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2 years ago

Last year a farmer dug

Mathematics

1 answer:

butalik [34]2 years ago

5 0

<h3>Answer: 935 tons</h3>

Explanation:

We'll add the last two values to get the amount dug this year.

2786+2862 = 5648

So the farmer dug 5648 tons of potatoes this year.

Subtract that result from the first value given

6583 - 5648 = 935

The farmer dug 935 more tons last year compared to this year.

In other words, the amount has dropped by 935 tons when going from last year to this year.

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The value of 30, to one decimal place, is approximately what?

andrew-mc [135]

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2 years ago

If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

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###

Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

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