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marin [14]
3 years ago
9

Find the tangent line equation of the curve at the given point. Y=arcsin(7x) at the point where x=sqrt2/14

Mathematics
1 answer:
Mumz [18]3 years ago
4 0

Answer:

Y-\frac{\pi}{2} =\frac{\pi}{2} (x+\sqrt{\frac{1}{7}})

Step-by-step explanation:

The equation of the curve is

Y = sin^{-1}(7x)

To find the equation of tangent we need to differentiate this equation w.r.t x

So, differentiating we get

Y'=\frac{7}{\sqrt{1-49x^2} }

This would give the slope of the tangent line at any given point of which x coordinate is known. In the present case it is  x = \sqrt{\frac{1}{7} }

Then slope would accordingly be

Y'=\frac{7}{\sqrt{1-49/49} }

= ∞

For, x = \sqrt{\frac{1}{7} }, Y = sin^{-1}(7/7)= \pi/2

Equation of tangent line, in the point slope form, would be Y-\frac{\pi}{2} =\frac{\pi}{2} (x+\sqrt{\frac{1}{7}})

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The midpoint of the line segment from P1 to P2 is (-6,5). If P1 = (-7,8), what is P2?
kipiarov [429]
You can determine midpoint by
x-midpoint = (x₁ + x₂)/2
y-midpoint = (y₁ + y₂)/2

Given from the question
x-midpoint = -6
x₁ = -7
y-midpoint = 5
y₁ = 8

Asked from the question
(x₂, y₂)

Solution
Find x₂, input the value of x₁ and x-midpoint to the formula
(x₁ + x₂)/2 = x-midpoint
(-7 + x₂)/2 = -6
-7 + x₂ = -6 × 2
-7 + x₂ = -12
x₂ = -12 + 7
x₂ = -5

Find y₂, input the value of y₁ and y-midpoint to the formula
(y₁ + y₂)/2 = 5
(8 + y₂)/2 = 5
8 + y₂ = 5 × 2
8 + y₂ = 10
y₂ = 10 - 8
y₂ = 2

Answer
P₂ = (-5,2)
5 0
3 years ago
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Answer:

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Answer:

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Step-by-step explanation:

The constant rate is 32

Mark me as Brainliest PLZ

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Answer:

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Step-by-step explanation:

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