Given that x² + y² + z² = 194, calculate z if x = 7 and \(\sqrt{y}\) = 3

imafinegyal

1 year ago

You're on the right track with the structure, but there’s a small mistake in the value of
𝑦
2
y
2
.

Let’s go through it step by step and fix it:

Given:
𝑥
2
+
𝑦
2
+
𝑧
2
=
194
x
2
+y
2
+z
2
=194
𝑥
=
7
and
𝑦
=
3
x=7andy=
3
​

Step 1: Square the known values
𝑥
2
=
7
2
=
49
x
2
=7
2
=49
𝑦
2
=
(
3
)
2
=
3
y
2
=(
3
​
)
2
=3
Step 2: Plug into the equation
49
+
3
+
𝑧
2
=
194
49+3+z
2
=194
52
+
𝑧
2
=
194
52+z
2
=194
𝑧
2
=
194
−
52
=
142
z
2
=194−52=142
𝑧
=
142
≈
11.91
z=
142
​
≈
11.91
​

Final Answer:
𝑧
≈
11.91
z≈
11.91
​