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Anna007 [38]
3 years ago
10

If f(x) = 5x2+2, then what is the slope of f(x) at x = 4?

Mathematics
1 answer:
REY [17]3 years ago
6 0

The slope of a function at a point is the value of its derivative there.

... f'(x) = 5·(2x) + 0 = 10x . . . . . . using the power rule: (d/dx)(xⁿ) = n·xⁿ⁻¹

Then

... f'(4) = 10·4 = 40 . . . . . the slope at x=4

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0.015 miles

Step-by-step explanation:

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The prime factor of 180
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Answer: 5*2*2*3*3

Step-by-step explanation:

First you divide 180 by 2 and you get 90. Then you proceed to divide that by 2 again and get 45. You will then divide 45 by 3 to get 15. Then divide 15 by 3 again and get 5, which cannot be divided any smaller.

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10. A perfect circle measuring 38 feet across was discovered on Brickell Avenue in Miami in 1998. Known as the Miami Circle at B
vivado [14]

Using an exponential function, it is found that the Tequesta settlement is 1845 years old.

<h3>What is an exponential function?</h3>

The exponential equation for a decaying amount of a substance is given by:

A(t) = A(0)e^{-rt}

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.

A(t) = A(0)e^{-rt}

0.5A(0) = A(0)e^{-5730r}

e^{-5730r} = 0.5

\ln{e^{-5730r}} = \ln{0.5}

5730r = -\ln{0.5}

r = -\frac{\ln{0.5}}{5730}

r = 0.00012096809

Hence, the equation is:

A(t) = A(0)e^{-0.00012096809t}

The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).

A(t) = A(0)e^{-0.00012096809t}

0.8A(0) = A(0)e^{-0.00012096809t}

e^{-0.00012096809t} = 0.8

\ln{e^{-0.00012096809t}} = \ln{0.8}

-0.00012096809t = \ln{0.8}

t = -\frac{\ln{0.8}}{0.00012096809}

t = 1845

The Tequesta settlement is 1845 years old.

You can learn more about exponential functions at brainly.com/question/25537936

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