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2 years ago

At what point on the curve y = 19 2x is the tangent line perpendicular to the line 20x 4y = 1?

Mathematics

1 answer:

Gennadij [26K]2 years ago

7 0

The points are; (7/2, -1/2).

<h3>What is the given point?</h3>

Now the tangent line is given as;20x 4y = 1. When we rewrite it in the slope intercept form, we have the equation as; y = 1 - 20x/4 or y = 1/4 - 5x.

Then to obtain the slope of the curve we have; y = 19 - 2x

dy/dx = 2

Using the relation;

m1m2 = -1

m2 = -1/2

Hence;

y = 1/4 - 5(-1/2)

y = 1/4 + 5/2

y = 7/2

Thus the points are; (7/2, -1/2)

Learn more about normal curve:brainly.com/question/10664419

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3 years ago

The population P of a small town, measured in hundreds, is modeled by the inverse of the function P−1(t) = 10ln(50t − 1000), whe

AleksandrR [38]

Using the inverse function, it is found that the equation is:

$P(t) = \frac{e^{0.1t}}{50} + 20$

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We want to find the inverse of:

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To do this, we <u>exchange y and t, and isolate y.</u>

Then:

$10\ln{50y - 1000} = t$

$\ln{50y - 1000} = \frac{t}{10}$

$e^{\ln{50y - 1000}} = e^{0.1t}$

$50y - 1000 = e^{0.1t}$

$50y = e^{0.1t} + 1000$

$y = \frac{e^{0.1t} + 1000}{50}$

$y = \frac{e^{0.1t}}{50} + \frac{1000}{50}$

$P(t) = \frac{e^{0.1t}}{50} + 20$

It's initial value is:

$P(0) = \frac{e^{0.1(0)}}{50} + 20 = 0.02 + 20 = 20.02$

Rounding, 20.

A similar problem is given at brainly.com/question/23950969

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3 years ago

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Answer:

$82.31

Step-by-step explanation:

First, we need to find the total amount of money paid

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Next, add the new price for the new total

$2050 + 90 = 2160$

Now divide by total members (25 +1 = 26)

$2160 / 90 = $82.31$

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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