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Lera25 [3.4K]
3 years ago
13

If y varies jointly with x and z, and y = 200 when x = 8 and z = 10, what is x when y = 165 and z = 11?

Mathematics
2 answers:
vova2212 [387]3 years ago
8 0

Answer:

The answer is 2.5

The next blank is 6

aksik [14]3 years ago
7 0

Answer:

Joint variation states:

if y varies jointly with x and z

then the equation we get;

y = k \cdot xz

where, k is the constant of variation.

As per the statement:

If y varies jointly with x and z

Using above definition we have;

⇒y = k \cdot xz       ....[1]

y = 200 when x = 8 and z = 10

Substitute these value in [1]  to solve for k;

200 = k \cdot 8 \cdot 10

⇒200 = 80k

Divide both sides by 80 we have;

2.5 = k

or

k = 2.5

then we get an equation:

y=2.5 \cdot xz

We have to find x when y = 165 and z = 11.

then;

165 = 2.5 \cdot x \cdot 11

⇒165 = 27.5x

Divide both sides by 27.5 we have;

6 = x

or

x = 6

Therefore, the value of k = 2.5  and value of x is 6 when  y = 165 and z = 11.

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