y varies directly as x and inversely as the square of z. y = 65 when x = 80 and z=4. Find y when x= 18 and z=3.

y

=

18

Explanation:

As

y

varies directly as

x

, we have

y

∝

x

. Also it varies inversely as square of

z

, which means

y

∝

1

z

2

.

Hence,

y

∝

x

z

2

or

y

=

k

×

x

z

2

, where

k

is a constant.

Now when

x

=

80

and

z

=

4

,

y

=

10

, so

10

=

k

×

80

4

2

=

k

×

80

16

=

5

k

Hence

k

=

10

5

=

2

and

y

=

2

x

z

2

.

So when

x

=

36

and

z

=

2

,

y

=

2

×

36

2

2

=

72

4

=

18

Step-by-step explanation:

the answer to the expression is 83

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺