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balandron [24]
2 years ago
9

Log_{7 }(5 - 3x)Find the derivative​

Mathematics
1 answer:
V125BC [204]2 years ago
6 0

Let <em>y</em> be the expression you want to differentiate:

y=\log_7(5-3x) \implies 7^y=5-3x

Now,

7^y=e^{\ln(7^y)}=e^{y\ln(7)}

Use the chain rule to differentiate both sides with respect to <em>x</em> :

\ln(7)e^{y\ln(7)}\dfrac{\mathrm dy}{\mathrm dx}=-3

Solve for d<em>y</em>/d<em>x</em> :

\ln(7)7^y\dfrac{\mathrm dy}{\mathrm dx}=-3

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac3{\ln(7)7^y}

\dfrac{\mathrm dy}{\mathrm dx}=\boxed{-\dfrac3{\ln(7)(5-3x)}}

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Mark used his debit card to buy groceries for $87 on Saturday and gas for $41 on Sunday. If his bank account balance is now $542
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URGENT HELP NEED!!! I WILL REWARD LOTS OF POINTS FOR THIS QUESTION!!! ANY IRRALEVENT OR SILLY QUESTION WILL BE INSTANTLY REPORTE
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Let the points be A,B,C

  • A(0,0)
  • B(24,16)
  • C(8,20)

#A

\\ \bull\sf\leadsto AB=\sqrt{(24-0)^2+(16-0)^2}=\sqrt{24^2-16^2}=\sqrt{576-256}=\sqrt{320}=17.4units(leg3)

\\ \bull\sf\leadsto AC=\sqrt{(8-0)^2+(20-0)^2}=\sqrt{8^2+20^2}=\sqrt{64+400}=\sqrt{464}=21.4units(leg1)

\\ \bull\sf\leadsto BC=\sqrt{(24-8)^2+(26-20)^2}=\sqrt{16^2+(-4)^2}=\sqrt{256+16}=\sqrt{272}=16.4units(leg2)

#B

We have to find perimeter

\\ \bull\sf\leadsto Perimeter=AB+AC+BC

\\ \bull\sf\leadsto Periemter=17.4+16.4+21.4

\\ \bull\sf\leadsto Perimeter=55.2units

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3 years ago
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This question is worth 20 points if someone answers it! ​
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The maximum number of tourists in the third week will be maximum in the numberville city.The solution of f(x)=h(x) will be x(5,2).

<h3>What are equations?</h3>

The equation is actually a relationship between the numbers and the variables.

To calculate the number of the tourists in the third week we will put the value 3 in every function:

f(x)=x^2+5x+10=(3)^2+(3\times 3)+10=29\\\\\\g(x)=3^x=3^3=27\\\\\\h(x)=10x=10\times 3=30

So we can see that the function third h(x) numberville city is having a maximum number of tourists.

The solution of f(x)=h(x) will be calculated as:

x^2-3x+10=10x\\\\\\x^2-7x+10=0\\\\\\x^2-5x-2x+10=0\\\\\\x(x-5)-2(x-5)=0\\\\\\x=5,2

Hence the solution of f(x)=h(x) will be x(5,2).

To know more about equations follow

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