Hello,
if the question is to solve the equation:
1) log must exist:
a)==>2r²-27>0==>(r-√(27/2))(r+√(27/2))==> outside the roots
r<-√(27/2) or r>√(27/2)
b)==>3r²+12r>0 ==>3r(r+4)>0 ==>outside the roots
r>0 or r<-4
==>r<-4 or r>√(27/2)=3.6742...
If this is realized:
2r-27=3r²+12r
==>r²+12r+27=0
Δ=12²-4*27=36=6²
r=(-12+6)/2=-3 or r=(-12-6)/2=-9
One solution r=-9
Proof
Answer:
1350m
Step-by-step explanation:
Let the distance ran by Denise, Farah and Elaine be D, F and E meters respectively.
From the given information,
D= ⅔(E +F) -----(1)
E= ½(D +F) -----(2)
Let's get rid of the fraction so the equations are much easier to work with.
From (1):
3D= 2(E +F) <em>(Multiply both sides by 3)</em>
3D= 2E +2F -----(3) <em>(</em><em>Expand</em><em>)</em>
From (2):
2E= D +F -----(4)
Substitute (4) into (3):
3D= D +F +2F
3D -D= 3F
2D= 3F
Given that Farah ran 360m, F= 360.
2D= 3(360)
2D= 1080
D= 1080 ÷2
D= 540
2E= D +F
2E= 540 +360
2E= 900
E= 900 ÷2
E= 450
Total distance the 3 girls ran
= D +F +E
= 540 +360 +450
= 1350m
Alternatively, you could start by substituting F= 360 to equations (1) and (2).
Answer:
a. y = 4,200 
b. 9.2%
Step-by-step explanation:
Given the information:
- The intinital value: 4,200
- The population is decreasing at a rate of 2.4% per year
=> the base number of the exponential function is:
100% - 2.4% = 97.6% = 0.976
Let t is quarter
Let y is the population
=> the following shows an exponential decay function to find the quarterly decay rate is:
y (t)= 4,200
b. The population is decreasing by how much percent per quarter?
Let t = 0 we have: y(0) = 4,200 
Let t = 1 we have: y(1) = 4,200 
=> the decreasing percentage is:
= (y(0) - y(1)) / y(0)*100%
= (4200 - 3811) / 4200 *100%
= 389/4200*100%
= 9.2%
Its 15 boats bcuz...252+288=540 and 540/36= 15 boats :D
