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rosijanka [135]
2 years ago
6

What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.

Mathematics
1 answer:
Bad White [126]2 years ago
6 0

Answer:

The value of log  43is 1.633

Step-by-step explanation:

Explanation:

Suppose you know that:

\begin{array}{l}{\log 2 \approx 0.30103} \\{\log 3 \approx 0.47712}\end{array}

Then note that:

43=\frac{129}{3} \approx \frac{128}{3}=\frac{2^{7}}{3}

So

\log 43 \approx \log \left(\frac{2^{7}}{3}\right)=7 \log 2-\log 3 \approx 7 \cdot 0.30103-0.47712=1.63009

We know that the error is approximately:

\log \left(\frac{129}{128}\right)=\log 1.0078125=\frac{\ln 1.0078125}{\ln 10} \approx 0.00782 .3=0.0034

So we can confidently give the approximation:

\log 43 \approx 1.633

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Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming poo
kolezko [41]

Let <em>x</em> and <em>y</em> be the unit rates at which one large pump and one small pump works, respectively.

Two large/one small operate at a unit rate of

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2<em>x</em> + <em>y</em> = 0.25

One large/three small operate at the same rate,

(1 pool)/(4 hours) = 0.25 pool/hour

<em>x</em> + 3<em>y</em> = 0.25

Solve for <em>x</em> and <em>y</em>. We have

<em>y</em> = 0.25 - 2<em>x</em>   ==>   <em>x</em> + 3 (0.25 - 2<em>x</em>) = 0.25

==>   <em>x</em> + 0.75 - 6<em>x</em> = 0.25

==>   5<em>x</em> = 0.5

==>   <em>x</em> = 0.1

==>   <em>y</em> = 0.25 - 2 (0.1) = 0.25 - 0.2 = 0.05

In other words, one large pump alone can fill a 1/10 of a pool in one hour, while one small pump alone can fill 1/20 of a pool in one hour.

Now, if you have four each of the large and small pumps, they will work at a rate of

4<em>x</em> + 4<em>y</em> = 4 (0.1) + 4 (0.05) = 0.6

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The function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

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The given parameters are:

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Let the length parallel to the wall be represented as z and the width be x

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The area of the wall is calculated as

A = xz

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A = 1/2(210 - z) * z

This gives

A = z/2(210 - z)

Rewrite as

A(z) = z/2(210 - z)

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