7D)
According to the question,
![\Rightarrow \dfrac{5x}{100}+\dfrac{3(6000-x)}{100}=220](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B5x%7D%7B100%7D%2B%5Cdfrac%7B3%286000-x%29%7D%7B100%7D%3D220)
![\Rightarrow \dfrac{5x+3(6000-x)}{100}=220](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B5x%2B3%286000-x%29%7D%7B100%7D%3D220)
![\Rightarrow 5x+3(6000-x)=22000](https://tex.z-dn.net/?f=%5CRightarrow%205x%2B3%286000-x%29%3D22000)
![\Rightarrow 5x+18000-3x=22000](https://tex.z-dn.net/?f=%5CRightarrow%205x%2B18000-3x%3D22000)
![\Rightarrow 5x-3x=22000-18000](https://tex.z-dn.net/?f=%5CRightarrow%205x-3x%3D22000-18000)
![\Rightarrow 2x=4000](https://tex.z-dn.net/?f=%5CRightarrow%202x%3D4000)
![\Rightarrow x=2000](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D2000)
Therefore, $2000 were invested at 5%
Complete the squares to get
![x^2+y^2=2x-6y+6](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D2x-6y%2B6)
![\implies(x^2-2x+1)+(y^2+6y+9)=16](https://tex.z-dn.net/?f=%5Cimplies%28x%5E2-2x%2B1%29%2B%28y%5E2%2B6y%2B9%29%3D16)
![\implies(x-1)^2+(y+3)^2=4^2](https://tex.z-dn.net/?f=%5Cimplies%28x-1%29%5E2%2B%28y%2B3%29%5E2%3D4%5E2)
which is the equation of a circle centered at (1, -3) with radius 4, and thus with area 16π.
Answer:
149
Step-by-step explanation:
because you take 89.1 to 89 and take 60.2 to 60
then you add 60+89 to get 149