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charle [14.2K]
3 years ago
5

Between x=2 and x=3, which function has a greater average rate of change than f(x)=2^x has?

Mathematics
1 answer:
maxonik [38]3 years ago
4 0

Answer: f(3)

Step-by-step explanation:

First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.

y=2^x\\\ln(y)=x \ln(2)

Implicitly differentiate the left side and take the derivative of the right side

\frac{y'}{y} =\ln(2)

Multiply both sides by 'y' which was defined as 2^x

y'=\ln(2)*2^x

Plug in x = 2 and x = 3 to see which slope is larger

y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)

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A sum of money is divided in the ratio 2 : 3 : 7 .Given the largest share is $112,calculate the smallest share.
emmasim [6.3K]

Answer:

$32

Step-by-step explanation:

A sum of money is divided in the ratio 2:3:7.

Let the share of each individual be represented by 2x,3x,7x respectively.

The largest share (7x) is given as $112.

\[7x = 112\]

\[=>x = \frac{112}{7}\]

\[=>x = 16\]

So the respective shares are \[2\times16,3\times16,7\times16\]

In other words, the shares are 32,48,112.

So the smallest share is $32

4 0
3 years ago
If m∠c=11x+85/3 and x=13 then what type of angle is c please help me with this
GuDViN [60]

Answer:

Acute angle

Step-by-step explanation:

Given that m<C = \frac{11x + 85}{3}, to find out the type of angle angle C is, evaluate the expression given by substituting x = 13, in the expression.

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m<C = \frac{11(13) + 85}{3}

m<C = \frac{228}{3}

m<C = 76°

Acute angles are less than 90°.

m<C is less than 90°, therefore it is an acute angle.

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3 years ago
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saw5 [17]
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7 0
3 years ago
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