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2 years ago

A wooden roller coaster at a theme park has a height restriction: passengers must be at least 45 inches tall.

Mathematics

1 answer:

sergij07 [2.7K]2 years ago

5 0

Answer:dsscsccxc

Step-by-step explanation:

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Differentiate x^2 e^x logx

zimovet [89]

Product rule:

$\dfrac{\mathrm d}{\mathrm dx}(x^2e^x\log x)$

$=\dfrac{\mathrm d(x^2)}{\mathrm dx}e^x\log x+x^2\dfrac{\mathrm d(e^x)}{\mathrm dx}\log x+x^2e^x\dfrac{\mathrm d(\log x)}{\mathrm dx}$

Power rule:

$\dfrac{\mathrm d(x^2)}{\mathrm dx}=2x$

The exponential function is its own derivative:

$\dfrac{\mathrm d(e^x)}{\mathrm dx}=e^x$

Assuming the base of $\log x$ is $e$ , its derivative is

$\dfrac{\mathrm d(\log x)}{\mathrm dx}=\dfrac1x$

But if you mean a logarithm of arbitrary base $b$ , we have

$y=\log_bx\implies x=b^y=e^{y\ln b}\implies1=e^{y\ln b}\ln b\dfrac{\mathrm dy}{\mathrm dx}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^{-y\ln b}}{\ln b}=\dfrac1{b^y\ln b}$

$\implies\dfrac{\mathrm d(\log_bx)}{\mathrm dx}=\dfrac1{x\ln b}$

So we end up with

$2xe^x\log x+x^2e^x\log x+\dfrac{x^2e^x}x$

$=xe^x(2\log x+x\log x+1)$

8 0

3 years ago

Solve 3[-x + (2 x + 1)2 = x - 1<br><br><br> X=?

Anna007 [38]

Answer:

x=−7/8

Step-by-step explanation:

3 0

3 years ago

Which is calculated by using an exponential function?

atroni [7]

Answer:

I am very confused on this question

5 0

3 years ago

A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the i

Burka [1]

The volume of the sphere is expressed in the formula V = 4/3 pi r^3. The rate of change of volume is determined by differentiating the formula: dV/dt = 4pi r^2 dr/dt. When we substitute 500 cm3/min as dV/dt and 30 cm as r. Then dr/dt is equal to 0.0442 cm/min

7 0

3 years ago

Answer the question in the pic below (math)

Marta_Voda [28]

Answer:

46.95 in.²

Step-by-step explanation:

Surface area of the kaleidoscope = surface area of a triangular prism = 2(BA) + P*H

Base area (B) = 2(½*bh) = 2(½*1.5*1.3) = 1.95 in.²

Perimeter of base (P) = 1.5 + 1.5 + 1.5 = 4.5 in.

Height of prism (H) = 10 in.

Plug in the values

Surface area = 1.95 + 4.5*10 = 46.95 in.²

7 0

2 years ago