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Nady [450]
3 years ago
8

What is a constant rate of change

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
5 0

Answer:

A constant rate of change- means that something changes by the same amount during equal intervals.

Step-by-step explanation:

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2ᵃ = 5ᵇ = 10ⁿ.<br> Show that n = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bab%7D%7Ba%20%2B%20b%7D%20" id="TexFormula1" titl
11Alexandr11 [23.1K]
There are two ways you can go about this: I'll explain both ways.
<span>
</span><span>Solution 1: Using logarithmic properties
</span>The first way is to use logarithmic properties.

We can take the natural logarithm to all three terms to utilise our exponents.

Hence, ln2ᵃ = ln5ᵇ = ln10ⁿ becomes:
aln2 = bln5 = nln10.

What's so neat about ln10 is that it's ln(5·2).
Using our logarithmic rule (log(ab) = log(a) + log(b),
we can rewrite it as aln2 = bln5 = n(ln2 + ln5)

Since it's equal (given to us), we can let it all equal to another variable "c".

So, c = aln2 = bln5 = n(ln2 + ln5) and the reason why we do this, is so that we may find ln2 and ln5 respectively.

c = aln2; ln2 = \frac{c}{a}
c = bln5; ln5 = \frac{c}{b}

Hence, c = n(ln2 + ln5) = n(\frac{c}{a} + \frac{c}{b})
Factorise c outside on the right hand side.

c = cn(\frac{1}{a} + \frac{1}{b})
1 = n(\frac{1}{a} + \frac{1}{b})
\frac{1}{n} = \frac{1}{a} + \frac{1}{b}

\frac{1}{n} = \frac{a + b}{ab}
and thus, n = \frac{ab}{a + b}

<span>Solution 2: Using exponent rules
</span>In this solution, we'll be taking advantage of exponents.

So, let c = 2ᵃ = 5ᵇ = 10ⁿ
Since c = 2ᵃ, 2 = \sqrt[a]{c} = c^{\frac{1}{a}}

Then, 5 = c^{\frac{1}{b}}
and 10 = c^{\frac{1}{n}}

But, 10 = 5·2, so 10 = c^{\frac{1}{b}}·c^{\frac{1}{a}}
∴ c^{\frac{1}{n}} = c^{\frac{1}{b}}·c^{\frac{1}{a}}

\frac{1}{n} = \frac{1}{a} + \frac{1}{b}
and n = \frac{ab}{a + b}
4 0
3 years ago
-4-square root of -75 / 60
Leto [7]
<span>the correct answer is -4 - 0.144337567 i</span>
3 0
3 years ago
. can someone help pls
disa [49]

Answer:

The answer is 3,906.25

Step-by-step explanation:

All you have to do is divide 15,625 by 4! :)

6 0
2 years ago
The answer to this word problem usinf discriminant
solniwko [45]
\bf h=-9.8t^2+45t+1.2\implies 64.5=-9.8t^2+45t+1.2&#10;\\\\\\&#10;0=-9.8t^2+45t-63.3\\\\&#10;-------------------------------

\bf \qquad \qquad \qquad \textit{discriminant of a quadratic}&#10;\\\\\\&#10;0=\stackrel{\stackrel{a}{\downarrow }}{-9.8}t^2\stackrel{\stackrel{b}{\downarrow }}{+45}t\stackrel{\stackrel{c}{\downarrow }}{-63.3}&#10;~~~~~~&#10;\stackrel{discriminant}{b^2-4ac}=&#10;\begin{cases}&#10;0&\textit{one solution}\\&#10;positive&\textit{two solutions}\\&#10;negative&\textit{no solution}&#10;\end{cases}&#10;\\\\\\&#10;(45)^2-4(-9.8)(-63.3)\implies -456.36

the discriminant is a negative value, thus no solution for such quadratic, meaning if we use h=64.5 like we did, there's no "t" seconds at which point the ball hits the batting cage.
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3 years ago
Write the slope intercept form of the equation of each line
Advocard [28]

Answer:

y = -1/3

Step-by-step explanation:

4 0
2 years ago
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