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2 years ago

What is the first derivative of 3\sqrt[3]{x^4}-12\sqrt[3]{x}?

1 answer:

8 0

$\bf y=3\sqrt[3]{x^4}-12\sqrt[3]{x}\implies y=3x^{\frac{4}{3}}-12x^{\frac{1}{3}}
\\\\\\
\cfrac{dy}{dx}=3\left( \frac{4}{3}x^{\frac{1}{3}} \right)-12\left( \frac{1}{3}x^{-\frac{2}{3}} \right)\implies \cfrac{dy}{dx}=4x^{\frac{1}{3}}-4x^{-\frac{2}{3}}
\\\\\\
\cfrac{dy}{dx}=4\sqrt[3]{x}-\cfrac{4}{\sqrt[3]{x^2}}$

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Gennadij [26K]

In around 6.35 years, the population will be 1 million.

<h3> how many years will it take for the population to reach one million?</h3>

The population is modeled by the exponential equation:

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Then we just need to solve the equation for t:

$P(t) = 232,012*e^{0.23*t} = 1,000,000$

Let's solve that:

$232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\$

If we apply the natural logarithm to both sides:

$ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35$

So in around 6.35 years, the population will be 1 million.

If you want to learn more about exponential equations:

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1 year ago

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Inessa [10]

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2 years ago

Read 2 more answers

I’m working on 3 and 4 only maybe if I can have some explanation so I can understand and do more of these next week.

guapka [62]

4.b.

Answer: See below.

Step-by-step explanation:

<h2><u>For the equation f(x) = 2x</u></h2>

3.a. f(6) means use x = 6 in the equation f(x) = 2x

so f(6) would be f(6)= 2(6)

3.b. f(-11) = 2(-11)

3.c. f(2.75) = 2(2.75)

3.d. This is turned around. We are told f(x)=20, so what would x need to be for f(x) to be 20? Since f(x) = 2x, we can say 20 = 2x. Therefore x = 10

f(10) = 20

<u>The rest of (3) are solved in the same fasion.h</u>

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<h2><u>For the equation f(x)= 5x+50</u></h2>

4.a. f(7) = 5(7)+50

4.b. f(-12)

f(-12) = 5*(-12)+50

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Continue in the same fashion for these types of problems.

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1 year ago

Diagram shows a cone and its axis of rotation which type of cross-section is formed when the cone is intersected by a plane cont

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Answer:

The cross section will be an isosceles triangle

Step-by-step explanation:

The picture of the question in the attached figure N 1

we know that

If a plane passes through the axis of rotation of the cone, then the resultant cross-section will be a triangle with one vertex as the vertex of the cone and the two sides of the triangle through the vertex A will be equal.

Where the base of the triangle will be equal to the diameter of the circular base of cone and the two congruent sides of triangle will be equal to the slant height of the cone

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21.6

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