In right triangle RST below, altitude SV is drawn to
1 answer:
Answer:
ST = 12.2
Step-by-step explanation:
See the attached diagram of the triangle.
Here, Δ RST, Δ RSV and Δ STV all are right triangles.
If we assume that, ST = x and SR = y, then
From Δ RSV and Δ STV we get,
SV² = RS² - RV² = ST² - VT²
⇒ y² - 4.2² = x² - 10.3²
⇒ x² - y² = 88.45 .......... (1)
Now, from Δ RST, we have
ST² + SR² = RT²
⇒ x² + y² = (10.3 + 4.2)² = 210.25 .............. (2)
Now, adding equations (1) and (2) we get,
2x² = 298.7
⇒ x² = 149.35
⇒ x = 12.2 (Rounded to the nearest tenth}
So, ST = 12.2 (Answer)
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Answer:
1/4
Step-by-step explanation:
The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.
The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...
(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4
