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3 years ago

The successor of a certain number when added to twice the number produces 61. What is the number?

Mathematics

1 answer:

Mademuasel [1]3 years ago

3 0

Answer:

Step-by-step explanation:

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Abigal read 5,or one fifth,of the pages in her book.teresa read 6, or one sixth of the pages in her book.whose book had more pag

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Step-by-step explanation:

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2 years ago

What 4 number add up to 47

vagabundo [1.1K]

20 + 6 + 11 + 10 adds up to 47

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2 years ago

Can anyone help me with 4-6

Nataliya [291]

4. 1,50

5. 0,50

6. Tawni swims the fastest because she swims at roughly 0,8 meters per second which is faster than the other two contestants.

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2 years ago

How much time has passed from the first clock to the second clock?

bonufazy [111]

Answer:

Step-by-step explanation:

Time for first clock is 8:34

Time for second clock is 11:48

subtract them: 11 hrs. 48 min.

- 8 hrs. 34 min.

_____________

3 hrs. 14 min.

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2 years ago

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