Find an equation for the line thatis tangent to the curve y=5x^3-5x at the point (1,0)

1 answer:

4 0

Hello,

The gradient of a tangent can be found by differentiating the equation:
$\frac{d}{dx}(5x^3-5x) = 15x^2-5$

Subbing in the x value of 1, the gradient therefore is 15-5 = 10, giving us m in our general equation for a line y=mx+c, i.e. y = 10x + c

We know at x=1, y is 0. Subbing this in:
0 = 10 + c, and solving for c = -10

Therefore, the equation of the tangential line at (1,0) is $y=10x-10$ .

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Answer:

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Step-by-step explanation:

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of the 50 U.S states, 4 have names that start with the letter W. What percentage of U.S. states have names that start with the l

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Answer:

8% of of the Us states have the names that start with W.

Step-by-step explanation:

We are told that, of the 50 states, 4 have names that start with letter W, and to figure out what percentage of U.S. states have names that start with the letter W, we need to know what what 4 is what percent of 50.

We figure this out the following way:

Percent = $\frac{4}{50} *100=0.08*100 =8$