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The curve y=x^2 + 3x + k has a tangent with the equation y=5 x +5 . Find the value of k. Can you please help me to understand this question?

The slope of the tangent line is 5.

The slope of the tangent line is given by the derivative of the function that defnes the curve.

y' = 2x + 3

Since the slope is 5 ,

5 = 2x + 3

x = 1

The point of tangency is where the tangent line meets the curve.

So the x coordinate of the point is 1 , and since the point is on the line ,

y = 5(1) + 5 = 10

So (1,10) is on the curve y = x^2 + 3x + k

This means 10 = 1^2 + (3)(1) + k

10 = 4 + k

k = 6

Calculus

Answers by Expert:

I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

Ph.D. in Mathematics and many years teaching Calculus at state universities.**Education/Credentials**

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