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mart [117]
2 years ago
12

The tangent of the curve f(t) =2+nt+mt^2 at point (1,1/2) is parallel to the normal g(t)= t^2+6t+13(-2,2), calculate the values

m and n.​
Mathematics
1 answer:
Anettt [7]2 years ago
7 0

Step-by-step explanation:

The slope of g(t) as (-2,2) is given by

g'(t)=2t+6

g'(-2)=2(-2)+6=2

Since the normal is parallel to the tangent of f(t) at (1, 1/2),

The tangent line of f(t) has a slope of

\dfrac{d}{dx}f(t)=n+2mt=2

At point (1, 1/2), we know

f'(1)=n+2m=2

f(1)=2+n(1)+m(1)^2=2+n+m=\frac12

Solving,

n=5, m=-\frac72

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Answer:

The smallest side is 7inches

Step-by-step explanation:

Let the shorter side be y.

The medium side is 4 more than the short side i.e

Meduim side = 4 + y

The longest side is 5 times the length of the shortest side i.e

Logest side = 5y.

Perimeter of the triangle = 53 inches

But the perimeter of a triangle is the Sum of all sides i.e

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53 = y + (4+y) + 5y

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Collect like terms

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Divide both side by 7

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3 years ago
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Answer:

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but where is the force?

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Hope this helps,

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