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3 years ago

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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Mike ran 1 mile in 4 minutes. How far did he run in 10seconds?

MrRissso [65]

Answer:

0.015 miles

Step-by-step explanation:

$1mile = 4min \\ 1mile = 240sec \\ 0.609km = 240sec \\ \frac{0.609}{24} = \frac{240}{24} \\ 10sec = 0.025km \\ 10sec = 0.015miles$

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3 years ago

The prime factor of 180

alisha [4.7K]

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.

180/2=90

90/2=45

45/3=15

15/3=5

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3 years ago

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2 years ago

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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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2 years ago

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Vlada [557]

The last one is the right answer

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3 years ago

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