verify that the given point is on the curve. find the lines that are (a) tangent and (b) normal to the curve…

verify that the given point is on the curve. find the lines that are (a) tangent and (b) normal to the curve at the given point.\n6xy + π sin y = 61π, (4, 5π/2)\nthe point is on the curve because when is substituted for x and is substituted for y, the resulting statement is = 61π, which is a false statement.\n(type an exact answer, using π as needed.)

verify that the given point is on the curve. find the lines that are (a) tangent and (b) normal to the curve at the given point.\n6xy + π sin y = 61π, (4, 5π/2)\nthe point is on the curve because when is substituted for x and is substituted for y, the resulting statement is = 61π, which is a false statement.\n(type an exact answer, using π as needed.)

Answer

Explanation:

Step1: Substitute x and y values

Substitute (x = 4) and (y=\frac{5\pi}{2}) into the left - hand side of the equation (6xy+\pi\sin y). [6\times4\times\frac{5\pi}{2}+\pi\sin\frac{5\pi}{2}]

Step2: Simplify the first term

[6\times4\times\frac{5\pi}{2}=60\pi]

Step3: Simplify the second term

Since (\sin\frac{5\pi}{2}=\sin(2\pi + \frac{\pi}{2})=\sin\frac{\pi}{2}=1), then (\pi\sin\frac{5\pi}{2}=\pi).

Step4: Find the sum of the two terms

[60\pi+\pi = 61\pi]

Answer:

The point is on the curve because when (4) is substituted for (x) and (\frac{5\pi}{2}) is substituted for (y), the resulting statement is (61\pi=61\pi), which is a true statement.