Xvaries directly with y and z. x = 40 when y = 10 and z = 20. find x when y = 30 and z = 40.

x = 60

Step-by-step explanation:

Direct variation is of the form

y= kxz

We know x =40 and y =10 and z= 20

10 = k * 40 * 20

10 = k * 800

Divide each side by 800

10/800 = k

1/80 = k

The equation becomes

y = 1/80 xz

Let y = 30 and z = 40 and find x

30 = 1/80 * x * 40

30= 40/80 x

30 = 1/2x

Multiply each side by 2

2 * 30 = 2 * 1/2 x

60 = x

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

idc

step-by-step explanation:

idk