Answer to Question #243854 in Math for MINU

Question #243854

The temperature of a particular country

n

 is the number of the month, starting at n

=


n=0

 for January. The temperature in the country is greater than 40 o

C

oC

 for months Jun, July, August, and September. It is less than 40 o

C

oC

 for months January, February, March, April, November and December, and 40 o

C

oC

 for months May and October. If a

a

 is a positive integer, then which of the following options might be correct

T

(

n

)

=

a

(

n

4

)

(

n

9

)

40

T(n)=a(n−4)(n−9)−40

 T

(

n

)

=

a

(

4

n

)

(

n

9

)

40

T(n)=a(4−n)(n−9)−40

 T

(

n

)

=

a

(

4

n

)

(

9

n

)

+

40

T(n)=a(4−n)(9−n)+40

 T

(

n

)

=

a

(

4

n

)

(

n

9

)

+

40

T(n)=a(4−n)(n−9)+40

 The temperature in December is 40

14

a

40−14a

.

 The temperature in April is 40

3

a

40−3a

.


1
Expert's answer
2021-09-29T14:50:25-0400
T(0)<40,T(1)<40,T(2)<40,T(3)<40,T(0)<40, T(1)<40, T(2)<40, T(3)<40,

T(4)=40,T(5)>40,T(6)>40,T(7)>40,T(4)=40, T(5)>40, T(6)>40, T(7)>40,

T(8)>40,T(9)=40,T(10)<40,T(11)<40.T(8)>40, T(9)=40, T(10)<40, T(11)<40.

a. T(n)=a(n4)(n9)40T(n)=a(n−4)(n−9)−40

False


T(4)=a(44)(49)40=40<0,a>0T(4)=a(4−4)(4−9)−40=-40<0, a>0

b. T(n)=a(4n)(n9)40T(n)=a(4-n)(n−9)−40

False


T(4)=a(44)(49)40=40<0,a>0T(4)=a(4-4)(4−9)−40=-40<0, a>0

c. T(n)=a(4n)(9n)+40T(n)=a(4-n)(9-n)+40

False


T(4)=a(44)(94)+40=40,a>0T(4)=a(4-4)(9-4)+40=40, a>0

T(9)=a(49)(99)+40=40,a>0T(9)=a(4-9)(9-9)+40=40, a>0

T(0)=a(40)(90)+40=36a+40>40,a>0T(0)=a(4-0)(9-0)+40=36a+40>40, a>0

d. T(n)=a(4n)(n9)+40T(n)=a(4-n)(n−9)+40


T(4)=a(44)(49)+40=40,a>0T(4)=a(4-4)(4-9)+40=40, a>0

T(9)=a(49)(99)+40=40,a>0T(9)=a(4-9)(9-9)+40=40, a>0

T(n)<40,a>0,n<4 or n>9T(n)<40, a>0,n<4 \ or\ n>9

T(n)>40,a>0,4<n<9T(n)>40, a>0,4<n<9

Might be the correct representation


e. The temperature in December is 4014a.40−14a.

T(11)=4014a<40,a>0T(11)=40-14a<40, a>0

Might be the correct representation


f. The temperature in April is 403a.40−3a.

T(3)=403a<40,a>0T(3)=40-3a<40, a>0

Might be the correct representation


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