The cost of the carpet prior to taxes is $1,212.64
- 16:10
- 24:15
- 40:25
8:5 is just a simplier version of these other ratios
Y=210-7X you have $210 and want to know how many books she can buy with that money.
To find this, you just need to plug it in and use some algebra to figure it out.
Initial: 2700 = 2200(1 + r)5
multiply 2200 and 5: 2700 = 11000(1 + r)
Divide both sides by 11000: .24 = 1 + r
subtract both sides by 1: -.754 = r
The problem is, a negative interest rate makes no sense if there was actually an increase of 500. We can try distributing the 11000 instead
Where we left off: 2700 = 11000(1 + r)
Distribute the 11000: 2700 = 11000 + 11000r
Subtract 11000 from both sides: -8300 = 11000r
Divide both sides by 11000: -.754 = r
As you can see, both methods reached the same impossible answer. I'm assuming that you didn't type out the equation right. Are you sure it wasn't
2700 = 2200(1 - r)5
? If you subtract the r to make it negative, it might make more sense. But that still leaves us with a .754 rate of interest, which seems too high. Double check where you're typing from
Answer:
Denote the center of circle as O, the 2 endpoints of shaded segment as AB, then we have:
section OAB area = pi x radius^2 x (120/360) = pi x 6^2 x (1/3) = 37.7 (cm2)
Considering triangle OAB, we have OA = OB = radius, angle AOB = 120 deg. Denote OH as the height of triangle. H lies on AB.
=> Applying cosine and sine theorem in right triangle AHO:
OH = OA x cos 60 = 6 x (1/2) = 3 (cm)
AH = OA x sin 60 = 6 x (sqrt3)/2 = 5.2 (cm)
=> triangle AOB area:
A = triangle AOH area x 2
= AH x OH x (1/2) x 2 = 3 x 5.2 x (1/2) x 2 = 15.6 (cm2)
=> shaded segment area = section OAB area - triangle AOB
= 37.7 - 15.6 = ~21.1 (cm2)
Hope this helps!
:)
